Binary Kripke Semantics for a Strong Logic for Naive Truth

Ben Middleton

DOI：: 10.1017/S175502032000043X

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

充分条件句与克里普克真理论

Adequate conditionals and Kripke's theory of truth

本文为克里普克真理论引入尊重演绎定理的条件句，提出强克里尼超赋值框架，以处理非单调概念在语义不确定性下的真值条件。

2024-07-19math.LO

克里普克真理论中的模态可定义性

Modal definability in Kripke's theory of truth

本文为克里普克真理论中的非正式模态定义引入模态语言，证明根基性和悖论性可表达而内在性不可表达，并刻画模态可定义关系及完全公理化其语义。

2025-03-26math.LO

Localizing Finite-Depth Kripke Models

We can look at a first-order (or propositional) intuitionistic Kripke model as an ordered set of classical models. In this paper, we show that for a finite-depth Kripke model in an arbitrary first-order language or propositional language, local (classical) truth of a formula is equivalent to non-classical truth (truth in the Kripke semantics) of a Friedman's translation of that formula, i.e. $ α\Vdash A^ρ\Leftrightarrow \mathfrak{M}_α\models A$. We introduce some applications of this fact. We extend the result of [Ardeshir and Hessam 2002] and show that semi-narrow Kripke models of Heyting Ari…

2017-10-24math.LO

The Modal Logics of Kripke-Feferman Truth

We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal{M}$, or an axiomatization $S$ thereof, we find a modal logic $M$ such that a modal sentence $φ$ is a theorem of $M$ if and only if the sentence $φ^*$ obtained by translating the modal operator with the truth predicate is true in $\mathcal{M}$ or a theorem of $S$ under all such translations. To this end, we introduce a novel version of possible worlds semantics featuring both classical and nonclassical worlds and es…

2020-05-06math.LO

超估值、真理与直觉逻辑

Supervaluations, truth, and intuitionistic logic

本文提出了一种基于超估值方法的直觉逻辑固定点真理理论，并展示了其在Kripke结构上的应用及与经典逻辑的对比。

2025-11-19math.LO

Effect of the Choice of Connectives on the Relation between the Logic of Constant Domains and Classical Predicate Logic

It is known that not only classical semantics but also intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth tables, or truth functions. In our previous work, it has been shown that the set of Kripke-valid propositional sequents and that of classically valid propositional sequents coincide if and only if all available propositional connectives are monotonic. The present paper extend this result to frst-order logic showing that, in the case of predicate logic, the condition that all available propositional connectives …

2021-07-08math.LO

更多相关论文收起更多论文

Truth and Subjunctive Theories of Knowledge: No Luck?

The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by mere luck as to be found in Gettier-style counterexamples to the analysis of knowledge as justified true belief. Because of the subjunctive nature of these conditions the resulting semantics turns out to be non-monotone, even if it is based on non-classical evaluation schemes such as strong Kleene or FDE. This blocks the usual road to fixed-point results for K…

2021-04-01cs.AImath.LO

Comparing truth theories based on Weak and Strong Kleene logic

We compare the conceptual strength of two axiomatic theories of truth: KF and WKF. The first one has been designed to capture Kripke's fixed-point construction based on Strong Kleene logic. The second one is based on the Weak Kleene evaluation schema. In the paper "Relative truth definability of axiomatic truth theories", Kentaro Fujimoto proved that WKF is relatively truth-definable in KF. However, it has been an open question whether KF is relatively truth-definable in WKF. We provide the negative answer to this question, one that does not depend on the choice of language and coding. We cons…

2018-07-21math.LO

What Kinds of Connectives Cause the Difference between Intuitionistic Predicate Logic and the Logic of Constant Domains?

It is known that intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth functions. We extend this generalized Kripke semantics to first-order logic, and study how the choice of connectives changes the relation between intuitionistic predicate logic and the logic of constant domains in terms of validity of sequents. Our main result gives a simple necessary and sufficient condition for the set of valid sequents in intuitionistic predicate logic to coincide with the set of valid sequents in the logic of constant domains.

2022-05-12math.LO

Truth and Feasible Reducibility

Let $\mathcal{T}$ be any of the three canonical truth theories $\textsf{CT}^-$ (Compositional truth without extra induction), $\textsf{FS}^-$ (Friedman--Sheard truth without extra induction), and $\textsf{KF}^-$ (Kripke--Feferman truth without extra induction), where the base theory of $\mathcal{T}$ is $\textsf{PA}$ (Peano arithmetic). We show that $\mathcal{T}$ is \textit{feasibly reducible to} $\textsf{PA}$, i.e., there is a polynomial time computable function $f$ such that for any proof $π$ of an arithmetical sentence $ϕ$ in $\mathcal{T}$, $f(π)$ is a proof of $ϕ$ in $\textsf{PA}$. In parti…

2019-02-01math.LO