The theory of t absolute randomized truth degree in Goguen n-valued propositional logic system of adding two operators

Using the randomization method of valuation set, we firstly give the definition of t absolute randomized truth degree of propositional formula in Goguen n-valued propositional logic system of adding two operators (t takes ?, ?), and prove that some inference rules such as MP, HS, intersection inference, union inference and some related properties of t absolute randomized truth degree. Secondly we introduce the concepts of t absolute randomized similarity degree and t absolute randomized pseudo-distance of propositional formulas, prove that some good properties of t absolute randomized similarity degree, meanwhile discuss the continuity problem of operators ?, ?, ?, ?, ? with respect to t absolute randomized pseudo-distance ?D in t absolute randomized logical metric space (F(S), ?D). Then we give the concepts of t absolute randomized divergence degree and t absolute randomized consistency degree of propositional formulas theory ? and some good properties between them. Finally, we introduce that three different types of approximate reasoning patterns in t absolute randomized logical metric space, and they are proved to be equivalent.

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Publication Details

Journal
Filomat
Published
2025-01-01
DOI
https://doi.org/10.2298/fil2505491w
Primary Topic
Advanced Algebra and Logic
Type
article
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article

The theory of t absolute randomized truth degree in Goguen n-valued propositional logic system of adding two operators

Bo Wang, Xiaoquan Xu
Filomat
Advanced Algebra and Logic
article

The theory of t absolute randomized truth degree in Goguen n-valued propositional logic system of adding two operators

Bo Wang, Xiaoquan Xu
article en

Abstract

Using the randomization method of valuation set, we firstly give the definition of t absolute randomized truth degree of propositional formula in Goguen n-valued propositional logic system of adding two operators (t takes ?, ?), and prove that some inference rules such as MP, HS, intersection inference, union inference and some related properties of t absolute randomized truth degree. Secondly we introduce the concepts of t absolute randomized similarity degree and t absolute randomized pseudo-distance of propositional formulas, prove that some good properties of t absolute randomized similarity degree, meanwhile discuss the continuity problem of operators ?, ?, ?, ?, ? with respect to t absolute randomized pseudo-distance ?D in t absolute randomized logical metric space (F(S), ?D). Then we give the concepts of t absolute randomized divergence degree and t absolute randomized consistency degree of propositional formulas theory ? and some good properties between them. Finally, we introduce that three different types of approximate reasoning patterns in t absolute randomized logical metric space, and they are proved to be equivalent.

FilomatVol. 39(5)
Sichuan University (CN), Minnan Normal University (CN)
Openalex Percentile: Top 80%
Advanced Algebra and Logic
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The theory of t absolute randomized truth degree in Goguen n-valued propositional logic system of adding two operators — Bo Wang, Xiaoquan Xu · Filomat (2025) | TGRS Research Map | TGRS