The joy of implications, aka pure Horn formulas: Mainly a survey

Marcel Wild
2017 Theoretical Computer Science  
Apart from a brief look at applications (Relational Databases, Formal Concept Analysis, data mining) 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
more » ... attices, ordered direct bases, generating all closed sets, general (i.e. impure) Horn functions. We pose four open problems to stimulate further research.
doi:10.1016/j.tcs.2016.03.018 fatcat:hrz2vsn66rdt3obw42or57h7pa