Identification of biological transition systems using meta-interpreted logic programs

Abstract

We adopt the principal idea from Plotkin’s Structural Operational Semantics (SOS), in which computation by a system is to be understood using: (a) a signature of configurations, $${\Gamma }$$ ; (b) a binary relation ( $$\rightarrow $$ ) defined over $${\Gamma }\times {\Gamma }$$ ; and (c) a meta-interpreter for general transition systems, defined at the level $${\Gamma }$$ and $$\rightarrow $$ . Using specific definitions for configurations and transition rules, the meta-interpreter generates an operational explanation of a system’s behaviour in the form of the stepwise computations (transitions) involved. This setting is of special interest to inductive logic programming (ILP), given recent developments in meta-interpretive learning. We focus here on the specific application of obtaining automatically Petri net models of biological system behaviour. Using a simple logic program as a meta-interpreter with a meta-rule for guarded transitions we show that using definitions of biologically-known transitions, proofs constructed by the meta-interpreter allow us, just as in SOS, to explain system behaviour as stepwise transitions in Petri nets. In the meta-interpretive learning setting, the proofs identify hypotheses that together with the meta-interpreter and domain-knowledge logically entail the observed behaviour. Meta-interpretive learning enables us to go beyond the explanations available in SOS, which are purely deductive, since the meta-interpreter is allowed abductive steps in the proof. This enables us to “invent” transitions which have not been specified in domain-knowledge. We use this facility to deal with noisy data by constructing first a hypothesis that includes abduced transitions, followed by the use of a Viterbi-style computation to find the most likely sequence of transitions for a system with a specified initial and final state. Extensive experiments with some well-known biological systems show that this approach can reliably identify the correct set of transitions even with fairly high levels of noise and with moderate amount of missing values.