Pat, (01)
One of the important points that Dunn emphasized is that the language
in which the laws and facts are stated is a pure FOL without any
modal operators. He assumed a plain vanilla GOFOL, but an extended
version of FOL such as Common Logic would be equally appropriate.
I explicitly used the term "model set", which suggested that I was
assuming the same kind of FOL that Hintikka assumed for his model
sets. But the method is the same for any version or subset of FOL. (02)
In Section 4 of the worlds.pdf paper (which you said you read), I
was very explicit about what I meant by the word 'proposition'.
I defined a proposition as an equivalence class of sentences
under a "meaning-preserving translation" (MPT), which I also
defined explicitly. (We had talked about that idea a few years
ago in connection with the IKRIS project.) The simplest example
of a "meaning-preserving translation" is the identity, which
implies that each syntactically distinct sentence states a
distinct proposition, but any other MPT would do as well. (03)
In any case, for the purpose of mapping Kripke's semantics to Dunn's,
the choice of MPT is irrelevant, since you get the same collection
of theorems and proofs with any choice discussed in that paper.
For example, you get the same theorems whether you call p&q the
"same" proposition as q&p or a "different" proposition. (04)
JFS>> Given a Kripke model (K,R,Phi) and for each world w in K,
>> let M (a Hintikka-style model set) be the set of propositions
>> true in w. (05)
PH> Whoa. That set is not yet fully defined. What do you mean by
> 'proposition'? If you mean 'sentence', you have to say what formal
> language your sentences are written in, because this is not
> specified by a Kripke (or any other model-theoretic) structure. If
> you mean something other than 'sentence', I am all ears to hear
> what it is that you do mean. (06)
Take your pick. Just take the modal language you choose for the Kripke
semantics (some version of FOL with the addition of modal operators),
then use the base language without the modal operators to state the
laws and facts for Dunn's semantics. (07)
John (08)
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