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This report presents an elementary theory of unification for positiveconjunctive queries. A positive conjunctive query is a formula constructed frompropositional constants, equations and atoms using the conjunction $\wedge$ andthe existential quantifier $\exists$. In particular, empty queries correspondto existentially quantified systems of equations -- called $\cal E$-formulas.We provide an algorithm which transforms any conjunctive query into a solvedform. We prove some lattice-theoretic properties of queries. In particular, thequotient set of $\cal E$-formulas under an equivalence relation forms acomplete lattice. Then we present another lattice -- a lattice of finitesubstitutions. We prove that the both lattices are isomorphic. Finally, weintroduce the notion of application of substitutions to formulas and clarifyits relationship to $\cal E$-formulas. This theory can be regarded as a basisfor alternative presentation of logic programming.

Conjunctive Queries, Existentially Quantified Systems of Equations and Finite Substitutions