Geodesic
Testing dependencies and inference rules in databases
Modelirovanie i analiz informacionnyh sistem, Tome 29 (2022) no. 3, pp. 210-227.

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The process of testing dependencies and inference rules can be used in two ways. First, testing allows verification hypotheses about unknown inference rules. The main goal, in this case, is to search for the relation - a counterexample that illustrates the feasibility of the initial dependencies and contradicts the consequence. The found counterexample refutes the hypothesis, the absence of a counterexample allows searching for a generalization of the rule and conditions for its feasibility (logically imply). Testing cannot be used as a proof of the feasibility of inference rules, since the process of generalization requires the search for universal inference conditions for each rule, which cannot be programmed, since even the form of these conditions is unknown. Secondly, when designing a particular database, it may be necessary to test the feasibility of a rule for which there is no theoretical justification. Such a situation can take place in the presence of anomalies in the superkey. The solution to this problem is based on using join dependency inference rules. For these dependencies, a complete system of rules (axioms) has not yet been found. This paper discusses: 1) a technique for testing inference rules using the example of join dependencies, 2) a scheme of a testing algorithm is proposed, 3) some hypotheses are considered for which there are no counterexamples and inference rules, 4) an example of using testing when searching for a correct decomposition of a superkey is proposed.
Keywords: relational databases, join dependencies, inference rules, testing. 
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S. V. Zykin. Testing dependencies and inference rules in databases. Modelirovanie i analiz informacionnyh sistem, Tome 29 (2022) no. 3, pp. 210-227. http://geodesic.mathdoc.fr/item/MAIS_2022_29_3_a4/

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