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A Resolution Method for Modal Logic S5

11 pagesPublished: December 18, 2015


The aim of this work is to define a resolution method for the modal logic S5. We
first propose a conjunctive normal form (S5-CNF) which is mainly based on using labels
referring to semantic worlds. In a sense, S5-CNF can be seen as a generalization of the
conjunctive normal form in propositional logic by using in the clause structure the modal
connective of necessity and labels. We show that every S5 formula can be transformed
into an S5-CNF formula using a linear encoding. Then, in order to show the suitability
of our normal form, we describe a modeling of the problem of graph coloring. Finally, we
introduce a simple resolution method for S5, composed of three deductive rules, and we
show that it is sound and complete. Our deductive rules can be seen as adaptations of
Robinson’s resolution rule to the possible-worlds semantics.

Keyphrases: conjunctive normal form, modal logic S5, resolution method

In: Georg Gottlob, Geoff Sutcliffe and Andrei Voronkov (editors). GCAI 2015. Global Conference on Artificial Intelligence, vol 36, pages 252--262

BibTeX entry
  author    = {Yakoub Salhi and Michael Sioutis},
  title     = {A Resolution Method for Modal Logic S5},
  booktitle = {GCAI 2015. Global Conference on Artificial Intelligence},
  editor    = {Georg Gottlob and Geoff Sutcliffe and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {36},
  pages     = {252--262},
  year      = {2015},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/1zgr}}
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