Complexity of modal logic

Publisher Summary This chapter introduces the field of computational complexity in modal logic and provides some fundamental answers. The basic modal language, when interpreted over relational models, can be regarded as a decidable fragment of classical logic. The chapter explores the computational complexity of determining validity, or of performing tasks like model checking. The parameters that affect modal complexity results are discussed. The chapter deals with modal systems whose class of models is definable in first-order logic expanded with a least fixed point operator (FO(LFP)), which implies that membership is decidable in polynomial time. The actual algorithms for deciding the satisfiability problem under constraints and the local satisfiability problem for a number of typical cases are reviewed. Hintikka set elimination is an algorithm, which constructs the model whose idea comes straight from the proof of the truth lemma. A globally satisfiable constraint, which, when satisfied, forces a branch in the model containing an exponential number of different Hintikka set is created.