The Unified Theory of Γ-t Absolute Randomized Truth Degree in Goguen∆,～ System

Abstract

In this paper, we mainly carry out quantitative research in Γ-t absolute randomized truth degree. Using the randomization method of valuation set, we firstly give the definition of Γ-t absolute randomized truth degree of formula relative to local finite theory Γ under the t conjunction in Goguen_∆,～ n-valued propositional logic system (t takes ∆,～), and prove some related properties of Γ-t absolute randomized truth degree and some inference rules such as MP, HS,intersection inference ,union inference; Secondly, we introduce the concepts of Γ-t absolute randomized similarity degree and Γ-t absolute randomized pseudo-distance of propositional formulas, and prove some good properties of Γ-t absolute randomized similarity degree. We also discuss in Γ-t absolute randomized logical metric space (F(S), ρ_D,Γ)the continuity of operators ∆, ～, →, ∨ and ∧ with respect to Γ-t absolute randomized pseudo-distance ρ_D. Finally we give the concepts of t absolute randomized divergence degree and t absolute randomized consistency degree of arbitrary theory Γ relative to the fixed theory Γ₀. Using the specific property of contradiction, we define non-absolute randomized consistent of arbitrary theory Γ relative to the fixed theory Γ₀, and establish the relationship between them.