International Symposium on Logical Foundations of Computer Science

Logical Foundations of Computer Science pp 1-13 | Cite as

Modal Logics with Hard Diamond-Free Fragments

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9537)


We investigate the complexity of modal satisfiability for certain combinations of modal logics. In particular we examine four examples of multimodal logics with dependencies and demonstrate that even if we restrict our inputs to diamond-free formulas (in negation normal form), these logics still have a high complexity. This result illustrates that having D as one or more of the combined logics, as well as the interdependencies among logics can be important sources of complexity even in the absence of diamonds and even when at the same time in our formulas we allow only one propositional variable. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multimodal logics in a general setting.


Modal logic Satisfiability Computational complexity Diamond-free fragments Multi-modal Lower bounds 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The Graduate Center of The City University of New YorkNew YorkUSA

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