Binary Kripke Semantics for a Strong Logic for Naive Truth

Review of Symbolic Logic:1-25 (forthcoming)
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Abstract

I show that the logic $\textsf {TJK}^{d+}$, one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by dropping the requirement that the accessibility relation is reflexive and only allowing reflexive worlds to serve as counterexamples to logical consequence. In addition, I provide a simplified natural deduction system for $\textsf {TJK}^{d+}$, in which a restricted form of conditional proof is used to establish conditionals.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Universal Logic.Ross Brady - 2006 - Bulletin of Symbolic Logic 13 (4):544-547.
Curry’s Paradox and ω -Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.

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