Monadic Σ11 and Modal Logic with Quantified Binary Relations

Authors:
Lauri Hella;Antti Kuusisto
Affiliations:
Department of Mathematics and Statistics, University of Tampere, Tampere, Finland;Department of Mathematics and Statistics, University of Tampere, Tampere, Finland
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2010

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Abstract

We investigate the expressive power of a range of modal logics extended with second-order prenex quantification of binary and unary relations. Our principal result is that @S"1^1(BML^=), i.e., Boolean modal logic extended with the identity modality and existential prenex quantification of binary and unary relations, translates into monadic@S"1^1. We also briefly discuss a variety of decidability results in multimodal logic implied by our result.