Knowledge base theory stimulates numerous applications of computer algebra and symbolic computations. The talk is aimed to explain the algebraic model of a knowledge base and to determine the criterion of knowledge bases informational equivalence. This criterion reduces the problem of informational equivalence of knowledge bases to the conjugacy problem of subgroups in a symmetric group. We study the case of linear knowledge bases in more detail and show that for such knowledge bases the generic algorithm uses the conjugacy of subgroups in a general linear group over a finite field.  Both conjugacy problems can be attacked with the means of computer algebra (see J.Cannon, D.Holt, “Automorphism group computation and isomorphism testing in finite groups”, J. Symbolic Comput. 35 (2003), no. 3, 241—267, and C.Roney-Dougal, “Conjugacy of subgroups of the general linear group” Experiment. Math. 13 (2004), no. 2, 151—163).