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Re: [ontolog-forum] formal systems, common logic and lbase

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 25 Nov 2007 20:21:19 -0600
Message-id: <F2B2D177-3018-4628-A7F6-C11E5C044AFB@xxxxxxxx>
> Pat Hayes wrote:
>>> Hi Pat and all
>>> remind me please whatis CL for? what does it add to FOL or  
>>> previous existing things?
>> If FOL were a single formal language with a single, uniformly  
>> accepted, universally used, syntax, then CL would add nothing. But  
>> it isn't. Almost everyone who writes about FOL or uses it, uses a  
>> slightly different notation. Everyone knows they are all  
>> equivalent, and logically proficient users can switch (or even  
>> muddle) notational conventions with impunity, and often do so; but  
>> for information exchange between programs this is a nightmare. The  
>> point of CL (and earlier, of KIF) was to provide a single standard  
>> interchange notation for first-order logic.
> But as a model of a formal system, this approach falls short of what's
> already been defined by information flow, the information flow  
> framework
> and category theory.    (01)

Well, that's hardly surprising, given that CL never attempts to be a  
"model of a formal system".  Once again, CL defines a broad class of  
(mostly first-order) languages + model theories (what I like to think  
of as logics) and provides rigorous, standardized mechanisms for  
translating information between them.    (02)

>> The original intention was to adopt a single surface syntax upon  
>> which everyone would agree: but when it became apparent that even  
>> the ten or so members of the working group could not agree, this  
>> idea was abandoned, and instead a system of a common 'abstract  
>> syntax' allowing for many different 'surface syntaxes' (aka  
>> dialects) was adopted. If you check the conformance conditions in  
>> the ISO spec, they require that each dialect specification provide  
>> a mechanizable process to parse that dialect into the abstract  
>> syntax categories.
> But thats only part of the answer    (03)

To *what question*?  CL a very complete answer to the question *we*  
set out to answer.  But there are tons of other questions and  
challenges in knowledge engineering (vagueness, incomplete  
information, poorly axiomatized knowledge bases, social/cultural  
presuppositions, etc etc) that CL does not address.  It strikes me  
that your remarks are all about *those*.    (04)

>> This should have been a simple exercise, but standardization  
>> processes tend to run very slowly and often in circles, so this  
>> limited goal took several years. Along the way, some of us (mostly  
>> Chris Menzel and myself) noticed that traditional textbook  
>> formulations of FOL contained a number of restrictions which were  
>> not in fact strictly necessary, and almost as a exercise in pure  
>> mathematics[1] set out out to see how far we could go in removing  
>> them, and what effect this might have on the resulting logic. This  
>> involved using a very neat mathematical trick which Chris showed to  
>> me, of how to generalize the traditional FO model theory. Shortly  
>> afterwards I became involved in the W3C RDF and OWL standardization  
>> efforts, and realized that this same mathematical trick could be  
>> applied to RDF and OWL, and would solve a number of small,  
>> technical but stubborn problems that were plaguing the W3C working  
>> groups, making RDF somewhat more intuitive (and simpler) than it  
>> would otherwise be. So the RDF, and then the OWL, specs were  
>> written using this same trick in their model theories, making the  
>> entire family of languages (RDF, OWL, CL and now IKL) semantically  
>> compatible in a rather strong sense. So this is another achievement  
>> of the CL work, realized in CL and used very centrally in IKL and  
>> OWL/RDF. But this is indeed rather a technical matter: it might be  
>> compared to having an engine which uses a new fuel additive, where  
>> the user of the logic is like the driver of the automobile. The  
>> driver doesn't need to know how its done exactly, but the engine  
>> responds better.
> Is there a paper available on this?    (05)

Several -- The RDF model theory (http://www.w3.org/TR/rdf-mt) and the  
OWL model theory (specifcally the "RDF-Compatible Model Theoretic  
Semantics": http://www.w3.org/TR/owl-semantics/rdfs.html) for  
starters.  Hopefully, the "freely released" status of the CL spec will  
be approved soon.    (06)

> So far it just sounds like abstraction which is ok on the way up,  
> but leave you hanging on the way down.    (07)

Well, uh, ok...    (08)

-chris    (09)

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