Complexity of the variable-free fragments of non-normal modal logics (extended version)

Abstract

We show that the satisfiability problem for the variable-free fragment of every modal logic containing classical propositional logic and contained in the weak Grzegorczyk logic is NP-hard. In particular, the variable-free fragments of the non-normal modal logics E, EM, EN, and EMN are coNP-complete.

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