Logica Universalis

, Volume 7, Issue 1, pp 7–20 | Cite as

Quantified Multimodal Logics in Simple Type Theory

Article

Abstract

We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.

Mathematics Subject Classification

Primary 03B45 Secondary 03B15 

Keywords

Quantified multimodal logics simple type theory semantic embedding proof automation 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceFree University BerlinBerlinGermany
  2. 2.Computer LaboratoryUniversity of CambridgeCambridgeUK

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