Lukasiewicz三值逻辑度量空间中的反射变换

The Properties of Reflective Transformation in 3-valued Lukasiewicz Logic Metric Space

在Lukasiewicz三值逻辑度量空间中定义了反射变换φ和(准)对称逻辑公式,探讨了反射变换φ的性质,证明了φ保持逻辑等价关系和(准)对称逻辑公式,且为同态变换.研究了φ在商代数——Lindenbaum代数上诱导的反射变换φ*的性质.证明了φ*是自同构的等距变换,进而讨论了φ*的不动点的性态,得到了4类特殊的不动点形式[A]∨φ*([A]),[A]∧φ*([A]),[A]φ*([A])和[A]φ*([A]).

In Lukasiewicz＇s 3-valued logic metric space the reflexive transformation φ and （pseudo--） symmetric logic formula are given. The properties of the reflexive transformation φ are studied in details. It is proved that the reflexive transformation φ on the Lukasiewicz＇s 3-valued logic metric space is a homomorphic mapping. Moreover, it keeps the logic equivalence relation and pseudo-symmetric logic formula unchanged. And studied the properties of a reflexive transformation φ＊ on the Lindenbaum algebra induced by φ which is an automorphic and isometric transformation of the Lindenbaum algebra. Then the four special forms of fixed points have been obtained by studying the features of fixed points, those are[A]∧φ＊（[A]）∨φ＊（[A]）,[A]十φ＊（[A]and [A]？φ＊（[A]）.