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Consistency, redundancy, and implied equalities in linear systems

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Abstract

Systems of linear inequalities have been studied for more than a century, but many of the results were developed during the early years of linear programming (1950s). New developments in linear programming plus interests in artificial intelligence have recently produced new results. One question is that of consistency: Does there exist a solution to satisfy all linear relations simultaneously? If so, are some of the relations redundant — that is, implied by the others? Are there implied equalities — that is, does some (weak) inequality have to hold with equality in every feasible solution? This paper brings together the main theorems that address these questions, unifies the framework, and presents some new results.

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Greenberg, H.J. Consistency, redundancy, and implied equalities in linear systems. Ann Math Artif Intell 17, 37–83 (1996). https://doi.org/10.1007/BF02284624

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