Behavioral Ontology Part 3: Computational Power Within a Declarative Framework

A companion paper 1 defines behavioral ontology as a formal system for specifying the behavior of automated systems, built from five orthogonal components and interpreted directly by a runtime. That formal system achieves its declarative character through structural declarations — classes, properties, methods, events, actions, and their bindings. But the computational content of the system — the actual operations that execute when behavior is triggered — resides in expressions embedded within Action declarations, written in an expression language (OEL in the OBI1 implementation). This paper examines the computational power of that expression language and its relationship to procedural programming languages. It argues that the expression language converges toward (and may reach) computational completeness — the ability to express any computable function — but that this convergence occurs within a declarative structural framework rather than outside one. The key distinction is not what the expression language can compute (which is equivalent to or approaching what procedural code can compute) but the context in which it computes: every expression operates on declared entities within a self-describing, decomposable specification. This structural constraint is what prevents the computational power of the expression language from undermining the declarative character of the formal system. This is a first draft; the formal completeness proof and the detailed equivalence analysis remain to be developed.