The aim of this work is to define a resolution method for the modal logic S5. Wefirst propose a conjunctive normal form (S5-CNF) which is mainly based on using labelsreferring to semantic worlds. In a sense, S5-CNF can be seen as a generalization of theconjunctive normal form in propositional logic by using in the clause structure the modalconnective of necessity and labels. We show that every S5 formula can be transformedinto an S5-CNF formula using a linear encoding. Then, in order to show the suitabilityof our normal form, we describe a modeling of the problem of graph coloring. Finally, weintroduce a simple resolution method for S5, composed of three deductive rules, and weshow that it is sound and complete. Our deductive rules can be seen as adaptations ofRobinson’s resolution rule to the possible-worlds semantics.
α-Quasi-Lock Semantic Resolution Method Based on Lattice-Valued Logic
