Complexity of Polyadic Boolean Modal Logics: Model Checking and Satisfiability

Abstract

<p>We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the model checking problem for the resulting logic is PTime-complete. Secondly, we show that the satisfiability problem of polyadic modal logic extended with negation on accessibility relations is ExpTime-complete. Finally, we show that the satisfiability problem of polyadic modal logic with permutations and Boolean operators on accessibility relations is ExpTime-complete, under the assumption that both the number of accessibility relations that can be used and their arities are bounded by a constant. If NExpTime is not contained in ExpTime, then this assumption is necessary, since already the satisfiability problem of modal logic extended with Boolean operators on accessibility relations is NExpTime-hard.</p>