Learning explanations for biological feedback with delays using an event calculus

We propose the identification of feedback mechanisms in biological systems by learning logical rules in R. Thomas’ Kinetic Logic (Thomas and D’Ari in Biological feedback. CRC Press, 1990). The principal advantages claimed for Kinetic Logic are that it captures an important class of regulatory networks at an appropriate level of precision, and that the representation is close to that used routinely by biologists, with a well-understood relationship to a differential description. In this paper we present a formalisation of Kinetic Logic as a labelled transition system and provide a provably correct implementation in a modified form of the Event Calculus. The behaviour of a system is then a logical consequence of the core-axioms of a (modified) Event Calculus C, the axioms K implementing Kinetic Logic and the axioms H describing the system. This formulation allows us to specify system identification in the manner adopted in Inductive Logic Programming (ILP), namely, given C, K, system behaviour S and possibly some additional domain-knowledge B, find H s.t. $$B \wedge C \wedge K \wedge H \models S$$ . Identifying a suitable Kinetic Logic hypothesis requires the simultaneous identification of definite clauses for: (a) logical definitions relating the occurrence of events to values of fluents; (b) delays in changes of the values of fluents arising from the occurrence of events; and possibly (c) exceptions to changes in fluent values, arising from asynchronous behaviour inherent to the system. We use a standard ILP engine for (a), and special-purpose abduction procedures for (b) and (c). We demonstrate this combination of induction and abduction on several canonical feedback patterns described by Thomas, and to identify the regulatory mechanism in two well-known biological problems (immune-response and phage-infection).