- From: Graham Klyne <Graham.Klyne@Baltimore.com>
- Date: Tue, 17 Jul 2001 08:40:57 +0100
- To: Aaron Swartz <me@aaronsw.com>
- Cc: rdf core <w3c-rdfcore-wg@w3.org>
At 09:08 PM 7/16/01 +0100, I wrote: >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. On reflection, that's not quite right... I think it's closer to say that an abstract syntax captures the essential forms of a language, without necessarily providing detailed rules for recognition of wffs. This group has decided to use N-triples as the basis for its abstract syntax, in which case it does define a specific form of wff, but I don't think this is necessarily true of all abstract syntax. Although I've often heard the term used, and think I have a feel for what it means, I don't believe I've ever seen a specific definition of "abstract syntax". #g -- >- 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. ------------------------------------------------------------ Graham Klyne Baltimore Technologies Strategic Research Content Security Group <Graham.Klyne@Baltimore.com> <http://www.mimesweeper.com> <http://www.baltimore.com> ------------------------------------------------------------
Received on Tuesday, 17 July 2001 03:41:46 UTC