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

[Till Mossakowski]

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

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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