Re: truth/falsity of sentences in first-order logic


H. J. Sander Bruggink wrote:
David C. Ullrich wrote:


An interpretation I for a language consists of a set S, relations
on M, one for each predicate in the language, etc. Given a
sentence w and an interpretation I, w is either true or false
in I. Then by definition a _model_ of w is an interpretation of
the language in which w turns out to be true.

I have never heard of this usage of the word

You have also not heard of the words (or at least didn't know the
meanings of) "represent" and (vs.) "express", despite their being used
by Raymnd Smullyan, one of the most prolific, well-read, and respected
authors on the subject, so why should there be any significance to your
not having heard of a particular term or usage?

C-B


interpretation.
What you call interpretation, I call model. Of course, a
model *of* w is a model in which w is true.

Apparently there exist some different, slightly incompatible,
definitions of these notions.

groente
-- Sander

.

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