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First-Order Resolution Methods for Modal Logics

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Programming Logics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7797))

Abstract

In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution. Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDL-like dynamic modal logics closely related to description logics. Without going into too much detail, we survey different ways of translating modal logics into first-order logic, we explore different ways of using first-order resolution theorem provers to solve a range of reasoning problems for modal logics, and we discuss a variety of results which have been obtained in the setting of first-order resolution.

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Authors and Affiliations

  1. The University of Manchester, UK

    Renate A. Schmidt

  2. University of Liverpool, UK

    Ullrich Hustadt

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  1. Renate A. Schmidt
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  1. University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

  2. Max-Planck-Institut für Informatik, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

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Schmidt, R.A., Hustadt, U. (2013). First-Order Resolution Methods for Modal Logics. In: Voronkov, A., Weidenbach, C. (eds) Programming Logics. Lecture Notes in Computer Science, vol 7797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37651-1_15

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