The Fundamental Role of Entailment in Knowledge Representation and Reasoning

The hot controversy about the role of logic in AI has been repeated so far and probably will continue on as usual. An important fact is that the “logic” as the center of the controversy is classical mathematical logic and/or its various extensions, though there are some “more logical” logic systems. Until recently, what is debated by the researchers working on the fundamentals of AI is, among other things, what role the classical mathematical logic and/or its various extensions plays in knowledge representation and reasoning. As a result, most work on the fundamentals of AI are directly or indirectly based on the classical mathematical logic. It is the time to investigate the role of logic in AI from a more general point of view. What notion plays the most fundamental role in knowledge representation and reasoning? This question is discussed in this paper from the viewpoint of logic. The proposition presented in the paper is that it is the notion of entailment that plays the most fundamental role in knowledge representation and reasoning because any reasoning must invoke it and many important issues in knowledge representation and reasoning have to find a calculus of entailment as the logical basis of their solutions. In order to establish a satisfactory logic calculus of entailment to underlie knowledge representation and reasoning, the paper proposes some new relevant logics and suggests some important research problems.