An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability

  • Rajeev Goré
  • Florian Widmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)


We give an optimal (exptime), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic. Our main contribution is a sound method to track unfulfilled eventualities “on the fly” which allows us to detect “bad loops” sooner rather than in multiple subsequent passes. We achieve this by propagating and updating the “status” of nodes throughout the underlying graph as soon as is possible. We give sufficient details to enable an easy implementation by others. Preliminary experimental results from our unoptimised OCaml implementation indicate that our algorithm is feasible.


Description Logic Preliminary Experimental Result Transition Frame Propositional Dynamic Logic Negation Normal Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rajeev Goré
    • 1
  • Florian Widmann
    • 2
  1. 1.Logic and Computation GroupThe Australian National UniversityCanberraAustralia
  2. 2.Logic and Computation Group and NICTAThe Australian National UniversityCanberraAustralia

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