Implementing Computational Law in Wolfram Language for the Governance of Artificial Intelligence

arXiv:2608.13958v1 Announce Type: new Abstract: How do we govern AI systems whose reasoning we cannot fully inspect? Governance does not require understanding a system's reasoning. It requires stating what the system is obliged, permitted, and forbidden to do, and checking whether it complied. I present an implementation of Reified Input/Output Logic, the formalism behind the DAPRECO knowledge base, in Wolfram Language: the core I/O axioms, obligations, permissions, constitutive norms, reified eventualities, and temporal operators. I then test whether GPT-4 can translate English legal statements into the formalism, and report the failures: hallucinated functions, omitted temporal scope, deviation from the formalism, and (in the worst cases) code that runs, reads plausibly, but silently encodes the wrong norm. A case study, an AI guard dog operating under a computational contract, shows how formalized rules can extend from a contract directly into the operational code of an embodied agent, producing symbolic, auditable justifications for its behaviour. I argue that computational law can be used as a governance tool and that a desirable goal would be to formalize the law that can and ought to be programmatically executable.

Abstract:How do we govern AI systems whose reasoning we cannot fully inspect? Governance does not require understanding a system's reasoning. It requires stating what the system is obliged, permitted, and forbidden to do, and checking whether it complied. I present an implementation of Reified Input/Output Logic, the formalism behind the DAPRECO knowledge base, in Wolfram Language: the core I/O axioms, obligations, permissions, constitutive norms, reified eventualities, and temporal operators. I then test whether GPT-4 can translate English legal statements into the formalism, and report the failures: hallucinated functions, omitted temporal scope, deviation from the formalism, and (in the worst cases) code that runs, reads plausibly, but silently encodes the wrong norm. A case study, an AI guard dog operating under a computational contract, shows how formalized rules can extend from a contract directly into the operational code of an embodied agent, producing symbolic, auditable justifications for its behaviour. I argue that computational law can be used as a governance tool and that a desirable goal would be to formalize the law that can and ought to be programmatically executable.

25 pages, 1 figure, 2 tables, 12 code listings. Wolfram Language implementation and verification script (31 assertions) available at this https URL

Artificial Intelligence (cs.AI); Computers and Society (cs.CY); Logic in Computer Science (cs.LO)

I.2.4; F.4.1; K.4.1

arXiv:2608.13958 [cs.AI]

(or arXiv:2608.13958v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.13958 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Implementing Computational Law in Wolfram Language for the Governance of Artificial Intelligence

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