  Let $\Theta$ be a variety of algebras, $(H, \Psi, f)$ be a model, where $H$
is an algebra from $\Theta$, $\Psi$ is a set of relation symbols $\varphi$, $f$
is an interpretation of all $\varphi$ in $H$. Let $X^0$ be an infinite set of
variables, $\Gamma$ be a collection of all finite subsets in $X^0$ (collection
of sorts), $\widetilde\Phi$ be the multi-sorted algebra of formulas. These data
define a knowledge base $KB(H,\Psi, f)$. In the paper the notion of isomorphism
of knowledge bases is considered. We give sufficient conditions which provide
isomorphism of knowledge bases. We also study the problem of necessary and
sufficient conditions for isomorphism of two knowledge bases.
