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28 March 2024
 
  » arxiv » 1411.6432

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The joy of implications, aka pure Horn functions: mainly a survey
Marcel Wild ;
Date 24 Nov 2014
AbstractApart from a brief look at applications (Relational Databases, Formal Concept Analysis et al.) this article is devoted to the mathematical t h e o r y of implications (=pure Horn formulas). It is mainly a survey of results obtained in the last thirty years, but features a few novelties as well. Some keywords: The Duquenne-Guiges (implicational) base, the canonical direct base, prime implicates, the consensus method, implications and meet irreducible closed sets, optimum bases for certain lattices, component-wise quadratic pure Horn functions, ordered direct bases, generating all closed sets, general (i.e. impure) Horn functions. We pose seven open problems to stimulate further research.
Source arXiv, 1411.6432
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