Mathematical Programming and Logical Inference

摘要

The object of this research is to develop new and effective methods for logicalinference that are based on mathematical programming. We investigated fast packing and covering algorithms as well as polyhedral properties of these problems. We identified classes of covering and inference problems that can be solved by linear programming. We also obtained several results in both deductive and inductive logic. In the area of deductive logic, we developed branch-and-cut algorithms for inference in propositional logic, generalized the notion of a Horn problem (widely used in expert systems), designed a new algorithm for verifying logic circuits, found new connections between propositional logical and cutting plane theory, developed an inference method for a generalized belief net (Bayesian logic), and proposed new computational methods for Dempster Shafer theory. In inductive logic, we proposed a new, regression based method for generating rules for an expert system.