[ontoiop-forum] DOL finalisation

[Pat Hayes]

> On Dec 20, 2017, at 4:00 PM, rick <rick at rickmurphy.org> wrote:
> 
> Maybe Pat can show the derivations to avoid further misunderstanding.

The mapping is pretty obvious once it is pointed out. 

(forall (…x)(FOO …x))

maps to (and has exactly the same semantic truth conditions as)

(and 
	(forall (x)(FOO x))
	(forall (x1 x2)(FOO x1 x2))
	(forall (x1 x2 x3)(FOO x1 x2 x3))
…)

I should have said, if one restricts this so that sequence markers occur only *universally quantified* on the LHS of sequents, then it is first-order. This covers every actual use case that any of the CL developers have ever seen.

Pat

> 
> --
> 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 <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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