Using connection method in modal logics: Some advantages

Abstract

For mechanizing modal logics, it is possible to distinguish the approach by translation and the direct approach. In our previous works, we advocate the use of translations to find a proof with a prover dedicated to the target logics but we introduced the notion of backward translation in order to present the proofs in the source logics. In this paper, we show that the connection method is well suited for the backward translation of proofs when first-order serial modal logics are involved. We use Wallen's matrix method for modal logics (extending Bibel's connection method) and Petermann's connection method for order-sorted logics with equational theories. We state that it is possible to build from a connection proof in the target logic a connection proof in the source logic in polynomial time with respect to the size of the proof in the target logic. Such a translation provides interesting insights to compare the approach by translation and the direct approach.KeywordsModal LogicClassical LogicAtomic FormulaPredicate SymbolAutomate DeductionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.