We introduce a context-dependent probabilistic execution structure strictly extending classical probabilistic transition systems. Unlike Segala systems [14], transition probabilities in our model may depend on execution context, represented as histories. We establish a strict non-embeddability theorem showing that classical probabilistic transition systems cannot capture such context-dependent behaviour. We then construct trace semantics via measurable trace spaces in the sense of Giry [4] and prove a final coalgebra representation theorem following standard coalgebraic methodology [13]. Furthermore, we derive a canonical minimal realisation through trace equivalence, yielding a probabilistic Myhill-Nerode theorem. Finally, we prepare the ground for modal and first-order logical characterisations developed in subsequent sections.

Contemporary artificial intelligence systems are increasingly shaped not only by what they represent, but by how their behavior is governed. Philosophical and technical discourse often treats such governing mechanisms as if they were forms of knowledge or wisdom. This paper argues that this treatment involves a category error. Drawing on distinctions between truth-apt representation and regulatory structure, the paper demonstrates that knowledge and control belong to different logical types. A representation may encode a norm without exercising normative force; normative force requires implementation-level constraint rather than semantic description. Conflating epistemic capacity with behavioral governance obscures the architecture of artificial agency and misdirects debates on responsibility. To clarify this confusion, the paper introduces the DIKCA framework (Data, Information, Knowledge, Control, Autonomy). DIKCA extends the classical DIKW hierarchy by identifying control as an irreducible regulatory layer and autonomy as meta-control—the functional capacity of a system to modify its own control structures. Intelligence, on this account, is not epistemic accumulation but the organization and reflexive reorganization of control under constraint. DIKCA is not a metaphysical thesis about the essence of intelligence, nor a new ethical theory. It is a diagnostic clarification of logical dependencies within contemporary AI systems, intended to restore analytic precision to philosophical debates on governance, agency, and responsibility.