基于改进的无穷值语义解释的中介谓词逻辑的λ-归结

λ-resolution for medium predicate logic based on an improved form of infinite-valued semantic interpretation

中介谓词逻辑系统MF的无穷值语义解释,反映了反对对立概念之间的可变过程,并且该解释不同于MF的其他任何语义解释。但在该无穷值语义解释下,"当A fuz时～A真"这种情况并未得到反映。在此基础上,进一步研究得到了中介谓词逻辑系统MF一种真值域为[0,1-λ)∪(1-λ,λ)∪(λ,1](λ∈(0.5,1))的无穷值语义解释,重新定义了MF的文字,给出了MF中λ-互补文字及弱无中介集的定义,提出了一种新的MF的λ-归结原理,并证明了其可靠性和完备性。在改进的MF的无穷值语义解释下,不仅较好的表达了"当A fuz时～A真"的情形,而且其λ值的确定,可根据一定的实例知识计算出来,具有客观性。该解释进一步表明用中介逻辑作为模糊知识的表示与推理的工具是可行的。

For the medium predicate system MF,the infinite-valued semantic interpretation shows the variable procedure of two opposite concepts and is differentiated from any other interpretation for MF.However,this type of infinite-valued semantic interpretation never reflects ＂～A true when A fuz＂.An improved kind of infinite-valued semantic interpretation as the truth-valued field is [0,1-λ）∪（1-λ,λ）∪（λ,1]（λ ∈（0.5,1）） for MF is further investivated and presented,and the notion of the literal in MF is redefined.Also,the notion of λ-complementary literal and the weak clause set without the literal ～A in MF are presented.A new kind of λ-resolution for MF is proposed,the soundness and completeness of which is proved.This new interpretation not only better expresses that situaton which is ＂～A true when A fuz＂,but also determines the λ truth in the interpretation by calculating according to some demonstration knowledge,so the λ truth possesses certain objectivity.This interpretation further shows that it is possible to represent fuzzy knowledge and reason using medium logic.