Affiliation:
1. Department of Computer Science, School of Technology, Reykjavik University, Menntavegur 1, 102 Reykjavik, Iceland
Abstract
Abstract
We investigate the complexity of modal satisfiability for a family of multi-modal logics with interdependencies among the modalities. In particular, we examine four characteristic multi-modal logics with dependencies and demonstrate that, even if we restrict the formulae to be diamond-free and to have only one propositional variable, these logics still have a high complexity. This result identifies and isolates two sources of complexity: the presence of axiom $D$ for some of the modalities and certain modal interdependencies. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multi-modal logics in a general setting.
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science