On the Complexity of Elementary Modal Logics

Edith Hemaspaandra; Henning Schnoor

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arXiv · 0802.1884

On the Complexity of Elementary Modal Logics

Edith Hemaspaandra·Henning Schnoor

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Abstract

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide class of relevant logics: Many important subclasses of modal logics can be obtained by restricting the allowed models with first-order Horn formulas. We show that the satisfiability problem for each of these logics is either NP-complete or PSPACE-hard, and exhibit a simple classification criterion. Further, we prove matching PSPACE upper bounds for many of the PSPACE-hard logics.

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Edith Hemaspaandra, Henning Schnoor. 2008-02-13. On the Complexity of Elementary Modal Logics. https://arxiv.org/abs/0802.1884

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