Subject: Re: SUO: Model theory for modal logics From: Chris Menzel Date: Sat, 9 Aug 2003 19:49:35 -0500 To: IEEE Standard Upper Ontology List CC: Stefano Borgo , Inquiry On Sat, Aug 09, 2003 at 02:07:51PM -0400, John Sowa wrote: >> PS to Chris Menzel: Do you wish to continue this discussion, >> or are you now satisfied that Dunn's semantics is a signifcant >> improvement over Kripke's? It is an improvement at least in the sense that it generalizes Kripke's semantics and does a bit of work towards spelling out a richer notion of laws. Extrapolating (and, guessing! a bit from the quick summary above (I confess to my shame that I've never studied Dunn's semantics carefully), the facts of a world, in Kripke's terms, are jointly just the set of sentences true at an index. And a Kripke model is just essentially the case where L is the set of logical truths and is fixed across all worlds. So yeah, Dunn's semantics is somewhat richer -- though Kripke's could obviously be enhanced to be formally equivalent. I think you see a great deal of significance in the fact that Dunn doesn't have "possible worlds". But he does. They are just the law/fact pairs. But they came to us "fully formed"; to be true at a world is just to be a fact there. An explicit set of indices would be superfluous. Kripke by contrast starts with indices -- heuristically, "possible worlds" -- and uses them to define truth. On this approach, introducing sets of facts would be superfluous. The approaches (ignoring the fact that Dunn's is more general) are essentially equivalent. But every *signficant* philosophical issue that arises for Kripke also arises for Dunn. In my view, you take *both* model theories too literally. Both give rise to hard philosophical problems of one sort if taken too literally (notably, the ontological status of "nonactual" individuals that exist at other worlds) and of another sort if not (notably, how the alleged semantics provides genuine truth conditions for modal statements). Bottom line: (i) Formally, Dunn's semantics is a robust and intuitively well-grounded generalization of Kripke semantics. (ii) I believe you vastly oversell its differences from and its philosophical and practical advantages over Kripke's, particular for KR applications. Chris Menzel