On the construction and algebraic semantics of relevance logic

Abstract

[en] The truth-functional interpretation of classical implication gives rise to relevance paradoxes, since it doesn't adequately model our usual understanding of a valid implication, which assumes the antecedent is relevant to the truth of the consequent. This work gives an overview of the system $\mathbf{R}$ of relevance logic, which aims to avoid said paradoxes. We present the logic $\mathbf{R}$ with a Hilbert calculus and then prove the Variable-sharing Theorem. We also give an equivalent algebraic semantics for $\mathbf{R}$ and a semantics for its first-degree entailment fragment.