EXPSPACE-Completeness of the Logics K4xS5 and S4xS5 and the Logic of Subset Spaces, Part 2: EXPSPACE-Hardness

Abstract

It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 are NEXPTIME-hard and that the satisfiability problem of the logic SSL of subset spaces is PSPACE-hard. We improve these lower bounds for the complexity of these problems by showing that all three problems are EXPSPACE-hard under logspace reduction. In another paper we show that these problems are in ESPACE. This shows that all three problems are EXPSPACE-complete.