Behavioral Ontology Part 4: Interpreter Semantics

The first paper in this series 1 defines a formal system for behavioral ontology specification and establishes that the specification language is context-free. The second 2 develops the algebraic structure of specifications. The third 3 examines the computational power of the expression language within specifications. This fourth paper addresses the question that connects them all: where does meaning live? A Dynamic Behavioral Ontology (DBO) specification declares what a system is and does. A runtime interpreter gives that declaration operational reality. But the same specification can be interpreted by radically different runtimes — producing a web application, a voice interface, a physical control system — all of which are implementations of the same intent. This paper formalizes the relationship between specification and interpreter. It defines the interpreter invariant (the set of properties any valid interpreter must preserve), proposes a formal execution model (the sequence of steps by which an interpreter derives behavior from a specification), and establishes that a DBO defines equivalence classes of systems: all instantiations that faithfully interpret the same specification are, at the level of intent, the same system. It argues that meaning resides neither in the specification alone nor in the interpreter alone, but in their pairing — and that formalizing this pairing is the foundation of the operational semantics of behavioral ontology.