Algebraic Semantics of Governed Execution: Monoidal Categories, Effect Algebras, and Coterminous Boundaries
arXiv:2605.01032v3 Announce Type: replace Abstract: We present an algebraic semantics for governed execution in which governance is axiomatized, compositional, and coterminous with expressibility. The framework, mechanized in 32 Rocq modules (~12,000 lines, 454 theorems, 0 admitted), is built on interaction trees and parameterized coinduction. A three-axiom GovernanceAlgebra record (safety, transparency, properness) induces a symmetric monoidal category with verified pentagon, triangle, and hexagon coherence, where every tensor composition preserves governance. An algebraic effect system const
The increasing complexity and autonomy of AI systems necessitate robust formal methods for ensuring predictable and safe behavior, pushing for foundational work in governed execution.
This work provides a foundational algebraic framework for building provably governed AI systems, addressing critical trust and control issues as AI becomes more pervasive and powerful.
The ability to formally axiomatize and verify governance means future AI applications can be designed with inherent safety and ethical constraints, rather than relying solely on empirical testing.
- · AI safety researchers
- · Developers of mission-critical AI
- · Organisations requiring verifiable AI compliance
- · Ad-hoc AI development methodologies
- · Systems lacking formal safety guarantees
New standards and certifications for AI governance emerge based on formal verification frameworks.
Increased consumer and regulatory trust in AI systems due to verifiable safety and control mechanisms.
The development of 'governance-by-design' AI architectures becomes a competitive advantage, potentially impacting market leadership.
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Read at arXiv cs.AI