On the methodology of possible worlds semantics. I: Correspondence theory (Q1115408)

The first part of the paper summarizes work by Johan van Benthem on the relation between systems of modal logic and the possible-worlds structures which interpret them. Sometimes the fit is perfect, as in a case like the system T whose frames are precisely the reflexive frames, and which is characterized by those frames. But often the fit is less than perfect, as in the case of systems which are not characterized by any class of frames. Further, one might get different results by varying the evaluation rules for the modal operator, or even the truth functional connectives. In the second part of the paper the authors claim that it is fruitful to view the semantic structures used in interpreting modal logic as if they were scientific theories which treat the formulae of modal logic as observation sentences.