Resolution for Weak Modal Logics
Résumé
We define modal resolution systems for the propositional weak modal logics C, CD and CT. These systems are based on the Enjalbert and Farinas Del Cerro'ss modal resolution systems with minor modifications. Roughly speaking, the axiom \Sigma(<> \perp, C) ->
\perp is added if each disjunct of the clause C is a necessity formula (\perp denotes the empty clause) and the simplification rule (<> \perp \approx \perp) is deleted. Non clausal resolution systems are also presented for these weak modal logics. They are variants of Abadi and Manna's non clausal resolution systems. The new resolution systems are proved to be sound and refutationnally complete for these logics. The completeness proofs are inspired by the completeness proofs of the systems for normal mo dal logics with adequate modifications.
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