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.
This paper is tightly connected with the book . Since this book had not been translated from Russian into English we give here the brief review of the basic definitions and results from . We prove also new results of the same spirit. They are related to dimension subgroups, varieties of representations of groups and varieties of associative… (More)
Let Θ be a variety of algebras, (H, Ψ, f) be a model, where H is an algebra from Θ, Ψ is a set of relation symbols ϕ, f is an interpretation of all ϕ in H. Let X 0 be an infinite set of variables, Γ be a collection of all finite subsets in X 0 (collection of sorts), Φ be the multi-sorted algebra of formulas. These data define a knowledge base KB(H, Ψ, f).… (More)