One Variable Relevant Logics are S5ish

IF 0.7 1区哲学 0 PHILOSOPHY

JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2024-03-22 DOI:10.1007/s10992-024-09753-8

Nicholas Ferenz

引用次数: 0

Abstract

Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain S5ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic L, a formula \(\mathcal {A}\) of the one-variable fragment is a theorem of LQ (QL) iff its translation is a theorem of L5 (L.5). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for quantified L are transformed into ternary (plus two binary) relational semantics for S5-like extensions of L (for a general presentation, see Seki [26, 27]). In the other direction, a valuation is given for the full first-order relevant logic based on L into a model for a suitable S5 extension of L. I also discuss this work’s relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which RQ is incomplete [11].

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一个变量的相关逻辑是 S5 级的

在这里，我证明了几个一阶相关逻辑的单变量片段对应于底层命题相关逻辑的某些S5ish扩展。特别是，给定模态语言和一元语言之间相当标准的翻译以及包络命题相关逻辑L，如果其翻译是L5（L.5）的定理，那么一元片段的公式（\mathcal {A}\）就是LQ（QL）的定理。证明是模型论的。在一个方向上，基于 Mares-Goldblatt [15] 语义的量化 L 语义被转化为 L 的 S5 类扩展的三元（加上两个二元）关系语义（一般介绍见 Seki [26, 27]）。我还讨论了这项工作与寻找常域、非一般框架三元关系语义的完整公理化的关系，而 RQ 对于常域、非一般框架三元关系语义是不完整的[11]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

JOURNAL OF PHILOSOPHICAL LOGIC PHILOSOPHY-

CiteScore

2.50

自引率

20.00%

发文量

期刊介绍： The Journal of Philosophical Logic aims to provide a forum for work at the crossroads of philosophy and logic, old and new, with contributions ranging from conceptual to technical. Accordingly, the Journal invites papers in all of the traditional areas of philosophical logic, including but not limited to: various versions of modal, temporal, epistemic, and deontic logic; constructive logics; relevance and other sub-classical logics; many-valued logics; logics of conditionals; quantum logic; decision theory, inductive logic, logics of belief change, and formal epistemology; defeasible and nonmonotonic logics; formal philosophy of language; vagueness; and theories of truth and validity. In addition to publishing papers on philosophical logic in this familiar sense of the term, the Journal also invites papers on extensions of logic to new areas of application, and on the philosophical issues to which these give rise. The Journal places a special emphasis on the applications of philosophical logic in other disciplines, not only in mathematics and the natural sciences but also, for example, in computer science, artificial intelligence, cognitive science, linguistics, jurisprudence, and the social sciences, such as economics, sociology, and political science.