A universally defined undecidable unimodal logic

Authors:
Edith Hemaspaandra;Henning Schnoor
Affiliations:
Department of Computer Science, Rochester Institute of Technology, Rochester, NY;Institute for Computer Science, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
Venue:
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Year:
2011

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Abstract

Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is an undecidable unimodal logic that can be obtained by restricting the allowed models with an equality-free first-order formula in which only universal quantifiers appear.