NEW LOGICAL TOOLS FOR ARTIFICIAL INTELLIGENCE

 

Burgin M.S.

 

Logic always has been very useful in AI. However, applications of logic in AI have many shortcomings. One of the most important of them is connected with fact that large knowledge systems are inherently inconsistent. Many specialists in the field of AI stressed that is an essential peculiarity of such systems. Thus, for example, M. Minsky had written that consistency is a delicate concept that assumes the absence of contradictions in systems of axioms. He suggested that in artificial intelligence systems this assumption is superfluous because no artificial intelligence system is completely consistent. On his opinion it is important how a human being solves paradoxes or finds a way out of a disputed situation. It is important how peoples learn something from their or somebody’s mistakes or how they recognize and exclude different inconsistencies.

Consequently, if logic has an intention to describe adequate inference processes and real systems of knowledge, then it has to elaborate such apparatus that provides means for working with possible inconsistencies and contradictions. One such direction in modern logic is connected with paraconsistent systems. Another approach to this problem based on the concept of a logical variety is considered in what follows. A logical variety being a natural extension of concept of a local calculus are much more powerful in description of real situations as well as for knowledge processing. Logical varieties give a possibility to describe such situations (for example, knowledge in dynamic expert systems or real mathematical or physical theories) when inconsistencies may appear if knowledge is represented by traditional logical structures but they do not appear in reality and in logical varieties. In addition to this they provide efficient means for representation of the various peculiarities of human thinking which influenced computer reasoning in many ways. One of them is connected with such internal property of human thinking as non-monotonicity.