From rick at rickmurphy.org Tue Jan 2 16:00:03 2018 From: rick at rickmurphy.org (rick) Date: Tue, 2 Jan 2018 10:00:03 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: Till & Fabian, consider the following under DOL public comment, open through March 2018 and relevant to the required Business Committee Questionnaire. I have cc'd Larry Johnson OMG's Technical Director. The recent email exchange confirmed that the authors of ISO 24707 determined the need for revisions to incorporate an unspecified "induction principle" after its publication. The DOL authors claim to "handle" sequence markers in HETS using "second order logic" which by conformance with MOF and fUML is outside the scope of DOL. Pat, thanks for taking the time to answer my questions. I am heads down this year on dependent types and univalence. -- Rick On 12/27/2017 02:44 PM, Pat Hayes wrote: > > >> On Dec 27, 2017, at 6:17 AM, rick wrote: >> >> On 12/21/2017 07:50 PM, Pat Hayes wrote: >>> >>> >>>> On Dec 21, 2017, at 9:54 AM, rick wrote: >>>> >>>> How about it, Pat? >>>> >>>> No derivations for "Common Logic"? >>>> >>>> ISO 24707 actually has no inference rules or proof theory at all, >>>> correct? How can they be "out of scope" for a logic? >>> >>> Did anyone suggest they are? >> >> You excluded them in 24707, 1 Scope which reads in part as follows: >> >> "The following are outside the scope of this International Standard: >> * the specification of proof theory or inference rules; ? > > Right. The standard does not include those. The intended purpose of CL was to be a ?standard format? for the variety of notations and syntactic conventions all in use for FOL. One gets to define this exactly by providing one (abstract) syntax with a rigorously described model theory. It is then up to users of other notations to define their mappings to this syntax and check that their semantics are preserved under that mapping. None of this requires the notation to have a proof theory: in fact, such a proof theory might well be an impediment to such use, as it would impose an extra burden on translation which would not be relevant to the intended use of 24707. > >> >> It's not logic without them. > > That is a matter of opinion. FOL is widely considered to be a (note singular) logic, yet there are probably 50 or more different proof theories and syntaxes for it. But only one model theory. > >>>> Shouldn't the ISO 24707 authors have released a Common LISP library by >>>> now? It's been 10 years. >>> >>> The CL effort was done pro bono, and AFAIK none of the authors have funding to work on it further. I certainly have not. Anyone who is interested is welcome to develop CL inference engines or other software, of course. >> >> Ten years gone and there's no reference implementation, right? > > Right. AFAIK, nobody is working on it. Feel free to pick up the reins if you want to: it?s not in any way proprietary. I myself have retired from academic work, and Chris Menzel is a full-time philosopher. > >> >> We are told that HETS parses CLIF syntax, but "handles" sequence markers >> in second order logic, likely as polymorphic list types. >> >> A consumer of 24707 and standards which depend on it assume significant >> risk. > > Not for the original intended use. > >> >>>> Fabian, Annex D is only informative, but the following sentence may be >>>> naively interpreted to mean that second order logic is required, or >>>> somehow provided. >>>> >>>> "Note that sequences are essentially a non-first-order feature that >>>> >>>> can be expressed in second-order logic.? >>> >>> Well, that sentence is of course true. >> >> Really? Where would I find sequence markers in the literature on >> second-order logic? Reference please. > > Sequence markers get you (a subset of) Lw1-w, which is strictly weaker than second-order. This is kind of obvious since you can define lists in second-order and quantify over them, and define integers to count how long they are, etc.. > >> >> Assuming a reference, the sentence would be equally true in let's say >> the calculus of constructions, right? > > I have no idea. We did not even look at CoC as being relevant to 24707. CoC is not easily relatable to FOL, is it? Curry-Howard gets you *intuitionist propositional* logic, which is a very small and idiosyncratic subset of FOL. > >> Everything that has lists, right? > > Not everything, surely. LISP has lists. but it doesn't have a logical model theory. I am not aware of any other extension of FOL that ?has lists? in the same sense. > >>> The mapping to Lw1w was not noticed until after that was written. We had a strong intuition that second-order was too strong, which is why this says 'can be expressed? rather than ?requires?. >> >> There's no mapping and there's no claim of induction related to sequence >> markers in 24707. 24707 has a vague reference to fix points. > > It would not have been appropriate to include such details in 24707 even if we had had them worked out. Standards documents are not academic papers: there are strict rules about what should be included and what not, and distinguishing normative from informative text, and being rather exact about requirements and so forth. 24707 gives a model theory for sequence markers. > > Perhaps it would have been better to have left them out, in retrospect, as they are not strictly FO; but they were part of KIF which was the origin of CL, and we had worked out a precise semantics for them (which KIF did not), and they are only a tiny step up from strict FO, so we decided to keep them. And they are very useful in defining embeddings, as we found when translating OWL into CL. > >> And all we've read is a post-hoc claim of an unspecified "induction >> principle." >> >> There's no proof, or inference rules, and there's no reference >> implementation. Given the related "handle" claim, it sounds like >> "requires" rather than "can be expressed" to me. >> >>> If someone reads that sentence in the way you imply, above, then I would suggest they are not competent to read a formal specification. >> >> That seems pervasive around standards organizations. > > Well, there are rules about how standards documents use language. Its a bit like being at a court: you have to be extra careful about how things are phrased, as these have consequences that you can ignore in less formal settings. > >>>> This is an example of how misinformation is being circulated about >>>> "Common Logic." I have discussed this before at OMG. >>>> >>>> How do you respond to the fact that Java and C# provide parametric >>>> polymorphism, but CL and DOL do not? >>> >>> With a puzzled frown, not understanding what possible relevance Java or C++ have to anything in this entire discussion (or in ISO 24707) >> >> They have lists similar to those in second order logic which seem to be >> required to implement sequence markers in 24707. > > They have lists, but thay aren?t logics. So they don?t have, for example, quantifiers or connectives or logical sentences or a model theory. They are about as relevant to 24707 as shopping lists. > > Pat > >> >> Turn that frown upside down. >> >> -- >> Rick >> >>> Pat >>> >>>> >>>> Good to see folks promoting Goguen's work though. >>>> >>>> -- >>>> Rick >>>> >>>> On 12/20/2017 07:00 PM, rick wrote: >>>>> Maybe Pat can show the derivations to avoid further misunderstanding. >>>>> >>>>> -- >>>>> Rick >>>>> >>>>> On 12/20/2017 05:32 PM, Pat Hayes wrote: >>>>>> I hadn?t seen that diagram before. I believe that it is inaccurate to describe CL as having ?some second-order constructs?. Sequence markers take CL outside FO expressivity, but not to second-order. CL with sequence markers is in fact a subset of the infinitary logic Lw1-w which allows countably infinite conjunctions. This is a long way short of full second-order logic. If one restricts CL (Lw1-w) so that sequence markers (infinite conjunctions) occur only on the LHS of sequents, it is first order. So sequence makers can be used in ontologies (ie as ?axioms?) without going beyond FO expressivity. >>>>>> >>>>>> Pat >>>>>> >>>>>>> On Dec 20, 2017, at 7:01 AM, John F Sowa wrote: >>>>>>> >>>>>>> Congratulations to everyone working on the DOL project. >>>>>>> >>>>>>> From Fabian via ontoiop-forum, >>>>>>>> Good news concerning the standardisation of DOL! During the last >>>>>>>> OMG Technical Meeting the Architecture Board approved the changes >>>>>>>> that we made to DOL during the ?Finalisation Phase? (which in our >>>>>>>> case lasted 2 years). Hence, we cleared the last major hurdle on >>>>>>>> our way to the release of DOL 1.0. I expect that this will happen >>>>>>>> in February 2018. >>>>>>> >>>>>>> And Fabian, I'm sending a copy of this note to Ontolog Forum, and >>>>>>> I also attached a copy of an earlier diagram (dol.jpg). >>>>>>> >>>>>>> Does this diagram reflect the current version? If so (or not), >>>>>>> could you please send the URL of the latest documentation to >>>>>>> Ontolog Forum? >>>>>>> >>>>>>> And is software available for the various mappings in that diagram? >>>>>>> >>>>>>> John >>>>>>> >>>>>>> _________________________________________________________________ >>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>> Community Wiki: http://ontoiop.org >>>>>> >>>>>> >>>>>> >>>>>> _________________________________________________________________ >>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>> Community Wiki: http://ontoiop.org >>>>>> >>>> >>>> >>> >>> >>> >>> >> >> > > > > From phayes at ihmc.us Tue Jan 2 19:25:22 2018 From: phayes at ihmc.us (Pat Hayes) Date: Tue, 2 Jan 2018 10:25:22 -0800 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: > On Jan 2, 2018, at 7:00 AM, rick wrote: > > Till & Fabian, consider the following under DOL public comment, open > through March 2018 and relevant to the required Business Committee > Questionnaire. > > I have cc'd Larry Johnson OMG's Technical Director. > > The recent email exchange confirmed that the authors of ISO 24707 > determined the need for revisions to incorporate an unspecified > "induction principle" after its publication. As one of the two main authors of the technical parts of ISO 24707, I do not agree with the previous sentence. The authors of ISO 24707 did /not/ determine a need for an unspecified induction principle, and my recent email exchanges with Rick Murphy (copied below) do /not/ confirm any such interpretation. As I pointed out to Rick in one of the emails, the intended purpose for ISO 24707 did not require a specification of any kind of proof theory for the CL language specified; the authors of that standard did not contemplate giving such a proof theory in any future revision to ISO 24707; and if they had done, the simple reduction of sequence marker syntax to the weak infinitary logic Lw1w would have sufficed, without mentioning induction. Pat Hayes > > The DOL authors claim to "handle" sequence markers in HETS using "second > order logic" which by conformance with MOF and fUML is outside the scope > of DOL. > > Pat, thanks for taking the time to answer my questions. I am heads down > this year on dependent types and univalence. > > -- > Rick > > On 12/27/2017 02:44 PM, Pat Hayes wrote: >> >> >>> On Dec 27, 2017, at 6:17 AM, rick wrote: >>> >>> On 12/21/2017 07:50 PM, Pat Hayes wrote: >>>> >>>> >>>>> On Dec 21, 2017, at 9:54 AM, rick wrote: >>>>> >>>>> How about it, Pat? >>>>> >>>>> No derivations for "Common Logic"? >>>>> >>>>> ISO 24707 actually has no inference rules or proof theory at all, >>>>> correct? How can they be "out of scope" for a logic? >>>> >>>> Did anyone suggest they are? >>> >>> You excluded them in 24707, 1 Scope which reads in part as follows: >>> >>> "The following are outside the scope of this International Standard: >>> * the specification of proof theory or inference rules; ? >> >> Right. The standard does not include those. The intended purpose of CL was to be a ?standard format? for the variety of notations and syntactic conventions all in use for FOL. One gets to define this exactly by providing one (abstract) syntax with a rigorously described model theory. It is then up to users of other notations to define their mappings to this syntax and check that their semantics are preserved under that mapping. None of this requires the notation to have a proof theory: in fact, such a proof theory might well be an impediment to such use, as it would impose an extra burden on translation which would not be relevant to the intended use of 24707. >> >>> >>> It's not logic without them. >> >> That is a matter of opinion. FOL is widely considered to be a (note singular) logic, yet there are probably 50 or more different proof theories and syntaxes for it. But only one model theory. >> >>>>> Shouldn't the ISO 24707 authors have released a Common LISP library by >>>>> now? It's been 10 years. >>>> >>>> The CL effort was done pro bono, and AFAIK none of the authors have funding to work on it further. I certainly have not. Anyone who is interested is welcome to develop CL inference engines or other software, of course. >>> >>> Ten years gone and there's no reference implementation, right? >> >> Right. AFAIK, nobody is working on it. Feel free to pick up the reins if you want to: it?s not in any way proprietary. I myself have retired from academic work, and Chris Menzel is a full-time philosopher. >> >>> >>> We are told that HETS parses CLIF syntax, but "handles" sequence markers >>> in second order logic, likely as polymorphic list types. >>> >>> A consumer of 24707 and standards which depend on it assume significant >>> risk. >> >> Not for the original intended use. >> >>> >>>>> Fabian, Annex D is only informative, but the following sentence may be >>>>> naively interpreted to mean that second order logic is required, or >>>>> somehow provided. >>>>> >>>>> "Note that sequences are essentially a non-first-order feature that >>>>> >>>>> can be expressed in second-order logic.? >>>> >>>> Well, that sentence is of course true. >>> >>> Really? Where would I find sequence markers in the literature on >>> second-order logic? Reference please. >> >> Sequence markers get you (a subset of) Lw1-w, which is strictly weaker than second-order. This is kind of obvious since you can define lists in second-order and quantify over them, and define integers to count how long they are, etc.. >> >>> >>> Assuming a reference, the sentence would be equally true in let's say >>> the calculus of constructions, right? >> >> I have no idea. We did not even look at CoC as being relevant to 24707. CoC is not easily relatable to FOL, is it? Curry-Howard gets you *intuitionist propositional* logic, which is a very small and idiosyncratic subset of FOL. >> >>> Everything that has lists, right? >> >> Not everything, surely. LISP has lists. but it doesn't have a logical model theory. I am not aware of any other extension of FOL that ?has lists? in the same sense. >> >>>> The mapping to Lw1w was not noticed until after that was written. We had a strong intuition that second-order was too strong, which is why this says 'can be expressed? rather than ?requires?. >>> >>> There's no mapping and there's no claim of induction related to sequence >>> markers in 24707. 24707 has a vague reference to fix points. >> >> It would not have been appropriate to include such details in 24707 even if we had had them worked out. Standards documents are not academic papers: there are strict rules about what should be included and what not, and distinguishing normative from informative text, and being rather exact about requirements and so forth. 24707 gives a model theory for sequence markers. >> >> Perhaps it would have been better to have left them out, in retrospect, as they are not strictly FO; but they were part of KIF which was the origin of CL, and we had worked out a precise semantics for them (which KIF did not), and they are only a tiny step up from strict FO, so we decided to keep them. And they are very useful in defining embeddings, as we found when translating OWL into CL. >> >>> And all we've read is a post-hoc claim of an unspecified "induction >>> principle." >>> >>> There's no proof, or inference rules, and there's no reference >>> implementation. Given the related "handle" claim, it sounds like >>> "requires" rather than "can be expressed" to me. >>> >>>> If someone reads that sentence in the way you imply, above, then I would suggest they are not competent to read a formal specification. >>> >>> That seems pervasive around standards organizations. >> >> Well, there are rules about how standards documents use language. Its a bit like being at a court: you have to be extra careful about how things are phrased, as these have consequences that you can ignore in less formal settings. >> >>>>> This is an example of how misinformation is being circulated about >>>>> "Common Logic." I have discussed this before at OMG. >>>>> >>>>> How do you respond to the fact that Java and C# provide parametric >>>>> polymorphism, but CL and DOL do not? >>>> >>>> With a puzzled frown, not understanding what possible relevance Java or C++ have to anything in this entire discussion (or in ISO 24707) >>> >>> They have lists similar to those in second order logic which seem to be >>> required to implement sequence markers in 24707. >> >> They have lists, but thay aren?t logics. So they don?t have, for example, quantifiers or connectives or logical sentences or a model theory. They are about as relevant to 24707 as shopping lists. >> >> Pat >> >>> >>> Turn that frown upside down. >>> >>> -- >>> Rick >>> >>>> Pat >>>> >>>>> >>>>> Good to see folks promoting Goguen's work though. >>>>> >>>>> -- >>>>> Rick >>>>> >>>>> On 12/20/2017 07:00 PM, rick wrote: >>>>>> Maybe Pat can show the derivations to avoid further misunderstanding. >>>>>> >>>>>> -- >>>>>> Rick >>>>>> >>>>>> On 12/20/2017 05:32 PM, Pat Hayes wrote: >>>>>>> I hadn?t seen that diagram before. I believe that it is inaccurate to describe CL as having ?some second-order constructs?. Sequence markers take CL outside FO expressivity, but not to second-order. CL with sequence markers is in fact a subset of the infinitary logic Lw1-w which allows countably infinite conjunctions. This is a long way short of full second-order logic. If one restricts CL (Lw1-w) so that sequence markers (infinite conjunctions) occur only on the LHS of sequents, it is first order. So sequence makers can be used in ontologies (ie as ?axioms?) without going beyond FO expressivity. >>>>>>> >>>>>>> Pat >>>>>>> >>>>>>>> On Dec 20, 2017, at 7:01 AM, John F Sowa wrote: >>>>>>>> >>>>>>>> Congratulations to everyone working on the DOL project. >>>>>>>> >>>>>>>> From Fabian via ontoiop-forum, >>>>>>>>> Good news concerning the standardisation of DOL! During the last >>>>>>>>> OMG Technical Meeting the Architecture Board approved the changes >>>>>>>>> that we made to DOL during the ?Finalisation Phase? (which in our >>>>>>>>> case lasted 2 years). Hence, we cleared the last major hurdle on >>>>>>>>> our way to the release of DOL 1.0. I expect that this will happen >>>>>>>>> in February 2018. >>>>>>>> >>>>>>>> And Fabian, I'm sending a copy of this note to Ontolog Forum, and >>>>>>>> I also attached a copy of an earlier diagram (dol.jpg). >>>>>>>> >>>>>>>> Does this diagram reflect the current version? If so (or not), >>>>>>>> could you please send the URL of the latest documentation to >>>>>>>> Ontolog Forum? >>>>>>>> >>>>>>>> And is software available for the various mappings in that diagram? >>>>>>>> >>>>>>>> John >>>>>>>> >>>>>>>> _________________________________________________________________ >>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>> Community Wiki: http://ontoiop.org >>>>>>> >>>>>>> >>>>>>> >>>>>>> _________________________________________________________________ >>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>> Community Wiki: http://ontoiop.org >>>>>>> >>>>> >>>>> >>>> >>>> >>>> >>>> >>> >>> >> >> >> >> > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org From sowa at bestweb.net Tue Jan 2 20:42:44 2018 From: sowa at bestweb.net (John F Sowa) Date: Tue, 2 Jan 2018 14:42:44 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: On 1/2/2018 1:25 PM, Pat Hayes wrote: > the intended purpose for ISO 24707 did not require a specification > of any kind of proof theory for the CL language specified; the authors > of that standard did not contemplate giving such a proof theory in any > future revision to ISO 24707 I agree. But there is a difference between classical FOL and intuitionistic FOL. In classical FOL, validity (determined by the model theory) is equivalent to provability (determined by the proof theory). The only reasons for preferring one proof theory to another are convenience and efficiency. Therefore, it would be a mistake for the ISO standard to state any preference for one proof theory or another. The model theory is compatible with any or all classical proof theories. But some kinds of logics -- for example, intuitionistic or relevance -- place restrictions on the rules of inference. Since Rick is advocating an intuitionistic type theory, I believe that is why he keeps asking about the proof theory. But Rick has not stated any reason why an intuitionistic logic is necessary or even desirable as a foundation for specifying ontology, software, programming languages, or any version of science or engineering. John From rick at rickmurphy.org Tue Jan 2 21:32:25 2018 From: rick at rickmurphy.org (rick) Date: Tue, 2 Jan 2018 15:32:25 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: Pat, Do you disagree with the following? TM> "due to the infinitary nature, there won't be any theorem provers, even with your restriction to axioms." It seems greater care is needed to confirm your understanding. See below for more fun. -- Rick On 01/02/2018 01:25 PM, Pat Hayes wrote: > > >> On Jan 2, 2018, at 7:00 AM, rick wrote: >> >> Till & Fabian, consider the following under DOL public comment, open >> through March 2018 and relevant to the required Business Committee >> Questionnaire. >> >> I have cc'd Larry Johnson OMG's Technical Director. >> >> The recent email exchange confirmed that the authors of ISO 24707 >> determined the need for revisions to incorporate an unspecified >> "induction principle" after its publication. > > As one of the two main authors of the technical parts of ISO 24707, I do not agree with the previous sentence. The authors of ISO 24707 did /not/ determine a need for an unspecified induction principle, and my recent email exchanges with Rick Murphy (copied below) do /not/ confirm any such interpretation. You had not rejected Till's recommendation regarding induction. Am I correct the record should reflect that you reject such an approach? You had previously said: PH> "I understand (and respect) your preference for 2OL over infinitary for prover-relevant reasons" > As I pointed out to Rick in one of the emails, the intended purpose for ISO 24707 did not require a specification of any kind of proof theory for the CL language specified; the authors of that standard did not contemplate giving such a proof theory in any future revision to ISO 24707; and if they had done, the simple reduction of sequence marker syntax to the weak infinitary logic Lw1w would have sufficed, without mentioning induction. As you said Lw-1,w was discovered by the authors after publication of 24707. Revisionism is only good in the next revision of the standard. -- Rick > Pat Hayes > >> >> The DOL authors claim to "handle" sequence markers in HETS using "second >> order logic" which by conformance with MOF and fUML is outside the scope >> of DOL. >> >> Pat, thanks for taking the time to answer my questions. I am heads down >> this year on dependent types and univalence. >> >> -- >> Rick >> >> On 12/27/2017 02:44 PM, Pat Hayes wrote: >>> >>> >>>> On Dec 27, 2017, at 6:17 AM, rick wrote: >>>> >>>> On 12/21/2017 07:50 PM, Pat Hayes wrote: >>>>> >>>>> >>>>>> On Dec 21, 2017, at 9:54 AM, rick wrote: >>>>>> >>>>>> How about it, Pat? >>>>>> >>>>>> No derivations for "Common Logic"? >>>>>> >>>>>> ISO 24707 actually has no inference rules or proof theory at all, >>>>>> correct? How can they be "out of scope" for a logic? >>>>> >>>>> Did anyone suggest they are? >>>> >>>> You excluded them in 24707, 1 Scope which reads in part as follows: >>>> >>>> "The following are outside the scope of this International Standard: >>>> * the specification of proof theory or inference rules; ? >>> >>> Right. The standard does not include those. The intended purpose of CL was to be a ?standard format? for the variety of notations and syntactic conventions all in use for FOL. One gets to define this exactly by providing one (abstract) syntax with a rigorously described model theory. It is then up to users of other notations to define their mappings to this syntax and check that their semantics are preserved under that mapping. None of this requires the notation to have a proof theory: in fact, such a proof theory might well be an impediment to such use, as it would impose an extra burden on translation which would not be relevant to the intended use of 24707. >>> >>>> >>>> It's not logic without them. >>> >>> That is a matter of opinion. FOL is widely considered to be a (note singular) logic, yet there are probably 50 or more different proof theories and syntaxes for it. But only one model theory. >>> >>>>>> Shouldn't the ISO 24707 authors have released a Common LISP library by >>>>>> now? It's been 10 years. >>>>> >>>>> The CL effort was done pro bono, and AFAIK none of the authors have funding to work on it further. I certainly have not. Anyone who is interested is welcome to develop CL inference engines or other software, of course. >>>> >>>> Ten years gone and there's no reference implementation, right? >>> >>> Right. AFAIK, nobody is working on it. Feel free to pick up the reins if you want to: it?s not in any way proprietary. I myself have retired from academic work, and Chris Menzel is a full-time philosopher. >>> >>>> >>>> We are told that HETS parses CLIF syntax, but "handles" sequence markers >>>> in second order logic, likely as polymorphic list types. >>>> >>>> A consumer of 24707 and standards which depend on it assume significant >>>> risk. >>> >>> Not for the original intended use. >>> >>>> >>>>>> Fabian, Annex D is only informative, but the following sentence may be >>>>>> naively interpreted to mean that second order logic is required, or >>>>>> somehow provided. >>>>>> >>>>>> "Note that sequences are essentially a non-first-order feature that >>>>>> >>>>>> can be expressed in second-order logic.? >>>>> >>>>> Well, that sentence is of course true. >>>> >>>> Really? Where would I find sequence markers in the literature on >>>> second-order logic? Reference please. >>> >>> Sequence markers get you (a subset of) Lw1-w, which is strictly weaker than second-order. This is kind of obvious since you can define lists in second-order and quantify over them, and define integers to count how long they are, etc.. >>> >>>> >>>> Assuming a reference, the sentence would be equally true in let's say >>>> the calculus of constructions, right? >>> >>> I have no idea. We did not even look at CoC as being relevant to 24707. CoC is not easily relatable to FOL, is it? Curry-Howard gets you *intuitionist propositional* logic, which is a very small and idiosyncratic subset of FOL. >>> >>>> Everything that has lists, right? >>> >>> Not everything, surely. LISP has lists. but it doesn't have a logical model theory. I am not aware of any other extension of FOL that ?has lists? in the same sense. >>> >>>>> The mapping to Lw1w was not noticed until after that was written. We had a strong intuition that second-order was too strong, which is why this says 'can be expressed? rather than ?requires?. >>>> >>>> There's no mapping and there's no claim of induction related to sequence >>>> markers in 24707. 24707 has a vague reference to fix points. >>> >>> It would not have been appropriate to include such details in 24707 even if we had had them worked out. Standards documents are not academic papers: there are strict rules about what should be included and what not, and distinguishing normative from informative text, and being rather exact about requirements and so forth. 24707 gives a model theory for sequence markers. >>> >>> Perhaps it would have been better to have left them out, in retrospect, as they are not strictly FO; but they were part of KIF which was the origin of CL, and we had worked out a precise semantics for them (which KIF did not), and they are only a tiny step up from strict FO, so we decided to keep them. And they are very useful in defining embeddings, as we found when translating OWL into CL. >>> >>>> And all we've read is a post-hoc claim of an unspecified "induction >>>> principle." >>>> >>>> There's no proof, or inference rules, and there's no reference >>>> implementation. Given the related "handle" claim, it sounds like >>>> "requires" rather than "can be expressed" to me. >>>> >>>>> If someone reads that sentence in the way you imply, above, then I would suggest they are not competent to read a formal specification. >>>> >>>> That seems pervasive around standards organizations. >>> >>> Well, there are rules about how standards documents use language. Its a bit like being at a court: you have to be extra careful about how things are phrased, as these have consequences that you can ignore in less formal settings. >>> >>>>>> This is an example of how misinformation is being circulated about >>>>>> "Common Logic." I have discussed this before at OMG. >>>>>> >>>>>> How do you respond to the fact that Java and C# provide parametric >>>>>> polymorphism, but CL and DOL do not? >>>>> >>>>> With a puzzled frown, not understanding what possible relevance Java or C++ have to anything in this entire discussion (or in ISO 24707) >>>> >>>> They have lists similar to those in second order logic which seem to be >>>> required to implement sequence markers in 24707. >>> >>> They have lists, but thay aren?t logics. So they don?t have, for example, quantifiers or connectives or logical sentences or a model theory. They are about as relevant to 24707 as shopping lists. >>> >>> Pat >>> >>>> >>>> Turn that frown upside down. >>>> >>>> -- >>>> Rick >>>> >>>>> Pat >>>>> >>>>>> >>>>>> Good to see folks promoting Goguen's work though. >>>>>> >>>>>> -- >>>>>> Rick >>>>>> >>>>>> On 12/20/2017 07:00 PM, rick wrote: >>>>>>> Maybe Pat can show the derivations to avoid further misunderstanding. >>>>>>> >>>>>>> -- >>>>>>> Rick >>>>>>> >>>>>>> On 12/20/2017 05:32 PM, Pat Hayes wrote: >>>>>>>> I hadn?t seen that diagram before. I believe that it is inaccurate to describe CL as having ?some second-order constructs?. Sequence markers take CL outside FO expressivity, but not to second-order. CL with sequence markers is in fact a subset of the infinitary logic Lw1-w which allows countably infinite conjunctions. This is a long way short of full second-order logic. If one restricts CL (Lw1-w) so that sequence markers (infinite conjunctions) occur only on the LHS of sequents, it is first order. So sequence makers can be used in ontologies (ie as ?axioms?) without going beyond FO expressivity. >>>>>>>> >>>>>>>> Pat >>>>>>>> >>>>>>>>> On Dec 20, 2017, at 7:01 AM, John F Sowa wrote: >>>>>>>>> >>>>>>>>> Congratulations to everyone working on the DOL project. >>>>>>>>> >>>>>>>>> From Fabian via ontoiop-forum, >>>>>>>>>> Good news concerning the standardisation of DOL! During the last >>>>>>>>>> OMG Technical Meeting the Architecture Board approved the changes >>>>>>>>>> that we made to DOL during the ?Finalisation Phase? (which in our >>>>>>>>>> case lasted 2 years). Hence, we cleared the last major hurdle on >>>>>>>>>> our way to the release of DOL 1.0. I expect that this will happen >>>>>>>>>> in February 2018. >>>>>>>>> >>>>>>>>> And Fabian, I'm sending a copy of this note to Ontolog Forum, and >>>>>>>>> I also attached a copy of an earlier diagram (dol.jpg). >>>>>>>>> >>>>>>>>> Does this diagram reflect the current version? If so (or not), >>>>>>>>> could you please send the URL of the latest documentation to >>>>>>>>> Ontolog Forum? >>>>>>>>> >>>>>>>>> And is software available for the various mappings in that diagram? >>>>>>>>> >>>>>>>>> John >>>>>>>>> >>>>>>>>> _________________________________________________________________ >>>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>>> Community Wiki: http://ontoiop.org >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> _________________________________________________________________ >>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>> Community Wiki: http://ontoiop.org >>>>>>>> >>>>>> >>>>>> >>>>> >>>>> >>>>> >>>>> >>>> >>>> >>> >>> >>> >>> >> >> _________________________________________________________________ >> To Post: mailto:ontoiop-forum at ovgu.de >> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >> Community Wiki: http://ontoiop.org > > > > From rick at rickmurphy.org Tue Jan 2 21:58:58 2018 From: rick at rickmurphy.org (rick) Date: Tue, 2 Jan 2018 15:58:58 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: <46ffbf99-094e-42c0-8efd-08e95e96adc9@rickmurphy.org> John, You're trolling again. I thought we had an agreement. -- Rick On 01/02/2018 02:42 PM, John F Sowa wrote: > On 1/2/2018 1:25 PM, Pat Hayes wrote: >> the intended purpose for ISO 24707 did not require a specification >> of any kind of proof theory for the CL language specified; the authors >> of that standard did not contemplate giving such a proof theory in any >> future revision to ISO 24707 > > I agree. But there is a difference between classical FOL and > intuitionistic FOL. In classical FOL, validity (determined by > the model theory) is equivalent to provability (determined by > the proof theory). The only reasons for preferring one proof > theory to another are convenience and efficiency. > > Therefore, it would be a mistake for the ISO standard to state > any preference for one proof theory or another. The model > theory is compatible with any or all classical proof theories. > > But some kinds of logics -- for example, intuitionistic or > relevance -- place restrictions on the rules of inference. > > Since Rick is advocating an intuitionistic type theory, I > believe that is why he keeps asking about the proof theory. > > But Rick has not stated any reason why an intuitionistic > logic is necessary or even desirable as a foundation for > specifying ontology, software, programming languages, or > any version of science or engineering. > > John > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org > > From sowa at bestweb.net Tue Jan 2 23:26:14 2018 From: sowa at bestweb.net (John F Sowa) Date: Tue, 2 Jan 2018 17:26:14 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <46ffbf99-094e-42c0-8efd-08e95e96adc9@rickmurphy.org> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <46ffbf99-094e-42c0-8efd-08e95e96adc9@rickmurphy.org> Message-ID: <6bdb10a8-d558-b735-0cf1-345b3d1903e5@bestweb.net> On 1/2/2018 3:58 PM, rick wrote: > You're trolling again. I thought we had an agreement. Our agreement was to be civil. My recent notes in this thread were factual and civil: 1. For classical FOL, the model theory is sufficient to specify the semantics. All sound and complete FOL proof theories are equivalent. Therefore, the choice of proof procedure is a matter of convenience and efficiency. The implementers should be free to choose whatever version they prefer. 2. As Pat has said, the only way anybody has ever used sequence markers in CL is to state the equivalent of axiom schemata. During the development of the ISO standard, I argued for that option as the only way that should be approved in the standard. But Pat and Chris wanted to leave the more general option open. 3. For proofs that depend heavily on a type hierarchy, proofs with a sorted version of FOL can be far more efficient than proofs with unsorted FOL. I argued for a sorted option in CL, but the committee did not approve. However, it is possible for implementers to use CL notation with a sorted theorem prover and gain that improvement in performance -- but only for those texts that abide by the sort restrictions. 4. A type hierarchy, by itself, can only specify a small part of what is necessary for ontology or software specifications. If you want to combine your type systems with a logic that has the full expressive power of FOL, how can you preserve the intuitionistic restrictions without using an intuitionistic theorem prover? Are there any practical applications that take advantage of a full intuitionistic system? 5. I do not know of any comparisons of the efficiency of sorted proof procedures vs. the intuitionistic methods that you have recommended. If you know of any such studies, I would very much like to see them. John From till at iks.cs.ovgu.de Tue Jan 2 23:33:44 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Tue, 2 Jan 2018 23:33:44 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> Am 02.01.2018 um 16:00 schrieb rick: > The DOL authors claim to "handle" sequence markers in HETS using "second > order logic" which by conformance with MOF and fUML is outside the scope > of DOL. second-order logic is not outside the scope of DOL. DOL is a meta-language that can be used for a variety of logics, provided they can be formalised as an institution. Such logics include propositional logic, OWL, Common Logic, first-order logic, second-order logic, modal logics, hybrid logics, temporal logics, higher-order logics (also variants including type constructors, subtypes and/or polymorphism), intuitionistic logics, program logics, and many more. Best, Till From sowa at bestweb.net Tue Jan 2 23:52:44 2018 From: sowa at bestweb.net (John F Sowa) Date: Tue, 2 Jan 2018 17:52:44 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> Message-ID: <063f6817-69af-cc7a-d32b-4c6a06020c5a@bestweb.net> On 1/2/2018 5:33 PM, Till Mossakowski wrote: > second-order logic is not outside the scope of DOL. DOL is a > meta-language that can be used for a variety of logics, provided they > can be formalised as an institution. Such logics include propositional > logic, OWL, Common Logic, first-order logic, second-order logic, modal > logics, hybrid logics, temporal logics, higher-order logics (also > variants including type constructors, subtypes and/or polymorphism), > intuitionistic logics, program logics, and many more. That is very impressive. Does Hets support all the logics that DOL can specify? What kind of performance do you get with some of those logics? For example, CL allows quantifiers to range over functions and relations without going beyond first-order proof procedures. What is the difference in performance of a proof with CL semantics vs. HOL semantics? John From phayes at ihmc.us Wed Jan 3 08:12:11 2018 From: phayes at ihmc.us (Pat Hayes) Date: Tue, 2 Jan 2018 23:12:11 -0800 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: Hi Rick Till may well be right that nobody is going to make a theorem prover for Lw1w, which has infinite expressions. However, CL is a finite notation, and I think there is no reason why it could not have a theorem prover. KIF had a version of sequence markers, and there have been KIF theorem provers. I have a natural-deduction proof system for CL with sequence markers which is complete, but not computationally efficient. It is pretty obvious: you just need an extra rule which unpacks sequence marker expressions to one instance, but with another marker appended to it: (forall (?x)S) |- (forall (?y)S[...x/t ?y]) for any term t and the empty-sequence rule (forall (?x)S) |- S[...x/ <>] Using the first rule enough times, then the second rule, will generate any finite number of instance sequences. So there is certainly no theoretical obstacle to a CL theorem-prover. However, as indicated in my earlier email, this issue is irrelevant to ISO 24707. Other responses in-line below. > On Jan 2, 2018, at 12:32 PM, rick wrote: > > Pat, > > Do you disagree with the following? > > TM> "due to the infinitary nature, there won't be any theorem provers, > even with your restriction to axioms." > > It seems greater care is needed to confirm your understanding. > > See below for more fun. > > -- > Rick > > On 01/02/2018 01:25 PM, Pat Hayes wrote: >> >> >>> On Jan 2, 2018, at 7:00 AM, rick wrote: >>> >>> Till & Fabian, consider the following under DOL public comment, open >>> through March 2018 and relevant to the required Business Committee >>> Questionnaire. >>> >>> I have cc'd Larry Johnson OMG's Technical Director. >>> >>> The recent email exchange confirmed that the authors of ISO 24707 >>> determined the need for revisions to incorporate an unspecified >>> "induction principle" after its publication. >> >> As one of the two main authors of the technical parts of ISO 24707, I do not agree with the previous sentence. The authors of ISO 24707 did /not/ determine a need for an unspecified induction principle, and my recent email exchanges with Rick Murphy (copied below) do /not/ confirm any such interpretation. > > You had not rejected Till's recommendation regarding induction. > > Am I correct the record should reflect that you reject such an approach? I have no opinion about any ?approach?. This thread started because I wished to place on record an exact statement about the expressiveness of CL; that is all. I have no views on any approach to implementing an inference system for CL. > > You had previously said: > > PH> "I understand (and respect) your preference for 2OL over infinitary > for prover-relevant reasons? Of course. To ask for an implementation to use infinite expressions would be rather unreasonable. >> As I pointed out to Rick in one of the emails, the intended purpose for ISO 24707 did not require a specification of any kind of proof theory for the CL language specified; the authors of that standard did not contemplate giving such a proof theory in any future revision to ISO 24707; and if they had done, the simple reduction of sequence marker syntax to the weak infinitary logic Lw1w would have sufficed, without mentioning induction. > > As you said Lw-1,w was discovered by the authors after publication of > 24707. Lw1w was not ?discovered' after the publication of 24707. That the (now obvious) mapping to Lw1w was semantically exact was noticed around the time the standard text was being published, but this entire issue was not considered centrally germane to the standard in any case. It continues to not be so. Pat > Revisionism is only good in the next revision of the standard. > > -- > Rick > >> Pat Hayes >> >>> >>> The DOL authors claim to "handle" sequence markers in HETS using "second >>> order logic" which by conformance with MOF and fUML is outside the scope >>> of DOL. >>> >>> Pat, thanks for taking the time to answer my questions. I am heads down >>> this year on dependent types and univalence. >>> >>> -- >>> Rick >>> >>> On 12/27/2017 02:44 PM, Pat Hayes wrote: >>>> >>>> >>>>> On Dec 27, 2017, at 6:17 AM, rick wrote: >>>>> >>>>> On 12/21/2017 07:50 PM, Pat Hayes wrote: >>>>>> >>>>>> >>>>>>> On Dec 21, 2017, at 9:54 AM, rick wrote: >>>>>>> >>>>>>> How about it, Pat? >>>>>>> >>>>>>> No derivations for "Common Logic"? >>>>>>> >>>>>>> ISO 24707 actually has no inference rules or proof theory at all, >>>>>>> correct? How can they be "out of scope" for a logic? >>>>>> >>>>>> Did anyone suggest they are? >>>>> >>>>> You excluded them in 24707, 1 Scope which reads in part as follows: >>>>> >>>>> "The following are outside the scope of this International Standard: >>>>> * the specification of proof theory or inference rules; ? >>>> >>>> Right. The standard does not include those. The intended purpose of CL was to be a ?standard format? for the variety of notations and syntactic conventions all in use for FOL. One gets to define this exactly by providing one (abstract) syntax with a rigorously described model theory. It is then up to users of other notations to define their mappings to this syntax and check that their semantics are preserved under that mapping. None of this requires the notation to have a proof theory: in fact, such a proof theory might well be an impediment to such use, as it would impose an extra burden on translation which would not be relevant to the intended use of 24707. >>>> >>>>> >>>>> It's not logic without them. >>>> >>>> That is a matter of opinion. FOL is widely considered to be a (note singular) logic, yet there are probably 50 or more different proof theories and syntaxes for it. But only one model theory. >>>> >>>>>>> Shouldn't the ISO 24707 authors have released a Common LISP library by >>>>>>> now? It's been 10 years. >>>>>> >>>>>> The CL effort was done pro bono, and AFAIK none of the authors have funding to work on it further. I certainly have not. Anyone who is interested is welcome to develop CL inference engines or other software, of course. >>>>> >>>>> Ten years gone and there's no reference implementation, right? >>>> >>>> Right. AFAIK, nobody is working on it. Feel free to pick up the reins if you want to: it?s not in any way proprietary. I myself have retired from academic work, and Chris Menzel is a full-time philosopher. >>>> >>>>> >>>>> We are told that HETS parses CLIF syntax, but "handles" sequence markers >>>>> in second order logic, likely as polymorphic list types. >>>>> >>>>> A consumer of 24707 and standards which depend on it assume significant >>>>> risk. >>>> >>>> Not for the original intended use. >>>> >>>>> >>>>>>> Fabian, Annex D is only informative, but the following sentence may be >>>>>>> naively interpreted to mean that second order logic is required, or >>>>>>> somehow provided. >>>>>>> >>>>>>> "Note that sequences are essentially a non-first-order feature that >>>>>>> >>>>>>> can be expressed in second-order logic.? >>>>>> >>>>>> Well, that sentence is of course true. >>>>> >>>>> Really? Where would I find sequence markers in the literature on >>>>> second-order logic? Reference please. >>>> >>>> Sequence markers get you (a subset of) Lw1-w, which is strictly weaker than second-order. This is kind of obvious since you can define lists in second-order and quantify over them, and define integers to count how long they are, etc.. >>>> >>>>> >>>>> Assuming a reference, the sentence would be equally true in let's say >>>>> the calculus of constructions, right? >>>> >>>> I have no idea. We did not even look at CoC as being relevant to 24707. CoC is not easily relatable to FOL, is it? Curry-Howard gets you *intuitionist propositional* logic, which is a very small and idiosyncratic subset of FOL. >>>> >>>>> Everything that has lists, right? >>>> >>>> Not everything, surely. LISP has lists. but it doesn't have a logical model theory. I am not aware of any other extension of FOL that ?has lists? in the same sense. >>>> >>>>>> The mapping to Lw1w was not noticed until after that was written. We had a strong intuition that second-order was too strong, which is why this says 'can be expressed? rather than ?requires?. >>>>> >>>>> There's no mapping and there's no claim of induction related to sequence >>>>> markers in 24707. 24707 has a vague reference to fix points. >>>> >>>> It would not have been appropriate to include such details in 24707 even if we had had them worked out. Standards documents are not academic papers: there are strict rules about what should be included and what not, and distinguishing normative from informative text, and being rather exact about requirements and so forth. 24707 gives a model theory for sequence markers. >>>> >>>> Perhaps it would have been better to have left them out, in retrospect, as they are not strictly FO; but they were part of KIF which was the origin of CL, and we had worked out a precise semantics for them (which KIF did not), and they are only a tiny step up from strict FO, so we decided to keep them. And they are very useful in defining embeddings, as we found when translating OWL into CL. >>>> >>>>> And all we've read is a post-hoc claim of an unspecified "induction >>>>> principle." >>>>> >>>>> There's no proof, or inference rules, and there's no reference >>>>> implementation. Given the related "handle" claim, it sounds like >>>>> "requires" rather than "can be expressed" to me. >>>>> >>>>>> If someone reads that sentence in the way you imply, above, then I would suggest they are not competent to read a formal specification. >>>>> >>>>> That seems pervasive around standards organizations. >>>> >>>> Well, there are rules about how standards documents use language. Its a bit like being at a court: you have to be extra careful about how things are phrased, as these have consequences that you can ignore in less formal settings. >>>> >>>>>>> This is an example of how misinformation is being circulated about >>>>>>> "Common Logic." I have discussed this before at OMG. >>>>>>> >>>>>>> How do you respond to the fact that Java and C# provide parametric >>>>>>> polymorphism, but CL and DOL do not? >>>>>> >>>>>> With a puzzled frown, not understanding what possible relevance Java or C++ have to anything in this entire discussion (or in ISO 24707) >>>>> >>>>> They have lists similar to those in second order logic which seem to be >>>>> required to implement sequence markers in 24707. >>>> >>>> They have lists, but thay aren?t logics. So they don?t have, for example, quantifiers or connectives or logical sentences or a model theory. They are about as relevant to 24707 as shopping lists. >>>> >>>> Pat >>>> >>>>> >>>>> Turn that frown upside down. >>>>> >>>>> -- >>>>> Rick >>>>> >>>>>> Pat >>>>>> >>>>>>> >>>>>>> Good to see folks promoting Goguen's work though. >>>>>>> >>>>>>> -- >>>>>>> Rick >>>>>>> >>>>>>> On 12/20/2017 07:00 PM, rick wrote: >>>>>>>> Maybe Pat can show the derivations to avoid further misunderstanding. >>>>>>>> >>>>>>>> -- >>>>>>>> Rick >>>>>>>> >>>>>>>> On 12/20/2017 05:32 PM, Pat Hayes wrote: >>>>>>>>> I hadn?t seen that diagram before. I believe that it is inaccurate to describe CL as having ?some second-order constructs?. Sequence markers take CL outside FO expressivity, but not to second-order. CL with sequence markers is in fact a subset of the infinitary logic Lw1-w which allows countably infinite conjunctions. This is a long way short of full second-order logic. If one restricts CL (Lw1-w) so that sequence markers (infinite conjunctions) occur only on the LHS of sequents, it is first order. So sequence makers can be used in ontologies (ie as ?axioms?) without going beyond FO expressivity. >>>>>>>>> >>>>>>>>> Pat >>>>>>>>> >>>>>>>>>> On Dec 20, 2017, at 7:01 AM, John F Sowa wrote: >>>>>>>>>> >>>>>>>>>> Congratulations to everyone working on the DOL project. >>>>>>>>>> >>>>>>>>>> From Fabian via ontoiop-forum, >>>>>>>>>>> Good news concerning the standardisation of DOL! During the last >>>>>>>>>>> OMG Technical Meeting the Architecture Board approved the changes >>>>>>>>>>> that we made to DOL during the ?Finalisation Phase? (which in our >>>>>>>>>>> case lasted 2 years). Hence, we cleared the last major hurdle on >>>>>>>>>>> our way to the release of DOL 1.0. I expect that this will happen >>>>>>>>>>> in February 2018. >>>>>>>>>> >>>>>>>>>> And Fabian, I'm sending a copy of this note to Ontolog Forum, and >>>>>>>>>> I also attached a copy of an earlier diagram (dol.jpg). >>>>>>>>>> >>>>>>>>>> Does this diagram reflect the current version? If so (or not), >>>>>>>>>> could you please send the URL of the latest documentation to >>>>>>>>>> Ontolog Forum? >>>>>>>>>> >>>>>>>>>> And is software available for the various mappings in that diagram? >>>>>>>>>> >>>>>>>>>> John >>>>>>>>>> >>>>>>>>>> _________________________________________________________________ >>>>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>>>> Community Wiki: http://ontoiop.org >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> _________________________________________________________________ >>>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>>> Community Wiki: http://ontoiop.org >>>>>>>>> >>>>>>> >>>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>> >>>>> >>>> >>>> >>>> >>>> >>> >>> _________________________________________________________________ >>> To Post: mailto:ontoiop-forum at ovgu.de >>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>> Community Wiki: http://ontoiop.org >> >> >> >> > > From phayes at ihmc.us Wed Jan 3 08:19:41 2018 From: phayes at ihmc.us (Pat Hayes) Date: Tue, 2 Jan 2018 23:19:41 -0800 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> Message-ID: > On Jan 2, 2018, at 2:33 PM, Till Mossakowski wrote: > > Am 02.01.2018 um 16:00 schrieb rick: >> The DOL authors claim to "handle" sequence markers in HETS using "second >> order logic" which by conformance with MOF and fUML is outside the scope >> of DOL. > second-order logic is not outside the scope of DOL. DOL is a > meta-language that can be used for a variety of logics, provided they > can be formalised as an institution. Such logics include propositional > logic, OWL, Common Logic, first-order logic, second-order logic, modal > logics, hybrid logics, temporal logics, higher-order logics (also > variants including type constructors, subtypes and/or polymorphism), > intuitionistic logics, program logics, and many more. I confess to finding this either (a) hard to believe, or (b) slightly meaningless. This plethora of logics has such a variety of wildly different semantics that I fail to see how anything, or indeed anyone, mechanical or human, can define meaningful - truth-preserving - mappings between them all. But perhaps (?) preservation of meaning is not part of the game? Are there any logics that *cannot* be formalized as an institution? (Nonmonotonic logics. perhaps?) I have no idea what kind of constraint this formalization represents. Pat > > Best, Till > > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org > > From till at iks.cs.ovgu.de Wed Jan 3 09:33:52 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Wed, 3 Jan 2018 09:33:52 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <063f6817-69af-cc7a-d32b-4c6a06020c5a@bestweb.net> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <063f6817-69af-cc7a-d32b-4c6a06020c5a@bestweb.net> Message-ID: <1e155b08-a0e1-a51f-1d27-1968e2a23ce0@iks.cs.ovgu.de> Am 02.01.2018 um 23:52 schrieb John F Sowa: > On 1/2/2018 5:33 PM, Till Mossakowski wrote: >> second-order logic is not outside the scope of DOL. DOL is a >> meta-language that can be used for a variety of logics, provided they >> can be formalised as an institution. Such logics include propositional >> logic, OWL, Common Logic, first-order logic, second-order logic, modal >> logics, hybrid logics, temporal logics, higher-order logics (also >> variants including type constructors, subtypes and/or polymorphism), >> intuitionistic logics, program logics, and many more. > > That is very impressive.? Does Hets support all the logics that > DOL can specify? > no, of course not. The theoretical framework of institutions has infinitely many examples. Here is the list of Hets-supported logics, copied (and slightly edited, will change that...) from http://hets.eu/ ??? general-purpose logics: Propositional, QBF, TPTP (FOL), THF (HOL), CASL (FOL), HasCASL (HOL), Isabelle/HOL ??? logical frameworks: Isabelle, LF, DFOL ??? modeling languages: Meta-Object Facility (MOF), Query/View/Transformation (QVT), UML class diagrams, state machines, sequence diagrams ??? ontologies and constraint languages: OWL, CommonLogic, RelScheme, ConstraintCASL ??? reactive systems: CspCASL, CoCASL, ModalCASL, ExtModal (modal, hybrid and temporal logic), Maude ??? programming languages: Haskell, VSE (dynamic logic) ??? logics of specific tools: Reduce, DMU (CATIA) > What kind of performance do you get with some of those logics? Hets' parsing and analysis generally is fast. Theorem proving and such greatly depends on the theorem provers that you use. Here is a list of provers that Hets can speak to, again taken from http://hets.eu/ ??? minisat and zChaff, which are SAT solvers, ??? SPASS, Vampire, Darwin, Hyper and MathServe, which are automatic first-order theorem provers, ??? Pellet and Fact++, description logic tableau provers, ??? Leo-II and Satallax, automated higher-order provers, ??? Isabelle, an interactive higher-order theorem prover, ??? CSPCASL-prover, an Isabelle-based prover for CspCASL, ??? VSE, an interactive prover for dynamic logic. > > For example, CL allows quantifiers to range over functions and > relations without going beyond first-order proof procedures. > What is the difference in performance of a proof with CL > semantics vs. HOL semantics? > I have not checked, but I would guess that proofs for CL are generally faster than for HOL, because you can use a first-order resolution prover, or an induction prover if you use sequence markers in a non-eliminable way. By constrast, most HOL logics include lambda abstraction, which makes unification and thus resolution much harder. So the crucial feature making HOL much harder is lambda abstraction, which is not (and cannot be) present in CL. Best, Till > John > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: > https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org From till at iks.cs.ovgu.de Wed Jan 3 12:02:48 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Wed, 3 Jan 2018 12:02:48 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> Message-ID: <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> Am 03.01.2018 um 08:19 schrieb Pat Hayes: >> second-order logic is not outside the scope of DOL. DOL is a >> meta-language that can be used for a variety of logics, provided they >> can be formalised as an institution. Such logics include propositional >> logic, OWL, Common Logic, first-order logic, second-order logic, modal >> logics, hybrid logics, temporal logics, higher-order logics (also >> variants including type constructors, subtypes and/or polymorphism), >> intuitionistic logics, program logics, and many more. > I confess to finding this either (a) hard to believe, or (b) slightly meaningless. This plethora of logics has such a variety of wildly different semantics that I fail to see how anything, or indeed anyone, mechanical or human, can define meaningful - truth-preserving - mappings between them all. But perhaps (?) preservation of meaning is not part of the game? First, DOL is about structuring logical theories (in DOL speak: OMS), declaring theory interpretations, conservative extensions, alignments, networks, refinement etc. This can be done separately for each logic. Formalising logics as institutions just provides the technical means to apply this general theory of structuring. Of course, the conditions on institutions are rather mild and the notion is rather general, so it is no surprise that so many logics can be formalised as institutions. But this is not a bug but a feature, because it means that DOL structuring can be applied to a wide variety of logics. Second, DOL is about translation between logics, and related, specification of heterogeneous logical theories (OMS). This is a different story. Of course, you cannot expect that all logics can be mapped into each other, especially because a certain preservation of meaning is required (otherwise logic mappings are not very useful). Still, one can define useful graphs of logics and mappings. Hets supports a particular such graph. > > Are there any logics that *cannot* be formalized as an institution? (Nonmonotonic logics. perhaps?) I have no idea what kind of constraint this formalization represents. Institution theory and DOL use the model-theoretic definition of logical consequence: Gamma |= phi iff for all models M, M |= Gamma implies M |= phi. This is necessarily monotonic. Hence, non-monotonic logics are outside the scope of DOL. That said, note that DOL provides a construct "minimize" that captures McCarthy's circumscription and that can be used to express closed-world assumptions in a fine-grained way (that is, also restricted to certain symbols). Best, Till From sowa at bestweb.net Wed Jan 3 17:17:55 2018 From: sowa at bestweb.net (John F Sowa) Date: Wed, 3 Jan 2018 11:17:55 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> Message-ID: <4806b8f6-d896-6a0a-9bbf-2a3a33f921df@bestweb.net> Till, Thanks for the answers to my questions and Pat's questions. Those answers and the diagram on the Hets web site clarify many of the issues: http://hets.eu/ As the diagram shows, Hets can support a large family of theorem provers for various logics. But can it support two or more theorem provers for different aspects of the same proof? For example, the method of using hybrid theorem provers began in the 1980s with a combination of a description logic for the T-Box and FOL for the A-Box. Does Hets support such combinations? Sorted logics can be considered hybrids, since they combine a DL method and an FOL method of theorem proving. Could Hets be used to create a sorted theorem prover by combining two such theorem provers? If not directly, could it combine them after suitable modifications to each? > By contrast, most HOL logics include lambda abstraction, which > makes unification and thus resolution much harder. So the crucial > feature making HOL much harder is lambda abstraction, which > is not (and cannot be) present in CL. That's an important point. But some languages use the keyword 'lambda' as a purely syntactic marker for defining functions. For example: (= f (lambda (x y) ("some expression that uses x and y"))) This is a convenient notation in LISP and other languages, but they don't use any of the mechanisms of lambda calculus. Is it true that this syntax could be used in CL without going beyond a first-order style of theorem proving? John From till at iks.cs.ovgu.de Wed Jan 3 17:46:28 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Wed, 3 Jan 2018 17:46:28 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <4806b8f6-d896-6a0a-9bbf-2a3a33f921df@bestweb.net> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> <4806b8f6-d896-6a0a-9bbf-2a3a33f921df@bestweb.net> Message-ID: John, Am 03.01.2018 um 17:17 schrieb John F Sowa: > Till, > > Thanks for the answers to my questions and Pat's questions. > Those answers and the diagram on the Hets web site clarify > many of the issues:? http://hets.eu/ > > As the diagram shows, Hets can support a large family of theorem > provers for various logics.? But can it support two or more > theorem provers for different aspects of the same proof? > > For example, the method of using hybrid theorem provers began > in the 1980s with a combination of a description logic for the > T-Box and FOL for the A-Box.? Does Hets support such combinations? > > Sorted logics can be considered hybrids, since they combine > a DL method and an FOL method of theorem proving.? Could Hets > be used to create a sorted theorem prover by combining two > such theorem provers?? If not directly, could it combine them > after suitable modifications to each? > With Hets, you can only use one theorem prover at a time. Of course, you can use multiple provers in parallel to attack one goal, but without any prover cooperation. A certain step towards prover cooperation is to speculate lemmas and then use a different theorem provers for the lemmas and the main theorem. >> By contrast, most HOL logics include lambda abstraction, which >> makes unification and thus resolution much harder. So the crucial >> feature making HOL much harder is lambda abstraction, which >> is not (and cannot be) present in CL. > > That's an important point.? But some languages use the keyword 'lambda' > as a purely syntactic marker for defining functions.? For example: > > ?? (= f (lambda (x y) ("some expression that uses x and y"))) > > This is a convenient notation in LISP and other languages, > but they don't use any of the mechanisms of lambda calculus. > Is it true that this syntax could be used in CL without going > beyond a first-order style of theorem proving? > If you restrict this to first-order definitions, then it seems harmless to me (though I cannot see what is gained by this notation). However, higher-order definitions won't work: (= russell (lambda (p) (lambda (x) (not (p x))))) produces an inconsistency. Best, Till From sowa at bestweb.net Wed Jan 3 20:25:29 2018 From: sowa at bestweb.net (John F Sowa) Date: Wed, 3 Jan 2018 14:25:29 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> <4806b8f6-d896-6a0a-9bbf-2a3a33f921df@bestweb.net> Message-ID: Till, Thanks for the clarifications. For now, that covers all the issues I was concerned about. > A certain step towards prover cooperation is to speculate lemmas > and then use a different theorem provers for the lemmas and > the main theorem. Yes. That could probably support a hybrid where a general FOL theorem prover has primary control, but it calls special-purpose theorem provers to prove lemmas expressed in more restricted subsets of FOL. For example, is S1 a subsort of S2? >> (= f (lambda (x y) ("some expression that uses x and y"))) >> >> This is a convenient notation in LISP and other languages, > If you restrict this to first-order definitions, then it seems harmless > to me (though I cannot see what is gained by this notation). For defining a function, I agree that this syntax has no advantage over (forall (x y) (= (f x y) ("some expression that uses x and y"))) But the lambda syntax is most useful when you want to use a function without giving it a name -- for example, when it's an argument of some other function or relation. John From rick at rickmurphy.org Wed Jan 3 20:34:55 2018 From: rick at rickmurphy.org (rick) Date: Wed, 3 Jan 2018 14:34:55 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> Message-ID: Dear Till, Thanks so much for pointing this out. See below. On 01/02/2018 05:33 PM, Till Mossakowski wrote: > Am 02.01.2018 um 16:00 schrieb rick: >> The DOL authors claim to "handle" sequence markers in HETS using "second >> order logic" which by conformance with MOF and fUML is outside the scope >> of DOL. > second-order logic is not outside the scope of DOL. I have reviewed the RFP and proposal a few times. I understand scope is defined 6.1 and 6.5.4 and conformance in 6.5.5 of the RFP. 6.5.5 establishes conformance of languages and translations of which none listed are second order logic. Also Annexes D-H do not include a conformance statement for second order logic. How do you justify your claim that second order logic is not outside the scope of DOL? 6.5.5 requires formal criteria for establishing conformance and specified in enough detail to be testable. How does your claim satisfy these criteria? It appears the RFP limits conformance to exclude second order logic and the proposal does not claim to establish conformance for second order logic. > DOL is a > meta-language that can be used for a variety of logics, provided they > can be formalised as an institution. Such logics include propositional > logic, OWL, Common Logic, first-order logic, second-order logic, modal > logics, hybrid logics, temporal logics, higher-order logics (also > variants including type constructors, subtypes and/or polymorphism), > intuitionistic logics, program logics, and many more. I am reasonably familiar with the broad applicability of institutions. My comment was specific to DOL and its scope and conformance criteria. As an aside, I have searched the for a System F comorphism. Would you be able to provide a pointer to a paper? I have a few follow-up questions for later. > Best, Till > > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org > > From till at iks.cs.ovgu.de Wed Jan 3 20:52:37 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Wed, 3 Jan 2018 20:52:37 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> <4806b8f6-d896-6a0a-9bbf-2a3a33f921df@bestweb.net> Message-ID: <6c5bb609-b3a6-b68a-ba28-2ae062646eb6@iks.cs.ovgu.de> John, Am 03.01.2018 um 20:25 schrieb John F Sowa: > > For defining a function, I agree that this syntax has no advantage over > (forall (x y) (= (f x y) ("some expression that uses x and y"))) > > But the lambda syntax is most useful when you want to use a function > without giving it a name -- for example, when it's an argument of > some other function or relation. but then you are in a higher-order setting, and no-one prevents you from writing (lambda (p) (not (p p))) which is a term that cannot have a denotation. Best, Till From till at iks.cs.ovgu.de Wed Jan 3 21:00:23 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Wed, 3 Jan 2018 21:00:23 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> Message-ID: <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> Rick, Am 03.01.2018 um 20:34 schrieb rick: > Dear Till, > > Thanks so much for pointing this out. See below. > > On 01/02/2018 05:33 PM, Till Mossakowski wrote: >> Am 02.01.2018 um 16:00 schrieb rick: >>> The DOL authors claim to "handle" sequence markers in HETS using "second >>> order logic" which by conformance with MOF and fUML is outside the scope >>> of DOL. >> second-order logic is not outside the scope of DOL. > I have reviewed the RFP and proposal a few times. I understand scope is > defined 6.1 and 6.5.4 and conformance in 6.5.5 of the RFP. > > 6.5.5 establishes conformance of languages and translations of which > none listed are second order logic. Also Annexes D-H do not include a > conformance statement for second order logic. > > How do you justify your claim that second order logic is not outside the > scope of DOL? see section 2.2 "Conformance of an OMS Language/a Logic with DOL" of the DOL standard at http://www.omg.org/spec/DOL/ : "The logical language aspect of an OMS language is conforming with DOL if each logic corresponding to a profile (including the logic corresponding to the whole logical language aspect) is presented as an institution in the sense of Definition 2 in clause 10 , and there is a mapping from the abstract syntax of the OMS language to signatures and sentences of the institution." For some specific logics, appendices of the DOL standard establish such a conformance, but of course the scope of DOL is not limited to these. > As an aside, I have searched the for a System F comorphism. Would you be > able to provide a pointer to a paper? > I am not aware of institution-theoretic work on system F. Best, Till From sowa at bestweb.net Thu Jan 4 16:31:30 2018 From: sowa at bestweb.net (John F Sowa) Date: Thu, 4 Jan 2018 10:31:30 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <6c5bb609-b3a6-b68a-ba28-2ae062646eb6@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7f613da6-c006-9558-62c7-fc6ac1277784@iks.cs.ovgu.de> <4806b8f6-d896-6a0a-9bbf-2a3a33f921df@bestweb.net> <6c5bb609-b3a6-b68a-ba28-2ae062646eb6@iks.cs.ovgu.de> Message-ID: On 1/3/2018 2:52 PM, Till Mossakowski wrote: > in a higher-order setting, no-one prevents you from writing > > (lambda (p) (not (p p))) > > which is a term that cannot have a denotation. Yes. I admit that a lambda expression as an argument of a function or relation could cause an inconsistency. For anyone who is not familiar with CL semantics, the above definition would be safe if it had been stated as an axiom: (forall (p) (= (f p) (not (p p)))) If you substitute f for p, this axiom would imply (= (f f) (not (f f))) This statement is false. Therefore, the axiom must be false. That may cause a problem for a particular theory, but it does not create an inconsistency in CL semantics. Examples such as these, explain why CL does *not* have a special notation for stating definitions, such as Define f as (= (f p) (not (p p))). Since definitions must be true "by definition", this statement must be true. And that would create an inconsistency in the CL methods for stating definitions. As Till's example illustrates, lambda expressions used as arguments of a function or relation could create the same kind of inconsistency as an explicit notation for definitions. John From rick at rickmurphy.org Thu Jan 4 21:47:55 2018 From: rick at rickmurphy.org (rick) Date: Thu, 4 Jan 2018 15:47:55 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> Message-ID: <6764f6e2-4a2e-232e-a6a1-69fa1148fc96@rickmurphy.org> Pat, Thanks much for taking the time to answer my questions. And great to hear about the natural deduction proof system. I understand you do not reject induction and do not assert a preference on approach to sequence markers and inference. You also believe Lw-1,w not central when published as it remains now. I will just take 24707 6.5 as written regarding sequence markers and recursion. Feel free to watch for comment on DOL Annex D. -- Rick On 01/03/2018 02:12 AM, Pat Hayes wrote: > Hi Rick > > Till may well be right that nobody is going to make a theorem prover for Lw1w, which has infinite expressions. However, CL is a finite notation, and I think there is no reason why it could not have a theorem prover. KIF had a version of sequence markers, and there have been KIF theorem provers. I have a natural-deduction proof system for CL with sequence markers which is complete, but not computationally efficient. It is pretty obvious: you just need an extra rule which unpacks sequence marker expressions to one instance, but with another marker appended to it: > > (forall (?x)S) |- (forall (?y)S[...x/t ?y]) for any term t > > and the empty-sequence rule > > (forall (?x)S) |- S[...x/ <>] > > Using the first rule enough times, then the second rule, will generate any finite number of instance sequences. > So there is certainly no theoretical obstacle to a CL theorem-prover. > > However, as indicated in my earlier email, this issue is irrelevant to ISO 24707. > > Other responses in-line below. > >> On Jan 2, 2018, at 12:32 PM, rick wrote: >> >> Pat, >> >> Do you disagree with the following? >> >> TM> "due to the infinitary nature, there won't be any theorem provers, >> even with your restriction to axioms." >> >> It seems greater care is needed to confirm your understanding. >> >> See below for more fun. >> >> -- >> Rick >> >> On 01/02/2018 01:25 PM, Pat Hayes wrote: >>> >>> >>>> On Jan 2, 2018, at 7:00 AM, rick wrote: >>>> >>>> Till & Fabian, consider the following under DOL public comment, open >>>> through March 2018 and relevant to the required Business Committee >>>> Questionnaire. >>>> >>>> I have cc'd Larry Johnson OMG's Technical Director. >>>> >>>> The recent email exchange confirmed that the authors of ISO 24707 >>>> determined the need for revisions to incorporate an unspecified >>>> "induction principle" after its publication. >>> >>> As one of the two main authors of the technical parts of ISO 24707, I do not agree with the previous sentence. The authors of ISO 24707 did /not/ determine a need for an unspecified induction principle, and my recent email exchanges with Rick Murphy (copied below) do /not/ confirm any such interpretation. >> >> You had not rejected Till's recommendation regarding induction. >> >> Am I correct the record should reflect that you reject such an approach? > > I have no opinion about any ?approach?. This thread started because I wished to place on record an exact statement about the expressiveness of CL; that is all. I have no views on any approach to implementing an inference system for CL. > >> >> You had previously said: >> >> PH> "I understand (and respect) your preference for 2OL over infinitary >> for prover-relevant reasons? > > Of course. To ask for an implementation to use infinite expressions would be rather unreasonable. > >>> As I pointed out to Rick in one of the emails, the intended purpose for ISO 24707 did not require a specification of any kind of proof theory for the CL language specified; the authors of that standard did not contemplate giving such a proof theory in any future revision to ISO 24707; and if they had done, the simple reduction of sequence marker syntax to the weak infinitary logic Lw1w would have sufficed, without mentioning induction. >> >> As you said Lw-1,w was discovered by the authors after publication of >> 24707. > > Lw1w was not ?discovered' after the publication of 24707. That the (now obvious) mapping to Lw1w was semantically exact was noticed around the time the standard text was being published, but this entire issue was not considered centrally germane to the standard in any case. It continues to not be so. > > Pat > >> Revisionism is only good in the next revision of the standard. >> >> -- >> Rick >> >>> Pat Hayes >>> >>>> >>>> The DOL authors claim to "handle" sequence markers in HETS using "second >>>> order logic" which by conformance with MOF and fUML is outside the scope >>>> of DOL. >>>> >>>> Pat, thanks for taking the time to answer my questions. I am heads down >>>> this year on dependent types and univalence. >>>> >>>> -- >>>> Rick >>>> >>>> On 12/27/2017 02:44 PM, Pat Hayes wrote: >>>>> >>>>> >>>>>> On Dec 27, 2017, at 6:17 AM, rick wrote: >>>>>> >>>>>> On 12/21/2017 07:50 PM, Pat Hayes wrote: >>>>>>> >>>>>>> >>>>>>>> On Dec 21, 2017, at 9:54 AM, rick wrote: >>>>>>>> >>>>>>>> How about it, Pat? >>>>>>>> >>>>>>>> No derivations for "Common Logic"? >>>>>>>> >>>>>>>> ISO 24707 actually has no inference rules or proof theory at all, >>>>>>>> correct? How can they be "out of scope" for a logic? >>>>>>> >>>>>>> Did anyone suggest they are? >>>>>> >>>>>> You excluded them in 24707, 1 Scope which reads in part as follows: >>>>>> >>>>>> "The following are outside the scope of this International Standard: >>>>>> * the specification of proof theory or inference rules; ? >>>>> >>>>> Right. The standard does not include those. The intended purpose of CL was to be a ?standard format? for the variety of notations and syntactic conventions all in use for FOL. One gets to define this exactly by providing one (abstract) syntax with a rigorously described model theory. It is then up to users of other notations to define their mappings to this syntax and check that their semantics are preserved under that mapping. None of this requires the notation to have a proof theory: in fact, such a proof theory might well be an impediment to such use, as it would impose an extra burden on translation which would not be relevant to the intended use of 24707. >>>>> >>>>>> >>>>>> It's not logic without them. >>>>> >>>>> That is a matter of opinion. FOL is widely considered to be a (note singular) logic, yet there are probably 50 or more different proof theories and syntaxes for it. But only one model theory. >>>>> >>>>>>>> Shouldn't the ISO 24707 authors have released a Common LISP library by >>>>>>>> now? It's been 10 years. >>>>>>> >>>>>>> The CL effort was done pro bono, and AFAIK none of the authors have funding to work on it further. I certainly have not. Anyone who is interested is welcome to develop CL inference engines or other software, of course. >>>>>> >>>>>> Ten years gone and there's no reference implementation, right? >>>>> >>>>> Right. AFAIK, nobody is working on it. Feel free to pick up the reins if you want to: it?s not in any way proprietary. I myself have retired from academic work, and Chris Menzel is a full-time philosopher. >>>>> >>>>>> >>>>>> We are told that HETS parses CLIF syntax, but "handles" sequence markers >>>>>> in second order logic, likely as polymorphic list types. >>>>>> >>>>>> A consumer of 24707 and standards which depend on it assume significant >>>>>> risk. >>>>> >>>>> Not for the original intended use. >>>>> >>>>>> >>>>>>>> Fabian, Annex D is only informative, but the following sentence may be >>>>>>>> naively interpreted to mean that second order logic is required, or >>>>>>>> somehow provided. >>>>>>>> >>>>>>>> "Note that sequences are essentially a non-first-order feature that >>>>>>>> >>>>>>>> can be expressed in second-order logic.? >>>>>>> >>>>>>> Well, that sentence is of course true. >>>>>> >>>>>> Really? Where would I find sequence markers in the literature on >>>>>> second-order logic? Reference please. >>>>> >>>>> Sequence markers get you (a subset of) Lw1-w, which is strictly weaker than second-order. This is kind of obvious since you can define lists in second-order and quantify over them, and define integers to count how long they are, etc.. >>>>> >>>>>> >>>>>> Assuming a reference, the sentence would be equally true in let's say >>>>>> the calculus of constructions, right? >>>>> >>>>> I have no idea. We did not even look at CoC as being relevant to 24707. CoC is not easily relatable to FOL, is it? Curry-Howard gets you *intuitionist propositional* logic, which is a very small and idiosyncratic subset of FOL. >>>>> >>>>>> Everything that has lists, right? >>>>> >>>>> Not everything, surely. LISP has lists. but it doesn't have a logical model theory. I am not aware of any other extension of FOL that ?has lists? in the same sense. >>>>> >>>>>>> The mapping to Lw1w was not noticed until after that was written. We had a strong intuition that second-order was too strong, which is why this says 'can be expressed? rather than ?requires?. >>>>>> >>>>>> There's no mapping and there's no claim of induction related to sequence >>>>>> markers in 24707. 24707 has a vague reference to fix points. >>>>> >>>>> It would not have been appropriate to include such details in 24707 even if we had had them worked out. Standards documents are not academic papers: there are strict rules about what should be included and what not, and distinguishing normative from informative text, and being rather exact about requirements and so forth. 24707 gives a model theory for sequence markers. >>>>> >>>>> Perhaps it would have been better to have left them out, in retrospect, as they are not strictly FO; but they were part of KIF which was the origin of CL, and we had worked out a precise semantics for them (which KIF did not), and they are only a tiny step up from strict FO, so we decided to keep them. And they are very useful in defining embeddings, as we found when translating OWL into CL. >>>>> >>>>>> And all we've read is a post-hoc claim of an unspecified "induction >>>>>> principle." >>>>>> >>>>>> There's no proof, or inference rules, and there's no reference >>>>>> implementation. Given the related "handle" claim, it sounds like >>>>>> "requires" rather than "can be expressed" to me. >>>>>> >>>>>>> If someone reads that sentence in the way you imply, above, then I would suggest they are not competent to read a formal specification. >>>>>> >>>>>> That seems pervasive around standards organizations. >>>>> >>>>> Well, there are rules about how standards documents use language. Its a bit like being at a court: you have to be extra careful about how things are phrased, as these have consequences that you can ignore in less formal settings. >>>>> >>>>>>>> This is an example of how misinformation is being circulated about >>>>>>>> "Common Logic." I have discussed this before at OMG. >>>>>>>> >>>>>>>> How do you respond to the fact that Java and C# provide parametric >>>>>>>> polymorphism, but CL and DOL do not? >>>>>>> >>>>>>> With a puzzled frown, not understanding what possible relevance Java or C++ have to anything in this entire discussion (or in ISO 24707) >>>>>> >>>>>> They have lists similar to those in second order logic which seem to be >>>>>> required to implement sequence markers in 24707. >>>>> >>>>> They have lists, but thay aren?t logics. So they don?t have, for example, quantifiers or connectives or logical sentences or a model theory. They are about as relevant to 24707 as shopping lists. >>>>> >>>>> Pat >>>>> >>>>>> >>>>>> Turn that frown upside down. >>>>>> >>>>>> -- >>>>>> Rick >>>>>> >>>>>>> Pat >>>>>>> >>>>>>>> >>>>>>>> Good to see folks promoting Goguen's work though. >>>>>>>> >>>>>>>> -- >>>>>>>> Rick >>>>>>>> >>>>>>>> On 12/20/2017 07:00 PM, rick wrote: >>>>>>>>> Maybe Pat can show the derivations to avoid further misunderstanding. >>>>>>>>> >>>>>>>>> -- >>>>>>>>> Rick >>>>>>>>> >>>>>>>>> On 12/20/2017 05:32 PM, Pat Hayes wrote: >>>>>>>>>> I hadn?t seen that diagram before. I believe that it is inaccurate to describe CL as having ?some second-order constructs?. Sequence markers take CL outside FO expressivity, but not to second-order. CL with sequence markers is in fact a subset of the infinitary logic Lw1-w which allows countably infinite conjunctions. This is a long way short of full second-order logic. If one restricts CL (Lw1-w) so that sequence markers (infinite conjunctions) occur only on the LHS of sequents, it is first order. So sequence makers can be used in ontologies (ie as ?axioms?) without going beyond FO expressivity. >>>>>>>>>> >>>>>>>>>> Pat >>>>>>>>>> >>>>>>>>>>> On Dec 20, 2017, at 7:01 AM, John F Sowa wrote: >>>>>>>>>>> >>>>>>>>>>> Congratulations to everyone working on the DOL project. >>>>>>>>>>> >>>>>>>>>>> From Fabian via ontoiop-forum, >>>>>>>>>>>> Good news concerning the standardisation of DOL! During the last >>>>>>>>>>>> OMG Technical Meeting the Architecture Board approved the changes >>>>>>>>>>>> that we made to DOL during the ?Finalisation Phase? (which in our >>>>>>>>>>>> case lasted 2 years). Hence, we cleared the last major hurdle on >>>>>>>>>>>> our way to the release of DOL 1.0. I expect that this will happen >>>>>>>>>>>> in February 2018. >>>>>>>>>>> >>>>>>>>>>> And Fabian, I'm sending a copy of this note to Ontolog Forum, and >>>>>>>>>>> I also attached a copy of an earlier diagram (dol.jpg). >>>>>>>>>>> >>>>>>>>>>> Does this diagram reflect the current version? If so (or not), >>>>>>>>>>> could you please send the URL of the latest documentation to >>>>>>>>>>> Ontolog Forum? >>>>>>>>>>> >>>>>>>>>>> And is software available for the various mappings in that diagram? >>>>>>>>>>> >>>>>>>>>>> John >>>>>>>>>>> >>>>>>>>>>> _________________________________________________________________ >>>>>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>>>>> Community Wiki: http://ontoiop.org >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> _________________________________________________________________ >>>>>>>>>> To Post: mailto:ontoiop-forum at ovgu.de >>>>>>>>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>>>>>>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>>>>>>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>>>>>>>> Community Wiki: http://ontoiop.org >>>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>> >>>>>> >>>>> >>>>> >>>>> >>>>> >>>> >>>> _________________________________________________________________ >>>> To Post: mailto:ontoiop-forum at ovgu.de >>>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>>> Community Wiki: http://ontoiop.org >>> >>> >>> >>> >> >> > > > > From rick at rickmurphy.org Thu Jan 4 22:29:20 2018 From: rick at rickmurphy.org (rick) Date: Thu, 4 Jan 2018 16:29:20 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> Message-ID: <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> Thanks Till, but I don't get it. I read section 2.2 and Definition 2 clause 10, but no institution was presented in the proposal to justify your claim, right? If so, where is it? While institutions are broadly applicable, the RFP restricts DOL scope and conformance to 6.5.5. Second order logic is not included in 6.5.5 and its not in the proposal. Also, if there's no institution-theoretic work on System F, there can't be, right? -- Rick On 01/03/2018 03:00 PM, Till Mossakowski wrote: > Rick, > > Am 03.01.2018 um 20:34 schrieb rick: >> Dear Till, >> >> Thanks so much for pointing this out. See below. >> >> On 01/02/2018 05:33 PM, Till Mossakowski wrote: >>> Am 02.01.2018 um 16:00 schrieb rick: >>>> The DOL authors claim to "handle" sequence markers in HETS using "second >>>> order logic" which by conformance with MOF and fUML is outside the scope >>>> of DOL. >>> second-order logic is not outside the scope of DOL. >> I have reviewed the RFP and proposal a few times. I understand scope is >> defined 6.1 and 6.5.4 and conformance in 6.5.5 of the RFP. >> >> 6.5.5 establishes conformance of languages and translations of which >> none listed are second order logic. Also Annexes D-H do not include a >> conformance statement for second order logic. >> >> How do you justify your claim that second order logic is not outside the >> scope of DOL? > see section 2.2 "Conformance of an OMS Language/a Logic with DOL" of the > DOL standard at http://www.omg.org/spec/DOL/ : > > "The logical language aspect of an OMS language is conforming with DOL > if each logic corresponding to a profile (including > the logic corresponding to the whole logical language aspect) is > presented as an institution in the sense of Definition 2 > in clause 10 , and there is a mapping from the abstract syntax of the > OMS language to signatures and sentences of the > institution." > > For some specific logics, appendices of the DOL standard establish such > a conformance, but of course the scope of DOL is not limited to these. > >> As an aside, I have searched the for a System F comorphism. Would you be >> able to provide a pointer to a paper? >> > I am not aware of institution-theoretic work on system F. > > Best, Till > > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org > > From till at iks.cs.ovgu.de Thu Jan 4 23:34:00 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Thu, 4 Jan 2018 23:34:00 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> Message-ID: <5718c3ca-9bc2-6d64-f91f-82771e4289ea@iks.cs.ovgu.de> Rick, Am 04.01.2018 um 22:29 schrieb rick: > Thanks Till, but I don't get it. > > I read section 2.2 and Definition 2 clause 10, but no institution was > presented in the proposal to justify your claim, right? If so, where is it? I can just repeat myself: the fact that a particular institution does not appear in the DOL standard does not entail that it is outside the scope of DOL. > > While institutions are broadly applicable, the RFP restricts DOL scope > and conformance to 6.5.5. Second order logic is not included in 6.5.5 > and its not in the proposal. Right, second-order logic is not mentioned in the standard. Still, it is within the scope of DOL. See section 2.2 "Conformance of an OMS Language/a Logic with DOL", which basically entails that any institution is within the scope of DOL. > > Also, if there's no institution-theoretic work on System F, there can't > be, right? I would not draw this conclusion. That said, indeed polymorphism is difficult to capture as an institution, because the satisfaction condition (the only, rather mild, condition governing institutions) easily fails if you do not take care. See [1]. Best, Till [1] Lutz Schr?der, Till Mossakowski and Christoph L?th. Type class polymorphism in an institutional framework. In: J. Fiadeiro, editor, Recent Trends in Algebraic Development Techniques, 17th International Workshop (WADT 2004), volume 3423, series Lecture Notes in Computer Science, pages 234-248. Springer; Berlin; http://www.springer.de, 2005. > > -- > Rick > > On 01/03/2018 03:00 PM, Till Mossakowski wrote: >> Rick, >> >> Am 03.01.2018 um 20:34 schrieb rick: >>> Dear Till, >>> >>> Thanks so much for pointing this out. See below. >>> >>> On 01/02/2018 05:33 PM, Till Mossakowski wrote: >>>> Am 02.01.2018 um 16:00 schrieb rick: >>>>> The DOL authors claim to "handle" sequence markers in HETS using "second >>>>> order logic" which by conformance with MOF and fUML is outside the scope >>>>> of DOL. >>>> second-order logic is not outside the scope of DOL. >>> I have reviewed the RFP and proposal a few times. I understand scope is >>> defined 6.1 and 6.5.4 and conformance in 6.5.5 of the RFP. >>> >>> 6.5.5 establishes conformance of languages and translations of which >>> none listed are second order logic. Also Annexes D-H do not include a >>> conformance statement for second order logic. >>> >>> How do you justify your claim that second order logic is not outside the >>> scope of DOL? >> see section 2.2 "Conformance of an OMS Language/a Logic with DOL" of the >> DOL standard at http://www.omg.org/spec/DOL/ : >> >> "The logical language aspect of an OMS language is conforming with DOL >> if each logic corresponding to a profile (including >> the logic corresponding to the whole logical language aspect) is >> presented as an institution in the sense of Definition 2 >> in clause 10 , and there is a mapping from the abstract syntax of the >> OMS language to signatures and sentences of the >> institution." >> >> For some specific logics, appendices of the DOL standard establish such >> a conformance, but of course the scope of DOL is not limited to these. >> >>> As an aside, I have searched the for a System F comorphism. Would you be >>> able to provide a pointer to a paper? >>> >> I am not aware of institution-theoretic work on system F. >> >> Best, Till >> >> >> _________________________________________________________________ >> To Post: mailto:ontoiop-forum at ovgu.de >> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >> Community Wiki: http://ontoiop.org >> >> > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org From rick at rickmurphy.org Fri Jan 5 01:18:48 2018 From: rick at rickmurphy.org (rick) Date: Thu, 4 Jan 2018 19:18:48 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <5718c3ca-9bc2-6d64-f91f-82771e4289ea@iks.cs.ovgu.de> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> <5718c3ca-9bc2-6d64-f91f-82771e4289ea@iks.cs.ovgu.de> Message-ID: Thanks Till for taking the time to answer my questions. I remain unconvinced that an institution that's not in the proposal is in scope. More important though is whether an institution of "second order logic" exists. And whether the required mapping from the abstract syntax of OMS to the signatures and sentences of "second order logic" exists. right? Just to be sure, when you say "second order logic" you mean Henkin Semantics, right? I will enjoy reading the reference on type class polymorphism. Do you claim the paper contains the institution and the mapping? It seems not as the paper predates (2004) DOL. If not, could you please provide a pointer? I briefly scanned the paper. Looks like a great paper. -- Rick On 01/04/2018 05:34 PM, Till Mossakowski wrote: > Rick, > > Am 04.01.2018 um 22:29 schrieb rick: >> Thanks Till, but I don't get it. >> >> I read section 2.2 and Definition 2 clause 10, but no institution was >> presented in the proposal to justify your claim, right? If so, where is it? > I can just repeat myself: the fact that a particular institution does > not appear in the DOL standard does not entail that it is outside the > scope of DOL. >> >> While institutions are broadly applicable, the RFP restricts DOL scope >> and conformance to 6.5.5. Second order logic is not included in 6.5.5 >> and its not in the proposal. > Right, second-order logic is not mentioned in the standard. Still, it is > within the scope of DOL. See section 2.2 "Conformance of an OMS > Language/a Logic with DOL", which basically entails that any institution > is within the scope of DOL. >> >> Also, if there's no institution-theoretic work on System F, there can't >> be, right? > I would not draw this conclusion. > That said, indeed polymorphism is difficult to capture as an > institution, because the satisfaction condition (the only, rather mild, > condition governing institutions) easily fails if you do not take care. > See [1]. > > Best, Till > > [1] Lutz Schr?der, Till Mossakowski and Christoph L?th. Type class > polymorphism in an institutional framework. In: J. Fiadeiro, editor, > Recent Trends in Algebraic Development Techniques, 17th International > Workshop (WADT 2004), volume 3423, series Lecture Notes in Computer > Science, pages 234-248. Springer; Berlin; http://www.springer.de, 2005. > >> >> -- >> Rick >> >> On 01/03/2018 03:00 PM, Till Mossakowski wrote: >>> Rick, >>> >>> Am 03.01.2018 um 20:34 schrieb rick: >>>> Dear Till, >>>> >>>> Thanks so much for pointing this out. See below. >>>> >>>> On 01/02/2018 05:33 PM, Till Mossakowski wrote: >>>>> Am 02.01.2018 um 16:00 schrieb rick: >>>>>> The DOL authors claim to "handle" sequence markers in HETS using "second >>>>>> order logic" which by conformance with MOF and fUML is outside the scope >>>>>> of DOL. >>>>> second-order logic is not outside the scope of DOL. >>>> I have reviewed the RFP and proposal a few times. I understand scope is >>>> defined 6.1 and 6.5.4 and conformance in 6.5.5 of the RFP. >>>> >>>> 6.5.5 establishes conformance of languages and translations of which >>>> none listed are second order logic. Also Annexes D-H do not include a >>>> conformance statement for second order logic. >>>> >>>> How do you justify your claim that second order logic is not outside the >>>> scope of DOL? >>> see section 2.2 "Conformance of an OMS Language/a Logic with DOL" of the >>> DOL standard at http://www.omg.org/spec/DOL/ : >>> >>> "The logical language aspect of an OMS language is conforming with DOL >>> if each logic corresponding to a profile (including >>> the logic corresponding to the whole logical language aspect) is >>> presented as an institution in the sense of Definition 2 >>> in clause 10 , and there is a mapping from the abstract syntax of the >>> OMS language to signatures and sentences of the >>> institution." >>> >>> For some specific logics, appendices of the DOL standard establish such >>> a conformance, but of course the scope of DOL is not limited to these. >>> >>>> As an aside, I have searched the for a System F comorphism. Would you be >>>> able to provide a pointer to a paper? >>>> >>> I am not aware of institution-theoretic work on system F. >>> >>> Best, Till >>> >>> >>> _________________________________________________________________ >>> To Post: mailto:ontoiop-forum at ovgu.de >>> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >>> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >>> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >>> Community Wiki: http://ontoiop.org >>> >>> >> _________________________________________________________________ >> To Post: mailto:ontoiop-forum at ovgu.de >> Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum >> Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum >> Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ >> Community Wiki: http://ontoiop.org > > > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org > From till at iks.cs.ovgu.de Fri Jan 5 12:00:43 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Fri, 5 Jan 2018 12:00:43 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> <5718c3ca-9bc2-6d64-f91f-82771e4289ea@iks.cs.ovgu.de> Message-ID: Rick, Am 05.01.2018 um 01:18 schrieb rick: > Thanks Till for taking the time to answer my questions. > > I remain unconvinced that an institution that's not in the proposal is > in scope. > > More important though is whether an institution of "second order logic" > exists. yes, it does. See p.415 bottom of my paper T. Mossakowski.? Relating CASL with Other Specification Languages: the Institution Level. Theoretical Computer Science, 286:367-475, 2002. > And whether the required mapping from the abstract syntax of OMS > to the signatures and sentences of "second order logic" exists. right? Hets provides an abstract syntax for second-order logic (as part of the CASL logic). The mapping to the institution is easy. > > Just to be sure, when you say "second order logic" you mean Henkin > Semantics, right? no, in my paper, I used standard semantics, which I need for translating first-order logic with induction to second-order logic (see p.429 of my paper). With Henkin semantics, it is not possible to specify inductive datatypes (like natural numbers, lists, trees etc.) in a monomorphic (i.e. unique up to isomorphism) way. > > I will enjoy reading the reference on type class polymorphism. > > Do you claim the paper contains the institution and the mapping? It > seems not as the paper predates (2004) DOL. > > If not, could you please provide a pointer? > > I briefly scanned the paper. Looks like a great paper. This paper (cited in my previous email) contains an institution for polymorphic higher-order logic, but not for system F. It does not contain any logic translations, except from a technical one linking two variants of the same logic. Best, Till From rick at rickmurphy.org Fri Jan 5 19:55:12 2018 From: rick at rickmurphy.org (rick) Date: Fri, 5 Jan 2018 13:55:12 -0500 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> <5718c3ca-9bc2-6d64-f91f-82771e4289ea@iks.cs.ovgu.de> Message-ID: <8620ed26-face-af0f-37eb-ef630c70f6fe@rickmurphy.org> Danke, Till. On 01/05/2018 06:00 AM, Till Mossakowski wrote: > Rick, > > Am 05.01.2018 um 01:18 schrieb rick: >> Thanks Till for taking the time to answer my questions. >> >> I remain unconvinced that an institution that's not in the proposal is >> in scope. >> >> More important though is whether an institution of "second order logic" >> exists. > yes, it does. See p.415 bottom of my paper > T. Mossakowski. Relating CASL with Other Specification Languages: the > Institution Level. > Theoretical Computer Science, 286:367-475, 2002. Could you please provide the reference to the institution of "second order logic" in the following paper? http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.401.2100&rep=rep1&type=pdf I could not following the pagination from the reference you provided. > >> And whether the required mapping from the abstract syntax of OMS >> to the signatures and sentences of "second order logic" exists. right? > Hets provides an abstract syntax for second-order logic (as part of the > CASL logic). The mapping to the institution is easy. Where is the mapping? >> >> Just to be sure, when you say "second order logic" you mean Henkin >> Semantics, right? > no, in my paper, I used standard semantics, which I need for translating > first-order logic with induction to second-order logic (see p.429 of my > paper). With Henkin semantics, it is not possible to specify inductive > datatypes (like natural numbers, lists, trees etc.) in a monomorphic > (i.e. unique up to isomorphism) way. Thanks. >> I will enjoy reading the reference on type class polymorphism. >> >> Do you claim the paper contains the institution and the mapping? It >> seems not as the paper predates (2004) DOL. >> >> If not, could you please provide a pointer? The institution for "second order logic" is in the "Relating CASL" paper, but not the typeclass polymorphism paper, right? >> I briefly scanned the paper. Looks like a great paper. > This paper (cited in my previous email) contains an institution for > polymorphic higher-order logic, but not for system F. Yes. Understood. I have read a few sections, but need to spend more time. > It does not > contain any logic translations, except from a technical one linking two > variants of the same logic. > Best, Till > > > > _________________________________________________________________ > To Post: mailto:ontoiop-forum at ovgu.de > Message Archives: https://listserv.ovgu.de//pipermail/ontoiop-forum > Config/Unsubscribe: https://listserv.ovgu.de/mailman/listinfo/ontoiop-forum > Community Files (open): http://interop.cim3.net/file/pub/OntoIOp/ > Community Wiki: http://ontoiop.org > From till at iks.cs.ovgu.de Sat Jan 6 12:01:10 2018 From: till at iks.cs.ovgu.de (Till Mossakowski) Date: Sat, 6 Jan 2018 12:01:10 +0100 Subject: [ontoiop-forum] DOL finalisation In-Reply-To: <8620ed26-face-af0f-37eb-ef630c70f6fe@rickmurphy.org> References: <087024B4-E7EC-4DD0-8811-8FCDD45AE4E8@ihmc.us> <91c25e4d-5f81-a218-bd99-f68dc5955b60@rickmurphy.org> <3F44F21A-2DCB-4FED-A358-DD1CB9BC7B3C@ihmc.us> <544a4f22-a6c8-a2de-8208-76d231f78480@iks.cs.ovgu.de> <7289d930-3413-76e9-49e0-6fb37bc6ce40@iks.cs.ovgu.de> <5e79617a-d5b7-3f44-4324-4d3530ba29a1@rickmurphy.org> <5718c3ca-9bc2-6d64-f91f-82771e4289ea@iks.cs.ovgu.de> <8620ed26-face-af0f-37eb-ef630c70f6fe@rickmurphy.org> Message-ID: Am 05.01.2018 um 19:55 schrieb rick: > >>> More important though is whether an institution of "second order logic" >>> exists. >> yes, it does. See p.415 bottom of my paper >> T. Mossakowski. Relating CASL with Other Specification Languages: the >> Institution Level. >> Theoretical Computer Science, 286:367-475, 2002. > Could you please provide the reference to the institution of "second > order logic" in the following paper? > > http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.401.2100&rep=rep1&type=pdf > > I could not following the pagination from the reference you provided. go to http://dx.doi.org/10.1016/S0304-3975(01)00369-3 and download the PDF there >>> And whether the required mapping from the abstract syntax of OMS >>> to the signatures and sentences of "second order logic" exists. right? >> Hets provides an abstract syntax for second-order logic (as part of the >> CASL logic). The mapping to the institution is easy. > Where is the mapping? it has not been written down, but it is easy to do so. > The institution for "second order logic" is in the "Relating CASL" > paper, but not the typeclass polymorphism paper, right? right Best, Till