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ExpTime Tableaux with Global Caching for Hybrid PDL

  • Linh Anh NguyenEmail author
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Abstract

We present the first direct tableau decision procedure with the ExpTime complexity for HPDL (Hybrid Propositional Dynamic Logic). It checks whether a given ABox (a finite set of assertions) in HPDL is satisfiable. Technically, it combines global caching with checking fulfillment of eventualities and dealing with nominals. Our procedure contains enough details for direct implementation and has been implemented for the TGC2 (Tableaux with Global Caching) system. As HPDL can be used as a description logic for representing and reasoning about terminological knowledge, our procedure is useful for practical applications.

Keywords

Modal logic Propositional dynamic logic Tableau-based decision procedures Global caching Complexity-optimal tableaux 

Notes

Acknowledgements

We would like to thank the anonymous reviewers for many comments and suggestions, which have helped us to improve the paper significantly.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Division of Knowledge and System Engineering for ICT, Faculty of Information TechnologyTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Institute of InformaticsUniversity of WarsawWarsawPoland

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