Algorithms for Relevant Logic

Abstract

The classical analytic tableau method has been extended successfully to modal logics (see e.g. Fitting 1983; Fitting 1993; Goré 1992) and also to relevant and paraconsistent logics Bloesch 1993a; Bloesch 1993b. The classical connection method has been extended to modal and intuitionistic logics Wallen 1990, and the purpose of this paper is to investigate whether a similar adaptation to relevant logic is possible. A hybrid method is developed for B⁺, with a specific solution to the “multiplicity problem”, as in the technique of modal semantic diagrams introduced in Hughes and Cresswell 1968. Proofs of soundness and completeness are also given.

The authors thank Prof. Jean-Paul van Bendegem, editor of “Logique et Analyse”, for permission to reprint “Algorithms for Relevant Logic” which was published in Logique et Analyse, 150-151-152 Special issue dedicated to the memory of Léo Apostel, pp.329–346, 1995.

We are grateful to the research team of the Automated Reasoning Project of the Australian National University (Canberra) for their invaluable help. We are very grateful to Dr. Bloesch for granting us the permission to quote his Ph.D. thesis. We received substantial help from Dr. Goré and Dr. Lugardon. We also thank Dr. van der Does and Dr. Herzig. This work was supported by a grant of the F.N.R.S. (project 8.4536.94) and an earlier version was discussed at the Centenary Conference of the Lvov-Warsaw School of Logic (Nov. 1995). We express our gratitude to our sponsors and our hosts, and to Dr. Gailly and Mrs Gailly Goffaux for several corrections. We owe the topic of this paper to the late Prof. Sylvan.