A Modal-Layered Resolution Calculus for K

  • Cláudia Nalon
  • Ullrich Hustadt
  • Clare Dixon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9323)


Resolution-based provers for multimodal normal logics require pruning of the search space for a proof in order to deal with the inherent intractability of the satisfiability problem for such logics. We present a clausal modal-layered hyper-resolution calculus for the basic multimodal logic, which divides the clause set according to the modal depth at which clauses occur. We show that the calculus is complete for the logics being considered. We also show that the calculus can be combined with other strategies. In particular, we discuss the completeness of combining modal layering and negative resolution. In addition, we present an incompleteness result for modal layering together with ordered resolution.


Automated reasoning normal modal logics resolution method 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Departament of Computer ScienceUniversity of BrasíliaBrasíliaBrazil
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUnited Kingdom

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