In Katalin Bimbó (ed.), Relevance Logics and other Tools for Reasoning. Essays in Honor of J. Michael Dunn. London: College Publications. pp. 261-265 (2022)

Authors
Saul Kripke
CUNY Graduate Center
Abstract
This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument uses semantic tableaux (with one exceptional rule not satisfying the subformula property). It avoids the previous arguments’ use of cutting down inconsistent sets of formulas to consistent sets. Like all tableau arguments, it extends partial valuations to total valuations.
Keywords Completeness  Partial valuation  Relevance logic  Rule γ  Semantic tableau
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Cut and Gamma I: Propositional and Constant Domain R.Yale Weiss - 2020 - Review of Symbolic Logic 13 (4):887-909.

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