Abstract
An autonomous AI agent that drafts a contract clause in Lagos on behalf of a principal incorporated in London, using a model hosted in the European Union, is simultaneously subject to the Nigeria Data Protection Act 2023, the United Kingdom's post-Brexit data protection regime, and the European Union's Artificial Intelligence Act. No existing technical or legal framework formally defines what it means for an agent's single action to satisfy multiple regulatory regimes simultaneously, nor does any framework specify the conditions under which such simultaneous satisfaction is even possible. Regulators treat jurisdiction as a tag attached after the fact. Protocol designers treat it as metadata. Conflict-of-laws scholars treat it as a question of which single law applies, not how several apply at once. This paper introduces jurisdictional composability as a formal object. We model each jurisdiction's regulatory regime as a deontic Kripke frame over a shared action space, define a composition operator that combines frames from multiple regimes into a single multi-modal structure, and characterise the algebraic and computational conditions under which composition is sound (composed obligations are jointly satisfiable), decidable (satisfiability of the composed system can be checked in finite time), and order-independent (the result does not depend on the sequence in which regimes are composed). We prove that composability is not guaranteed in general; it depends on structural properties of the underlying accessibility relations that we identify and name, and we give a complexity-theoretic account of why checking composability for n jurisdictions is, in the worst case, intractable. We then instantiate the framework on a concrete three-jurisdiction case (Nigeria, the United Kingdom, and the European Union) drawn from an artificial intelligence accountability protocol (TAP) deployed in production legal technology, and we propose an empirical research program using a real-world AI failure registry (HalluCase, with over 1,450 incidents) to measure how often documented AI accountability failures correspond to provably non-composable obligation sets rather than to engineering or governance failures. We argue that jurisdictional composability is the formal prerequisite that cross-border AI accountability protocols, including our own, have so far assumed rather than established, and we situate this gap precisely against the most recent literature on agent delegation, identity, and accountability.