A New and Useful Syntactic Restriction on Rule Semantics for Tabular Datasets

Different rule semantics have been successively defined in many contexts such as implications in artificial intelligence, functional dependencies in databases or association rules in data mining. We are interested in defining on tabular datasets a class of rule semantics for which Armstrong’s axioms are sound and complete, so-called

well-formed semantics

. The main contribution of this paper is to show that an

equivalence

does exist between some syntactic restrictions on the natural definition of a given semantics and the fact that this semantics is well-formed. From a practical point of view, this equivalence allows to prove easily whether or not a new semantics is well-formed. We also point out the relationship between our generic definition of rule satisfaction and the underlying data mining problem, i.e. given a well-formed semantics and a tabular dataset, discover a cover of rules satisfied in this dataset. This work takes its roots from a bioinformatics application, the discovery of gene regulatory networks from gene expression data.