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Relational Proof System for Relevant Logics

Ewa Orlowska
The Journal of Symbolic Logic
Vol. 57, No. 4 (Dec., 1992), pp. 1425-1440
DOI: 10.2307/2275375
Stable URL: http://www.jstor.org/stable/2275375
Page Count: 16
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Relational Proof System for Relevant Logics
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Abstract

A method is presented for constructing natural deduction-style systems for propositional relevant logics. The method consists in first translating formulas of relevant logics into ternary relations, and then defining deduction rules for a corresponding logic of ternary relations. Proof systems of that form are given for various relevant logics. A class of algebras of ternary relations is introduced that provides a relation-algebraic semantics for relevant logics.

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