A Resolution Method for Modal Logic S5
نویسندگان
چکیده
In this work, we aim 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 including the modal connective of necessity and labels in the clause structure. 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 graph coloring problem. 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.
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