泛“蕴含”运算和泛“串行推理”运算研究

Studies on Generalized Implication Operation and Generalized Series Reasoning Operation

泛“蕴含”运算是广泛存在于经验性思维、不确定性推理和各种多值逻辑系统具有普遍意义的逻辑运算之一．但常见蕴含算子往往凭主观经验给定，缺乏理论指导和使用的有效性分析，具有很大的随意性和盲目性．本文首先研究了“蕴含”运算的思想基础，认为“蕴含”运算是“串行推理”运算的逆运算．然后提出了“蕴含”公理，从代数系统角度给出了“蕴含”运算的定义，提出并证明了“蕴含”运算的表示定理，对常见的蕴含算子进行了有效性分析．最后研究了“蕴含”运算在“串行推理”运算中的运用．从而克服了已有的蕴含运算理论存在的不足．这样实际应用就可根据“蕴含”公理和“蕴含”运算的表示定理设计“蕴含”算子和泛“蕴含”运算公式簇。

Generalized “IMPLICATION” operation (IO) is one of the logical operations that widely exist in experienced thinking, uncertain reasoning, and all kinds of multi valued logical systems and have general significance. But the applications often give the logical operators without theoretic guide and the analyses of their effectiveness. In addition, they are often given at will and blindly. The authors first study the thinking foundation of IO, hold that IO is the inverse operation of series reasoning operation, then put forward the IO axiom, give the definition of IO from the viewpoint of algebraic system, raise and prove the representation theorem of IO which guarantees that the operators generated by it belong to IO and all operators belonging to IO can be generated by it, compare and analyse the implication operators in common use, finally study the utilization of IO in series reasoning operation. Thus the faults that the existing theory about IO have been overcome, the applications can design the implication operators according to the IO axiom and the representation theorem of IO which provide the theoretic foundation for the designing of generalized implication operators and ensure the reasoning conclusions exact and believable.