Pat, (01)
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. (02)
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. (03)
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. (04)
It certainly doesn't determine the syntax, but it definitely
determines semantics. That's the whole point of a model.
There are two points to consider: (05)
1. The two basic modal operators, say Necs and Psbl,
where Psbl is defined as ~Necs~. (06)
2. The nonmodal base, which could be propositional logic
or some version of FOL. (07)
The two operators in #1 (and the axioms that define them)
are completely determined by the accessibility relation.
For generality, the nonmodal base could be a very general
version of FOL, such as Common Logic, which includes a
very large number of other versions as subsets. That
choice would be sufficient to determine a Dunn model
by the construction I suggested earlier. (08)
John (09)
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