Maximal Reduction of Deterministic Semantics of Rule-based Models: Syntax-independent Setup

We develop a syntax-independent rule-based specification in a set-theoretical framework. The reactants of rules are usually defined as partially defined objects, called patterns, to denote that we can apply a reaction by substituting a pattern with any species that contains the context described by the pattern. We choose a very general data structure to represent the patterns: we write a pattern as a set of species which comply the pattern, and we call it a macro-species. We define the deterministic (ODE) semantics on such a rule set, and we define its reduction imposed by aggregation of species. We characterize for which aggregations we can correctly compute the reduced ODE semantics directly from the rule set, ie which aggregations are self-consistent. Finally, we propose an algorithm that, given a set of initial aggregates, computes the least-refined self-consistent aggregation which contains the initial aggregates.