Nonmonotonic Reasoning

Classical logic is the study of " safe " formal reasoning. Western Philosophers developed classical logic over a period of thirty-three centuries after its introduction in the form of syllogistic by Aristotle [1] in the third century B. C. Beginning in the nineteenth century with De Morgan [2] and Boole [3], responsibility for the development of classical logic moved from the philosophical to the mathematical community. Tarski [10] showed how to make classical logic into a mathematical discipline which led to model theory, set theory, recursion theory, and proof theory. The discovery of recursive function theory by and Turing [15] in the nineteen thirties, the development of digital computers with a Von Neumann architecture in the 1950's, the interest in machine simulation of hu