A huge amount of interaction knowledge among biological materials has been accumulated and it is most urgent that they are properly used to discover hidden phenomena in life. These data of interactions describe those among many kinds of objects and reactions on different levels of life or different time scales in similar way. In this paper, we formalize two general concepts of biological interaction functions i.e. inhibition and activation, and present a formal system of the ontology of them. This formal system is an axiomatic system which represents the general concepts of interactions not only between objects but also between reactions and on pathways of reactions. We demonstrate the applicability of the formal system to the real world phenomena of drugs poisoning in pharmacy.