From worlds to probabilities: A probabilistic semantics for modal logic (Q2366248)

The author presents a semantics for modal logic in which the role played by possible worlds in standard treatments is played by probability functions (Popper functions). Using an accessibility relation between probability functions, and requiring that the value of \(\diamondsuit A\) conditional on \(B\) for a given probability function be less than the value of \(A\) conditional on \(B\) for all accessible probability functions the author is able to prove soundness for T(M), B, S4 and S5. The use of degenerate functions whose values are 0 or 1 enables standard completeness results to apply to the author's semantics.