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A General Tableau Method for Deciding Description Logics, Modal Logics and Related First-Order Fragments

  • Renate A. Schmidt
  • Dmitry Tishkovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5195)

Abstract

This paper presents a general method for proving termination of tableaux-based procedures for modal-type logics and related first-order fragments. The method is based on connections between filtration arguments and tableau blocking techniques. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be applied to many well-known description and modal logics. The class includes traditional modal logics such as S4 and modal logics with the universal modality, as well as description logics such as \(\mathcal{ALC}\) with nominals and general TBoxes. Also contained in the class are harder and less well-studied modal logics with complex modalities and description logics with complex role operators such as Boolean modal logic, and the description logic \(\mathcal{ALBO}\). In addition, the techniques allow us to specify tableau-based decision procedures for related solvable fragments of first-order logic, including the two-variable fragment of first-order logic.

Keywords

Modal Logic Decision Procedure Description Logic Closure Operator Open Branch 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Renate A. Schmidt
    • 1
  • Dmitry Tishkovsky
    • 1
  1. 1.School of Computer ScienceThe University of Manchester 

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