计量逻辑学中的反射变换

Reflexive Transformation in Quantitative Logic

首先在连续值L*逻辑度量空间中,给出了公式集F(S)上的反射变换φ:F(S)→F(S)的概念,证明了该反射变换φ是F(S)上的自同构映射。其次证明了计量逻辑学中公式的真度,公式间的相似度与伪距离在反射变换下保持不变,而且证明了在反射变换下三种近似推理是等价的。最后,研究了反射变换φ的不动点的性质。

In this paper, a reflexive transformation φ:F(S)→F(S) on F(S) in the logic system L* is proposed, which is an automorphism of F(S). In Quantitative Logic, it is proved that the concepts of truth degree, similarity degree and pseudo-distance are remain under the reflexive transformation φ. Moreover, three different approximate reasoning patterns are equivalent in the system L*. Finally, the properties of fixed points under the reflexive transformation φ are researched.