Knowledge bases over algebraic models. Some notes about informational equivalence

The recent advances in knowledge base research and the growing importance of effective knowledge management raised an important question of knowledge base equivalence verification. This problem has not been stated earlier, at least in a way that allows speaking about algorithms for verification of informational equivalence, because the informal definition of knowledge bases makes formal solution of this problem impossible. The goal of this paper is to provide an implementable formal algorithm for knowledge base equivalence verification based on the formal definition of knowledge base given in [24, 26, 28, 29] and to study some important properties of automorphic equivalence of models. We will describe the concept of equivalence and formulate the criterion for the equivalence of knowledge bases defined over finite models. Further we will define multi-models and automorphic equivalence of models and multi-models that are generalization of automorphic equivalence of algebras.