International Conference on Automated Reasoning with Analytic Tableaux and Related Methods

Automated Reasoning with Analytic Tableaux and Related Methods pp 38-53 | Cite as

Modal Tableau Systems with Blocking and Congruence Closure

  • Renate A. Schmidt
  • Uwe Waldmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9323)

Abstract

Our interest in this paper are semantic tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and description logics have these properties and can therefore be decided in this way. This paper integrates congruence closure, which is probably the most powerful and efficient way to realise reasoning with ground equations, into a modal tableau system with equality-based blocking. The system is described for an extension of modal logic K characterised by frames in which the accessibility relation is transitive and every world has a distinct immediate predecessor. We show the system is sound and complete, and discuss how various forms of blocking such as ancestor blocking can be realised in this setting. Though the investigation is focussed on a particular modal logic, the modal logic was chosen to show the most salient ideas and techniques for the results to be generalised to other tableau calculi and other logics.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Renate A. Schmidt
    • 1
  • Uwe Waldmann
    • 2
  1. 1.School of Computer ScienceThe University of ManchesterManchesterUK
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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