Multiset-Multiset Frames

IF 0.7 1区哲学 0 PHILOSOPHY

JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2024-06-19 DOI:10.1007/s10992-024-09764-5

Takuro Onishi

引用次数: 0

Abstract

This paper presents the notion of multiset-multiset frame (mm-frame for short), a frame equipped with a relation between (finite) multisets over the set of points which satisfies the condition called compositionality. This notion is an extension of Restall and Standefer’s multiset frame, a frame that relates a multiset to a single point. While multiset frames serve as frames for the positive fragments of relevant logics RW and R, mm-frames are for the full RW and R with negation. We show this by presenting a way of constructing an mm-frame from any GS-frame, a frame with two dual ternary relations in which the Routley star is definable.

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多集合-多集合框架

本文提出了多集-多集框架（简称 mm-框架）的概念，它是一种在点集合上配备了（有限）多集之间关系的框架，这种关系满足称为组成性的条件。这一概念是 Restall 和 Standefer 的多集框架的扩展，多集框架将多集与单点联系起来。多集框架是相关逻辑 RW 和 R 的正片段的框架，而毫米框架则是带否定的完整 RW 和 R 的框架。我们提出了一种从任意 GS 框架构建毫米框架的方法来证明这一点，GS 框架是一种具有两个对偶三元关系的框架，其中的鲁特利星是可定义的。

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.