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Clausal Resolution for Modal Logics of Confluence

  • Cláudia Nalon
  • João Marcos
  • Clare Dixon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)

Abstract

We present a clausal resolution-based method for normal multimodal logics of confluence, whose Kripke semantics are based on frames characterised by appropriate instances of the Church-Rosser property. Here we restrict attention to eight families of such logics. We show how the inference rules related to the normal logics of confluence can be systematically obtained from the parametrised axioms that characterise such systems. We discuss soundness, completeness, and termination of the method. In particular, completeness can be modularly proved by showing that the conclusions of each newly added inference rule ensures that the corresponding conditions on frames hold. Some examples are given in order to illustrate the use of the method.

Keywords

normal modal logics combined logics resolution method 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Cláudia Nalon
    • 1
  • João Marcos
    • 2
  • Clare Dixon
    • 3
  1. 1.Departament of Computer ScienceUniversity of BrasíliaBrasíliaBrazil
  2. 2.LoLITA and Dept. of Informatics and Applied MathematicsUFRNBrazil
  3. 3.Department of Computer ScienceUniversity of LiverpoolLiverpoolUnited Kingdom

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