On May 11, 2008, at 4:05 PM, Pat Hayes wrote:
The papers I've seen on possible worlds seem to cover a wide variety of other topics like, necessity, possibility, etc ...
Yes. Modal logics require a single interpretation to encompass many 'worlds' at once, with
relations on them. Hence the term 'possible world' comes up rather often. Each of these
defines a single interpretation in the conventional sense, if you work through the semantics: each one determines the truth of all non-modal sentences of the language.
Some of the modal ones as well (as Pat knows) if the accessibility relation is reflexive. Of course, the idea is not so much to consider each "world" individually but all of them together: all the worlds jointly determine the truth values of all modal and nonmodal sentences alike at each world.