Relational proof system for relevant logics

Journal of Symbolic Logic 57 (4):1425-1440 (1992)
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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DOI 10.2307/2275375
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Marcelo Frias & Ewa Orlowska (1998). Equational Reasoning in Non-Classical Logics. Journal of Applied Non-Classical Logics 8 (1-2):27-66.

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