Model checking
Modal logic
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
TARK '01 Proceedings of the 8th conference on Theoretical aspects of rationality and knowledge
Logics of communication and change
Information and Computation
Expressive Power and Decidability for Memory Logics
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Completeness Results for Memory Logics
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Dynamic Epistemic Logic
Basic model theory for memory logics
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
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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 $\mathcal {ML}$(***, ***, ***) (the basic modal language extended with the operator *** used to memorize a state, the operator *** used to wipe out the memory, and the operator *** used to check if the current point of evaluation is memorized) and some of its sublanguages. As the satisfiability problem of $\mathcal {ML}$(***, ***, ***) 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.