Focus games for satisfiability and completeness of temporal logic

Abstract

Introduce a simple game-theoretic approach to satisfiability checking of temporal logic, for LTL (linear time logic) and CTL (computation tree logic), which has the same complexity as using automata. The mechanisms involved are both explicit and transparent, and underpin a novel approach to developing complete axiom systems for temporal logic. The axiom systems are naturally factored into what happens locally and what happens in the limit. The completeness proofs utilise the game-theoretic construction for satisfiability: if a finite set of formulas is consistent then there is a winning strategy (and therefore construction of an explicit model is avoided).