- From: Graham Klyne <Graham.Klyne@Baltimore.com>
- Date: Mon, 16 Jul 2001 21:08:07 +0100
- To: Aaron Swartz <me@aaronsw.com>
- Cc: rdf core <w3c-rdfcore-wg@w3.org>

At 01:56 PM 7/16/01 -0500, Aaron Swartz wrote: >I'm unclear on the difference between model theory and abstract syntax. >Can someone clarify? I'll take a shot; I guess the real formal systems folks will put me right... I think they are clearly different, but related, issues. - Abstract syntax defines a language (i.e. a set of well formed formulae, or wff) in terms of some set of terminal symbols. Given a formula, it allows us to say whether or not it is a well formed sentence (instance) of the language. It also provides us with an annotation for the the structure of a wff that can be used as a reference point for defining semantics for the various allowed forms. In summary: abstract syntax is primarily about forms. - Model theory defines semantics for the various allowed forms, by telling us how they can be interpreted in terms of some universe of discourse. The elements of the language refer to members of the universe, and statements can be interpreted to be true or false of of such a universe. An "interpretation" of a formula is an assignment of values from the domain of discourse to symbols in the formula, such that the formula can be said to true or false. A "model" of a formula is an interpretation for which the formula evaluates to true. Hence "model theory". - A third related concept is "proof theory": a deductive apparatus based on syntactic transformations of wffs that preserves truth. #g ------------------------------------------------------------ Graham Klyne Baltimore Technologies Strategic Research Content Security Group <Graham.Klyne@Baltimore.com> <http://www.mimesweeper.com> <http://www.baltimore.com> ------------------------------------------------------------

Received on Monday, 16 July 2001 16:11:15 UTC