Armstrong's Inference Rules in Dedekind Categories

Authors:
Toshikazu Ishida;Kazumasa Honda;Yasuo Kawahara
Affiliations:
Center for Fundamental Education, The University of Kitakyushu, Kitakyushu, Japan 802-8577;Department of Informatics, Kyushu University, Fukuoka, Japan 819-0395;Department of Informatics, Kyushu University, Fukuoka, Japan 819-0395
Venue:
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Year:
2009

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Abstract

It is well-known that Armstrong's inference rules are sound and complete for functional dependencies of relational data bases and for implication in the theory of formal concepts by Wille and Ganter. In this paper the authors treat Armstrong's inference rules and the implication as (binary) relations in an upper semi lattice in a Dedekind category, and give a relation algebraic proof of the completeness theorem for Armstrong's inference rules in a Schröder category.