The Completeness and Decidability of Intuitive Implication Logic System

Abstract

One key matter we meet when classical logic is used in analysis and information mining to massive knowledge system is the problem of Scott Law. Up to the present, the existent resolvents are far from our logical intuition. This paper gives a new strategy - to build an intuitive implication logic system, D, in which: (1) the property of implication should be in accordance with intuition; (2) the fundamental laws of classical logic should be reserved; (3) the properties of negation and conjunction should be not changed; (4) Scott Law should not generally hold Scott Law. Then, basing on the strict formal semantics, we demonstrate the soundness and consistency of system D.