Mathematical Programming and Logical Inference

Abstract

The object of this research is to develop new and effective methods for logical inference 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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1990
Accession Number
ADA232955

Entities

People

  • Egon Balas
  • Gérard Cornuéjols
  • John Hooker

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Artificial Intelligence
  • Bayesian Networks
  • Circuits
  • Computational Science
  • Computer Programming
  • Coverings
  • Evolutionary Algorithms
  • Expert Systems
  • Integer Programming
  • Linear Programming
  • Logic Gates
  • Mathematical Programming
  • Mathematics
  • Operations Research
  • Probability

Fields of Study

  • Computer science

Readers

  • Artificial Intelligence
  • Operations Research

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms