Re: Model theory, abstract syntax

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.

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Graham Klyne                    Baltimore Technologies
Strategic Research              Content Security Group
<Graham.Klyne@Baltimore.com>    <http://www.mimesweeper.com>
                                 <http://www.baltimore.com>
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Received on Tuesday, 17 July 2001 03:41:46 UTC