Open AccessQuantitative Method Based on Cotangent Similarity Degree in Three‐Valued Łukasiewicz Logic
Author(s) -
Peng Yu
Publication year - 2021
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2020.11.011
Subject(s) - truth function , trigonometric functions , similarity (geometry) , degree (music) , mathematics , propositional calculus , cosine similarity , logical connective , tautology (logic) , metric (unit) , set (abstract data type) , metric space , pure mathematics , discrete mathematics , algebra over a field , propositional variable , artificial intelligence , computer science , intermediate logic , pattern recognition (psychology) , programming language , image (mathematics) , physics , geometry , acoustics , description logic , operations management , economics
The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three‐valued Łukasiewicz propositional logic system Ł 3 . We introduce the concepts of the cotangent similarity degree, cotangent pseudo‐distance and cotangent truth degree of the propositions, together with their basic properties in Ł 3 . We investigate the relationship between the cotangent truth degree and contangent pseudo‐distance, and prove the continuity of the logical connectives ¬ , ∨ and → in the Ł 3 logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F ( S ), and provide several examples and basic properties of it.