Knowledge bases over algebraic models. Some notes about informational equivalence

TL;DR

This paper introduces a formal algorithm for verifying the informational equivalence of knowledge bases over algebraic models, addressing a previously informal and unsolvable problem in knowledge management.

Contribution

It provides a formal, implementable algorithm for knowledge base equivalence verification and explores properties of automorphic equivalence of models and multi-models.

Findings

Developed a formal criterion for knowledge base equivalence over finite models

Analyzed properties of automorphic equivalence in algebraic models

Generalized automorphic equivalence to multi-models

Abstract

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. In this paper we provide an implementable formal algorithm for knowledge base equivalence verification based on the formal definition of knowledge base proposed by Plotkin B. and Plotkin T., and study some important properties of automorphic equivalence of models. We also describe the concept of equivalence and formulate the criterion for the equivalence of knowledge bases defined over finite models. Further we define multi-models and automorphic equivalence of models and multi-models, that is generalization of automorphic equivalence of algebras.