An equational approach to logic programming

In this paper we follow ideas from our Equational approach to argumentation, [3,4], and develop the Equational approach to Logic programs. We regard a logic program P as a template for generating a system of equations Eq(P), where the literals are considered variables ranging over the unit interval [0, 1], and where the solutions to the equations give us the logical meaning of the logic program. We show soundness of the equational approach with respect to traditional Prolog computation and with respect to answer set programming. We prove completeness of answer sets for P with respect to {0,1} solutions of Eq(P) for programs with only negated atoms in the body of clauses. We offer equational semantics for logic programs with negation as failure in the spirit of Clark's completion.