Logica Universalis

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

Quantified Multimodal Logics in Simple Type Theory

  • Christoph BenzmüllerEmail author
  • Lawrence C. Paulson


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 


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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