Combining and automating classical and non-classical logics in classical higher-order logics

Article

Abstract

Numerous classical and non-classical logics can be elegantly embedded in Church’s simple type theory, also known as classical higher-order logic. Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Off-the-shelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about embedded logics and logics combinations. In this article we focus on combinations of (quantified) epistemic and doxastic logics and study their application for modeling and automating the reasoning of rational agents. We present illustrating example problems and report on experiments with off-the-shelf higher-order automated theorem provers.

Keywords

Classical and non-classical logics Quantified multimodal logics Logic combinations Classical higher-order logic Semantic embeddings Knowledge representation Higher-order automated theorem proving 

Mathematics Subject Classifications (2010)

03B62 03B42 03B44 03B45 03B35 03B20 03B15 68T27 68T30 68T15 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Articulate SoftwareAngwinUSA

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