[ontoiop-forum] [ontolog-forum] Re: DOL finalisation

[rick]

Till, Pat & All:
On 12/21/2017 06:20 PM, Till Mossakowski wrote:
> Dear Pat,
> 
> the expressivity of CL is more precisely captured as "first-order logic
> with induction", which recently has gained interest in the theorem
> proving community [1].

TIP noticeably uses polymorphism and higher order functions. No surprise
from Chalmers.

I have not found any evidence of specific tests on Lw-1,w rather
parameterized lists and similar functional programming constructs.

DOL's MOF and fUML conformance rather than UML Templates precludes
claims of second order capabilities at least in the broad sense of
Girard-Reynolds.

> The latter can be embedded both into second-order
> logic and into infinitary first-order logic.

Classification should be on the smallest capabilities.

> For me, infinitary
> first-order logic is much worse to handle than second-order logic: due
> to the infinitary nature, there won't be any theorem provers, even with
> your restriction to axioms.

This is significant.

I understand this to mean there are no known provers of Lw-1,w. In order
to "handle" Lw-1,w, a higher order prover is required.

But as above DOL's conformance with MOF & fUML do not support second
order capabilities.

That's a problem.

Of course handling is different than classification.

> Therefore, in our graph, we only show the
> connection to second-order logic, which has theorem proving support
> (take any higher-order prover like Leo, Satallax or Isabelle).

But its outside the standard at least by Girard-Reynolds criteria. This
needs to be addressed.

> Best, Till
> 
> [1] Koen Claessen, Moa Johansson, Dan Rosén, Nicholas Smallbone: TIP:
> Tons of Inductive Problems. CICM 2015: 333-337
> http://www.cse.chalmers.se/~jomoa/papers/cicm15-TIP.pdf
> https://tip-org.github.io/
> 
> Am 20.12.2017 um 23:32 schrieb Pat Hayes:
>> 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 <sowa at bestweb.net> 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
>>> <dol.jpg>
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>>
> 
> 
>