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Partial Implications in Data Mining and Logic

One of the most widely studied notions in Data Mining, namely Association Rules, is in fact a probabilistic logic notion: a minor variation of propositional partial implications; in turn, these are a natural variant of Horn clauses. The difference is in the semantics: we allow for a limited amount of exceptions. Some of the studies of redundancy in data mining are casted, as well, in a natural form as the corresponding logic notion of entailment, where the presence of exceptions, and the ways to measure them, fully change the rules of the game. We discuss in some depth the main practical notion of redundancy; characterize it in several ways, both model-theoretic and in terms of syntactic calculi; explore some applications, and propose a natural open problem on which we will be able to report ongoing partial progress.

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