A Formal Ontology of Interactions with Intensional Quantitative Semantics

The concepts promotion and inhibition are commonly used to explain the effects of interactions. These concepts are used with inference rules among them, such as “X inhibits Y, and Y promotes Z, therefore X inhibits Z.” Even when considering highly complex systems such as biological processes, many experimental facts can be explained using a few critical chains of reactions and their promotion/inhibition effects. The overall interaction effect of paths can be determined by considering relative properties, for example when an interaction effect of certain paths is stronger than that of others. In this paper, we present a formal ontology of interactions by providing a set of rules for the quantitative relations of the interaction effects of paths. Quantitative relations can be used to infer the overall interaction effect of all paths in a reaction network. Additionally, we present denotational semantics based on mass action kinetics with linear approximation at a steady state and prove the soundness of the given rules.