A One-Pass Tree-Shaped Tableau for LTL+Past

Linear Temporal Logic (LTL) is a de-facto standard formalism for expressing properties of systems and temporal constraints in formal verification, artificial intelligence, and other areas of computer science. The problem of LTL satisfiability is thus prominently important to check the consistency of these temporal specifications. Although adding past operators to LTL does not increase its expressive power, recently the interest for explicitly handling the past in temporal logics has increased because of the clarity and succinctness that those operators provide. In this work, a recently proposed one-pass tree-shaped tableau system for LTL is extended to support past operators. The modularity of the required changes provides evidence for the claimed ease of extensibility of this tableau system.