The satisfiability problems of K4×S5, S4×S5, and subset-space logic are proven EXPSPACE-hard, giving EXPSPACE-completeness with the companion upper bounds.
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EXPSPACE-Completeness of the Logics K4xS5 and S4xS5 and the Logic of Subset Spaces, Part 2: EXPSPACE-Hardness
The satisfiability problems of K4×S5, S4×S5, and subset-space logic are proven EXPSPACE-hard, giving EXPSPACE-completeness with the companion upper bounds.