The notion of rules is very popular and appears in different flavors, for example as association rules in data mining or as functional dependencies in databases. Their syntax is the same but their semantics widely differs. In the context of gene expression data mining, we introduce three typical examples of rule semantics and for each one, we point out that Armstrong’s axioms are sound and complete. In this setting, we propose a unifying framework in which any “well-formed” semantics for rules may be integrated. We do not focus on the underlying data mining problems posed by the discovery of rules, rather we prefer to emphasize the expressiveness of our contribution in a particular domain of application: the understanding of gene regulatory networks from gene expression data. The key idea is that biologists have the opportunity to choose - among some predefined semantics - or to define the meaning of their rules which best fits into their requirements. Our proposition has been implemented and integrated into an existing open-source system named MeV of the TIGR environment devoted to microarray data interpretation. An application has been performed on expression profiles of a sub-sample of genes from breast cancer tumors.