Isotypeness of models and knowledge bases equivalence Elena Aladova, Eugene Plotkin and Tatjana Plotkin Abstract. The aim of this work is to study the notions of elementarily equivalent and isotypic knowledge bases. We prove that isotypic knowledge bases are informationally equivalent. Mathematics Subject Classification (2010). Primary 08A70; Secondary 68T30. Keywords. Knowledge base, model, algebra, elementary equivalence, isotypic knowledge bases. 1. Introduction 1.1. Motivation The Knowledge Bases world is extremely diverse and we would like to think over the question about some classes of equivalent bases, yet not defining what do we exactly mean by equivalence by now. The outcome we expect of equivalence is that the bases work equally. The knowledge need not be represented in exactly the same way but there should be a transition allowing to infer the replies in one knowledge base using the knowledge kept in another one. The same observation relates also to queries, that is, queries to a knowledge base need not be literally the same but they have to be considered up to a certain syntactical/semantical equivalence. So, the knowledge bases are informationally equivalent if they produce the equivalent knowledge under equivalent queries. One can also say that two knowledge bases are informationally equivalent if the whole information that can be retrieved from one of them could be also obtained from the other one and vice versa. 1.2. Equivalence of databases Genetically, the equivalence problem for knowledge bases goes back to the similar one for databases. To the best of our knowledge, it was first posed in [6] and [1] and gave rise to the notion of databases schemes equivalence. Algorithms for verification of databases equivalence using database schemes were proposed by Beniaminov, Beeri-Mendelzon-Sagiv-Ullman and others. In this setting two rela- tional database schemes are equivalent if their sets of fixed points coincide. Correspondingly, two relational databases are equivalent if their sets of all fixed points intersected with the sets of feasible instances coincide. This and other approaches to the database equivalence problem had been studied in numerous papers (see [7], [2], [31], [14], [4], [3], [29], etc.). 1.3. Symmetries and automorphic equivalence of knowledge bases Informational equivalence for knowledge bases requires a more extended technique (see [30] and references therein). Being inspired by Galois theory of algebras of relations invented by M. Krasner [17], we used the notion of automorphic equivalence of knowledge bases in [30], [28]. In plane words the general idea behind this approach is as follows. We are very grateful to the anonymous reviewers for their valuable and helpful comments and suggestions.