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Re: [ontolog-forum] Sorted for ∃s and whizz (was Re: type free logic an

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sat, 20 Aug 2011 02:18:54 -0400
Message-id: <4E4F51CE.2080509@xxxxxxxxxxx>
On 8/20/2011 1:30 AM, Pat Hayes wrote:
> This was several years ago, so is based upon recollection.
> Others who were involved may remember other details.    (01)

I agree with Pat about the basic issues we discussed.    (02)

We decided that most (perhaps all) versions of sorted FOL could be
translated to Common Logic with restricted quantifiers.    (03)

For each sort S and any x, specify a monadic relation S such that
(S x) is true iff x is an element of sort S.    (04)

Then use those sort relations to restrict the quantifiers; e.g.,    (05)

   (forall ((x S1) (y S2)) (exists (z S3)) (f x y z))))    (06)

> In order to be fully general, it would have to provide a general
> notation for defining the sorts and the sort constraints upon the
> arguments of all sorted relations, and relationships that hold
> between sorts. The major problem is that there is no single notion
> of a sorted logic, and no rational way to choose between the many
> alternatives.    (07)

That's true.  But if the sorted logic has some systematic way of
specifying sorts, it should be possible to map that method into
a way of defining corresponding CL relations.  If sort S1 includes
sort S2, then for any x, the relation (S2 x) would imply (S1 x).    (08)

The design goal for Common Logic is to provide an abstract syntax
with a very general semantics (model theory) that can support
a very wide range of logics that are used in many different
branches of computer science.    (09)

That would enable different logics to be mapped to CL in a way
that preserves the truth conditions of the original languages.
Then multiple knowledge sources could be related to one another
by means of the CL semantics as their common foundation.    (010)

John    (011)

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