Existing and past generations of Prolog compilers have left deduction to run-time and this may account for the poor run-time performance of existing Prolog systems. Our work tries to minimize run-time deduction by shifting the deductive process to compile-time. In addition, we offer an alternative inferencing procedure based on translating logic to mixed integer programming. This makes available for research and implementation in deductive databases, all the theorems, algorithms, and software packages developed by the operations research community over the past 50 years. The method keeps the same query language as for disjunctive deductive databases, only the inferencing procedure changes. The language is purely declarative, independent of the order of rules in the program, and independent of the order in which literals occur in clause bodies. The technique avoids Prolog's problem of infinite looping. It saves run-time by doing primary inferencing at compile-time. Furthermore, it is incremental in nature. The first half of this article translates disjunctive clauses, integrity constraints, and database facts into Boolean equations, and develops procedures to use mixed integer programming methods to compute equations, and develops procedures to use mixed integer programming methods to compute equations, and develops procedures to use mixed integer programming methods to compute equations, and develops procedures to use mixed integer programming methods to compute —least models of definite deductive databases, and —minimal models and the Generalized Closed World Assumption of disjunctive databases.

Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logic programs based on mixed integer linear programming methods for automated deduction introduced by R. Jeroslow. We subsequently discuss the relative efficiency of these algorithms. The results of experiments with a prototype compiler implemented by us tend to confirm our theoretical discussion. In contrast to resolution, the mixed integer programming methodology is both fully declarative and handles reuse of old computations gracefully. We also introduce, compare, implement, and experiment with linear constraints corresponding to four semantics for “explicit” negation in logic programs: the four-valued annotated semantics [Blair and Subrahmanian 1989], the Gelfond-Lifschitz semantics [1990], the over-determined models [Grant and Subrahmanian 1989], the Gelfond-Lifschitz semantics [1990], the over-determined models [Grant and Subrahmanian 1990], and the classical logic semantics. Gelfond and Lifschitz[1990] argue for simultaneous use of two modes of negation in logic programs, “classical” and “nonmonotonic,” so we give algorithms for computing “answer sets” for such logic programs too.