Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
A quantitative approach to logical inference
Decision Support Systems
Communications of the ACM
Implementing deductive databases by linear programming
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Elements of the Theory of Computation
Elements of the Theory of Computation
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The inference problem in propositional logic is important for expert system and deductive database applications. Although in practice the use of propositional logic is not sufficient it is basic for first order predicate logic and also for inference problems under uncertainty. It is well known that such inference problems may be modelled as mixed integer linear programs. This approach was recently used to build a deductive database system.In this paper we first show that an inference problem in propositionals logic may be rewritten as a standard quadratic program. Thus the use of Wolfe's or Beale's algorithm becomes possible. Moreover we introduce a modification of the simplex method which is very easy to implement and which allows a rather efficient solution of the inference problem. Some empirical results have been included in the paper to give a first idea.