Qualitative probability in a modal setting

Abstract

This chapter presents propositional calculi that are obtained by adding to modal propositional calculi a binary operator ɳ carrying the intuitive meaning of ‘at least as probable as.’ Extending ideas because of Kripke, a semantic modeling suitable for this kind of logic is presented in the chapter. It is shown that filtration theory can be modified in such a way that completeness can be established by using well-known theorem from measurement theory. It is assumed that the reader has some familiarity with Kripke type semantics for modal logic and with filtration theory. The basic logic for PK is that P is for probability and K is for Kripke, and it is axiomatized by the following axiom system. © 1971, Academic Press Inc.