An Efficient Reasoning Method for Dependencies over Similarity and Ordinal Data
We present a new axiomatization of logic for dependencies in data with grades, including ordinal data and data in an extension of Codd’s model that takes into account similarity relations on domains. The axiomatization makes possible an efficient method for automated reasoning for such dependencies that is presented in the paper. The presented method of automatic reasoning is based on a new simplification equivalence which allows to simplify sets of dependencies while retaining their semantic closures. We include two algorithms for computing closures and checking semantic entailment from sets of dependencies and present experimental comparison showing that the algorithms based on the new axiomatization outperform the algorithms proposed in the past.
KeywordsOrdinal Data Axiomatic System Automate Reasoning Heyting Algebra Deduction Rule
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