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BINARY KRIPKE SEMANTICS FOR A STRONG LOGIC FOR NAIVE TRUTH

Part of: General logic

Published online by Cambridge University Press:  21 December 2020

BEN MIDDLETON
BEN MIDDLETON*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF NOTRE DAMENOTRE DAME, IN46556, USAE-mail: bmiddlet@nd.edu
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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 (i) dropping the requirement that the accessibility relation is reflexive and (ii) 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.

Keywords

Naive truthTJKcompletenessdisjunction propertyexistence propertysubintuitionisticbinary Kripke semanticsnatural deductionconditional proof

MSC classification

Primary: 03B60: Other nonclassical logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 3 , September 2022 , pp. 668 - 692
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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