From Explainability to System Language: Why AI Accountability Requires a Formal Execution Vocabulary

The preceding papers in this series showed that explainability cannot provide the foundations of accountable AI. In probabilistic systems, explanations may describe how outputs were generated, but they do not establish verifiable responsibility, nor can they resolve the epistemic problem that arises when systems are structurally compelled to answer under conditions of insufficient grounding. Once an output has crossed the decision boundary, retrospective interpretation cannot determine whether that output was permissible in the first place. This paper addresses the next question: what would accountability require if it cannot be derived from explanation? It argues that the missing element is not better interpretation, but a formal system language for responsibility, validity, commitment, and non-decision. Explainability operates at the level of intelligibility. Accountability, by contrast, requires enforceable execution semantics that define when generated language may become an accountable system action. The paper introduces system language as the structural counterpart to explainability. Rather than explaining decisions after the fact, system language represents the conditions under which decisions are authorized, withheld, committed, and attributable. Concepts such as non-decision, decision boundary, commit event, system state, provenance, reliability tiers, and technical truth are analyzed as minimal semantic primitives required for accountable AI architectures, independent of particular implementations. The contribution is therefore not a technical design proposal, but a conceptual shift: accountability is not achieved by making AI behavior more interpretable, but by making responsibility machine-readable and operationally enforceable. On this view, governance mechanisms such as auditability, certification, and liability cannot rest on narrative reconstruction alone; they require a formal execution vocabulary that precedes interpretation and turns accountability from an external demand into an internal system capability. By formulating this requirement, the paper prepares the next step in the series. Once accountability depends on formal permission rather than retrospective explanation, a further distinction becomes unavoidable: probabilistic inference is not yet a decision. The question then is no longer only how systems speak about responsibility, but whether always-answer architectures can be trusted to decide at all. This paper is part of a series examining accountability, auditability, and operational viability in probabilistic and agentic AI systems. A German-language version is available on Zenodo with DOI: 10.5281/zenodo.18663875