Tableaux and Model Checking for Memory Logics

Memory logics are modal logics whose semantics is specified in terms of relational models enriched with additional data structure to represent memory. The logical language is then extended with a collection of operations to access and modify the data structure. In this paper we study their satisfiability and the model checking problems. We first give sound and complete tableaux calculi for the memory logic ML(©k ,©r ,©e ) (the basic modal language extended with the operator©r used to memorize a state, the operator ©e used to wipe out the memory, and the operator ©k used to check if the current point of evaluation is memorized) and some of its sublanguages. As the satisfiability problem of ML(©k ,©r ,©e ) is undecidable, the tableau calculus we present is non terminating. Hence, we furthermore study a variation that ensures termination, at the expense of completeness, and we use model checking to ensure soundness. Secondly, we show that the model checking problem is PSpace-complete.