Relational Similarity-Based Model Of Data Part 2: Dependencies In Data

This paper is a sequel to our previous paper on relational similarity-based model of data and its fundamental query systems. The present paper elaborates on the dependency theory in the similarity-based model, focusing mainly on similarity-based functional dependencies, their semantic entailment, model-theoretic properties, complete axiomatizations, characterization of nonredundant bases, computational issues, and related algorithms. The paper shows that various aspects of dependencies in ranked data tables over domains with similarities can be properly formalized using complete residuated lattices as structures for similarities and ranks. In addition to their theoretical importance, the results can be directly applied in the areas of similarity-based constraints, query result analysis, and knowledge discovery from relational data which involves similarity-based reasoning. We assume that readers are acquainted with the prequel of this paper.