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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: paola.dimaio@xxxxxxxxx
Date: Sat, 24 Jan 2009 22:18:03 +0700
Message-id: <c09b00eb0901240718t7dd2406fw9066a5919157ffbd@xxxxxxxxxxxxxx>

> and yes, category theory relies on logic

called categorical logic perhaps?

4, A little piece of categorical logic
One of the major achievements of category theory in mathematical logic and in computer science, has been a uni ed treatment of semantics for all kinds of logical systems and term calculi which are the basis for programming languages. One can say that mathematical logic, seen as the study of classical fi rst order logic, rst started to be a real subject with the discovery, by Godel, of the completeness theorem for set-theoretic interpretations: a sentence ' is provable if and only if ' is true in all possible interpretations. This unites the two approaches to logic: proof theory and model theory, makes logic accessible for mathematical methods and enables one to give nice and elegant proofs of proof theoretical properties by model theory (for example, the Beth and Craig de nability and interpolation theorems).

Jaap van Oosten
Department of Mathematics
Utrecht University
The Netherlands
Revised, July 2002



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