Different rule semantics have been defined successively in many contexts such as functional dependencies in databases or association rules in data mining to mention a few. In this paper, we focus on the class of rule semantics for tabular data for which Armstrong's axiom system is sound and complete, so-called \emph{well-formed semantics}. The main contribution of this paper is to show that an \emph{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. Moreover, the same reasoning on rules can be performed over any well-formed semantics. 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 relation, discover a cover of rules satisfied in this relation. This work takes its roots from a bioinformatics application, the discovery of gene regulatory networks from gene expression data.