Problems with introduction to model theory
about the "Resource Description Framework (RDF):Concepts and
Abstract Data Model" document, I have comments about one minor part
(viz. 2.3.1 Formal semantics):
| To serve this purpose, certain meanings of RDF statements must
| be defined in a very precise manner
why "certain" and which ones?
>Model-theoretic semantics assumes that a language refers to a
>'world', and describes the minimal conditions that such world must
>satisfy in order to assign an appropriate meaning for every
>expression in the language.
"a language refers to a 'world'" is at least misleading:
- this is rather the assertions in the language which refer to the world.
- the word "a" here could lead the reader to equate one language or
one set of assertion to one world, though the purpose of model theory
is not to tie the assertion to one world but rather to consider all
the possible worlds.
I offer the replacement:
"Model-theoric semantics defines the meaning of expressions in the
language through a mapping (called interpretation) from a language to
worlds. A set of assertions in the language, thus induce constraints
on the acceptable interpretation (called model) of these assertions.
The meaning of an expression is defined with regard to its
interpretation in all the models."
I am sure that this is too technical, maybe reducing this part and
refering to RDF-MT document is an easier alternative.
> A particular world is called an interpretation, so that model
>theory might be better called 'interpretation theory'.
Not accurate: an interpretation is a mapping from the language to the
world. Indeed there can be many interpretations mapping to the same
world.
A model of a set of assertions is an interpretation that satifies all
the assertions in the set (i.e., which maps it to the element of a
distinguished subset of the world for being very general, very often
the set { true }). So model theory is well named.
See: http://lists.w3.org/Archives/Public/www-rdf-comments/2002JulSep/0164.html
Concerns raised with the introduction to concepts of formal semantics.
[GK] Editorial fixes clearly in GK's text.
See: http://lists.w3.org/Archives/Public/www-rdf-comments/2002JulSep/0170.html
[GK] Pat Hayes' response to this comment.
See: http://lists.w3.org/Archives/Public/www-rdf-comments/2002JulSep/0171.html
[GK] Jerome Euzenat response to Pat Hayes.
Revisions, based in part on Pat Hayes' response (thanks Pat!):
1. Replace "certain meanings..." with "formal meanings...".
2. Replace "'world'" with "set of possible 'worlds'", so that the sentence
reads: "Model-theoretic semantics assumes that a language refers to a set of
possible 'worlds', ..."
The wording has been refined through further exchanges with Pat Hayes.
See: http://www.ninebynine.org/wip/RDF-concepts/2002-10-18/rdf-concepts.html
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