In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer will be played by existentially quantified systems of equations. This allows us to avoid problems when we deal with substitutions. In particular, we need no ''global'' variable separated conditions when new variables are introduced by input clauses. Moreover, this formalization can be regarded as a basis for the theory of concurrent logic languages, since it also includes a wide spectrum of parallel computational methods. Moreover, the parallel composition of answers can be defined directly -- as a consistent conjunction of answers.

26 pages; reprint of the technical report TR mff-ii-11-1992, September 1992. arXiv admin note: substantial text overlap with arXiv:2207.08572