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.
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Ishida, T., Honda, K., Kawahara, Y. (2009). Armstrong’s Inference Rules in Dedekind Categories. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_13
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DOI: https://doi.org/10.1007/978-3-642-04639-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04638-4
Online ISBN: 978-3-642-04639-1
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