Testing Dependencies and Inference Rules in Databases

Abstract

The process of testing dependencies and inference rules can be used in two ways. First of all, testing allows verifying hypotheses about unknown inference rules. In this case, the main goal is to search for a counterexample relation that showcases the feasibility of the initial dependencies and contradicts the consequence. A found counterexample refutes the hypothesis, and the absence of a counterexample allows searching for a generalization of the rule and for conditions of its feasibility. Testing cannot be used to prove the feasibility of inference rules because generalization requires searching for universal inference conditions for each rule, which is impossible to program 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. This problem is solved by using join dependency of the inference rules. A complete system of rules (axioms) for these dependencies is yet to be found. This article discusses (1) a technique for testing inference rules through the example of join dependencies, (2) proposes a testing algorithm scheme, (3) considers some hypotheses for which there are no counterexamples or inference rules, and (4) proposes an example of testing used to search for the correct decomposition of a superkey.