Armstrong ’ s Axioms 1
نویسندگان
چکیده
We present a formalization of the seminal paper by W. W. Armstrong [1] on functional dependencies in relational data bases. The paper is formalized in its entirety including examples and applications. The formalization was done with a routine effort albeit some new notions were defined which simplified formulation of some theorems and proofs. The definitive reference to the theory of relational databases is [16], where saturated sets are called closed sets. Armstrong’s “axioms” for functional dependencies are still widely taught at all levels of database design, see for instance [14].
منابع مشابه
Białystok Armstrong ’ s Axioms 1 William W . Armstrong Dendronic Decisions Ltd
We present a formalization of the seminal paper byW.W. Armstrong [1] on functional dependencies in relational data bases. The paper is formalized in its entirety including examples and applications. The formalization was done with a routine effort albeit some new notions were defined which simplified formulation of some theorems and proofs. The definitive reference to the theory of relational d...
متن کاملMath 230 D Fall 2015 Homework 4 Drew Armstrong
(a) Prove that the sum and product of abstract symbols is well-defined. That is, if [a1, b1] = [a2, b2] and [c1, d1] = [c2, d2], prove that we have [a1, b1] · [c1, d1] = [a2, b2] · [c2, d2] and [a1, b1] + [c1, d1] = [a2, b2] + [c2, d2] . (b) One can check that Q satisfies all of the axioms of Z except for the Well-Ordering Axiom (please don’t check this), with additive identity [0, 1] ∈ Q and m...
متن کاملCyclic Sieving and Rational Catalan Theory
Let a < b be coprime positive integers. Armstrong, Rhoades, and Williams (2013) defined a set NC(a, b) of ‘rational noncrossing partitions’, which form a subset of the ordinary noncrossing partitions of {1, 2, . . . , b− 1}. Confirming a conjecture of Armstrong et. al., we prove that NC(a, b) is closed under rotation and prove an instance of the cyclic sieving phenomenon for this rotational act...
متن کاملExplorer Drosophila circadian rhythms in semi - natural environments ; the summer afternoon component is not an artifact and requires TrpA 1 channels
Citation for published version: Green, EW, O'Callaghan, EK, Hansen, CN, Bastianello, S, Bhutani, S, Vanin, S, Armstrong, JD, Costa, R & Kyriacou, CP 2015, 'Drosophila circadian rhythms in semi-natural environments; the summer afternoon component is not an artifact and requires TrpA1 channels' Proceedings of the National Academy of Sciences, vol 112, no. 28, pp. 8702-8707. DOI: 10.1073/pnas.1506...
متن کاملWe look forward to your response
Author(s): Jorunn I. B. Bos, Miles R. Armstrong,c,1, Eleanor M. Gilroy,1, Petra C. Boevink,1, Ingo Hein,1, Rosalind M. Taylor, Tian Zhendong,f, Stefan Engelhardt, Ramesh R. Vetukuri, Brian Harrower, Christina Dixelius, Glenn Bryan, Ari Sadanandom, Stephen C. Whisson, Sophien Kamoun,2, and Paul R. J. Birch Article Title: Phytophthora infestans effector AVR3a is essential for virulence and manipu...
متن کامل