Consistency degrees of theories in some systems of propositional fuzzy logic

The generalized truth degree of quantitative logic in the logic system Ln∗ (n-valued Wu1 2010Computers & Mathematics with Applications6000View full textAdd to dashboardCite

“…The theory of truth degree in [20,25] has been applied to studying of fuzzy reasoning and semantic properties like consistency, satisfiability, etc., and some interesting results have been acquired [25][26][27][28][29][30]. In this paper, the Σ Γ -truth degree is proposed which is an expanded version of the truth degree, and Γ -pseudo-metric is introduced in the system L * n .…”

A new theory consistency index based on deduction theorems in several logic systems

“…This requires a unified definition of ¬x, i.e., ¬x = R(x, 0) should be accepted in the above-mentioned logic systems. One may think that this would cause mistakes when we use the concepts of truth degrees and resemblance degrees of formulas and pseudo-metric on F (S) of [21,16] in the present paper. Fortunately, the differences mentioned above are not essential for us to use these concepts of [21,16], i.e., such concepts in [21,16] also hold when ¬x = R(x, 0) is defined instead for R ∈ {R G , R }.…”

“…The careful reader may find that the definition of unary operator ¬ differs from the one given in [21,16] when R ∈ {R G , R }, but is identical with the one given in [4]. In [21,16] …”

“…Zhou and Wang introduced a kind of concept of consistency degree of theories [21]. Let us recall the definitions.…”

“…Hence it seems that the definition of inconsistent degree of given by ( * ) is dependent on the above-mentioned special type of formulas rather than analyzing the disparity of the whole set consisting of all conclusions of . Keeping this situation in mind, Zhou and Wang [21] introduced in four different fuzzy logic systems, i.e., Łukasiewicz fuzzy logic system Łuk, Gödel fuzzy logic system Göd, product fuzzy logic system and the R 0 -fuzzy logic system L * , the concept of consistency degree R ( ) of a fuzzy theory based on the concept of polar index i R ( ) and the divergence degree div R ( ) (see Section 5) of as follows:…”