On Sep 15, 2008, at 11:12 PM, John F. Sowa wrote: (01)
> Pat,
>
> PH> But now we get back to my earlier objection. Propositions, in
>> this sense, might as well be sentences: a set of propositions is
>> just a set of sentences with an equivalence defined on it.
>
> I agree that the additional equivalence relation does not make
> any critical difference. In my note to Chris, I agreed that it
> would have been better to use the word 'sentence' since it would
> have avoided that distracting point.
>
> PH> A Kripke structure does not itself define a particular language
>> to interpret against it, so your mapping from Kripke to Dunn
>> seems to be under-defined.
>
> It certainly doesn't determine the syntax, but it definitely
> determines semantics. That's the whole point of a model. (02)
Of course, but that is beside the point. Your construction takes a
Kripke structure - no mention there of a language or a signature - and
begins by mentioning a set of [sentences] .. And my point is simply
that no such set is defined by the Kripke structure. You still have
not defined it. Until you do, your construction isn't well-defined.
What is the signature of the language? Does it have binary relations
in it? Etc. . It's not enough to say 'use FOL' or some such reply.
That does not determine a set of sentences. (03)
Pat (04)
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