摘要
研究了模糊命题演算的形式演绎系统L 以及在语义上相关的修正的Kleene逻辑系统 W ,W ,Wk 和R0 代数 ,讨论了算子 :F(S)×F(S)→F(S)的一些基本性质 ,给出了L 系统中的模糊演绎定理 .结果表明 ,在L 系统中 ,(1 )如果Γ∪ {A} B ,那么Γ A2 →B ;(2 )Γ∪ {A2 } B的充要条件是Γ A2 →B ;(3) (A B) C≈A (B C) (≈表示可证等价 ) ;(4)A B≈B A ;(5 ) A (A→B)→B ;(6 ) A2 →Ak(k∈N) .
The formal deductive system L * for fuzzy propositional calculus and the revised Kleene logic system 、W、W k, that are relevant to the former in semantics, have been studied, both of which are first proposed by Professor Guo jun Wang. The basic properties of operator :F(S)×F(S)→F(S) have been investigated, and a fuzzy deductive theorem has been given. The main results of this paper are: In the system L *(1)if Γ∪{A}B,then ΓA 2→B,(2)Γ∪{A 2}B iff ΓA 2→B, (3)(AB)C≈A(BC),(4)AB≈BA,(5)A(A→B)→B,(6)A k→A 2 (k∈N).
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2001年第1期17-22,共6页
Journal of Shaanxi Normal University：Natural Science Edition
