Generalized Modal Satisfiability

It is well-known that modal satisfiability is PSPACE-complete [Lad77]. However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACEcomplete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Edith Hemaspaandra, Henning Schnoor, Ilka Schnoor
• Keywords: CORR 2008, Education, Infinite Number, Modal Satisfiability, Propositional Operators