Postdiction Problems in Dynamic Logic

Abstract

We present a framework for backward and forward temporal projection that combines dynamic and temporal logic. A propositional dynamic logic for reasoning about actions is extended with temporal modalities; the syntax of this extension differs from the syntax of the converse of programs, previously understood as backwards modalities. An application is carried out to benchmark postdiction examples such as the Stanford Murder Mystery [1] and the Two-Buses Problem [8]. A method for automatically generating frame axioms is used; the axioms so generated are treated as supplementary axioms in the associated proof theory. In future work, we hope to embed this system into a more comprehensive logic for reasoning about actions that enables a unified treatment of the frame, qualification and ramification problems and to work with more ‘scaled-up’ examples.