A 4-valued logic for double Stone algebras

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2024-10-24 DOI:10.1016/j.ijar.2024.109309

Arun Kumar, Neha Gaur, Bisham Dewan

引用次数: 0

Abstract

This paper investigates the logical structure of the 4-element chain considered as a double Stone algebra. It has been shown that any element of a double Stone algebra can be identified as monotone ordered triplet of sets. As a consequence, we obtain the 4-valued semantics for the logic

L_{D}

of double Stone algebras. Furthermore, the rough set semantics of the logic

L_{D}

is provided by dividing the boundary region (uncertainty) into two disjoint subregions.

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双石代数的 4 值逻辑

本文研究了被视为双石代数的四元素链的逻辑结构。研究表明，双石代数的任何元素都可以被识别为单调有序的三重集合。因此，我们得到了双斯通代数逻辑 LD 的 4 值语义。此外，通过将边界区域（不确定性）划分为两个互不相交的子区域，还提供了逻辑 LD 的粗糙集语义。

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

International Journal of Approximate Reasoning 工程技术-计算机：人工智能

CiteScore

6.90

自引率

12.80%

发文量

170

审稿时长

67 days

期刊介绍： The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.