In this paper, we propose a formulation for inference rules in Drug Interaction Ontology (DIO). Our formulation for inference rules is viewed from the standpoint of process-description. The relations in DIO are now described as resource-sensitive linear logical implications. The compositional reasoning on certain drug-interactions discussed in our previous work on DIO is represented as a construction of a linear logical proof. As examples of our formulation, we use some anti-cancer drug interactions.