A class of 4-valued implicative expansions of first-degree entailment logic (FDE) with the variable-sharing property
A class of 4-valued implicative expansions of first-degree entailment logic (FDE) with the variable-sharing property
[EN] Anderson and Belnap consider the variable-sharing property (VSP) a necessary property a relevance logic has to fulfill. A logic L has the VSP if in all L-theorems of implication form antecedent and consequent share at least a propositional variable. If a propositional logic has the VSP then it is free from "paradoxes of relevance." The aim of this paper is to define a class of implicative expansions with the VSP of the well-known first-degree entailment logic, FDE. The properties the elements in this class enjoy make them important logics, not mere artificial constructs.
Ministerio de Ciencia e Innovación (10.13039/501100011033)
- University of Leon Spain
11 Lógica, Two-valued Belnap–Dunn semantics, First degree entailment logic, Lógica, 4-valued relevance logics, Variable-sharing property, Relevance logics
11 Lógica, Two-valued Belnap–Dunn semantics, First degree entailment logic, Lógica, 4-valued relevance logics, Variable-sharing property, Relevance logics
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