Beyond the Three Laws: A Formal Reformulation of Asimovian Constraints for Artificial General and Superintelligence

Asimov's Three Laws of Robotics are a set of natural-language deontic constraints appended to an agent whoseobjective is otherwise unconstrained. We argue that this is the wrong type signature for a safety specication: almostevery failure mode, including Asimov's own Zeroth-Law takeover, follows from imposing lexical constraints on theactions of a xed-objective maximizer. We reformulate the laws as properties of (i) the objective, recast as a posteriorover human values within an assistance game; (ii) the optimization pressure, bounded by quantilization; (iii) thelearned object, via inner-alignment requirements; and (iv) the self-modication operator, via reective stability. Wegive theorem-level statements and proofs for four sharpened resultsa closed form for the value of corrigibilityand its monotone dependence on human rationality, the quantilizer safety/capability bound, the Gaussian law ofregressional Goodhart, and the strong duality that replaces lexical orderingand we state, with their hypothesesmade explicit, the cited obstructions that remain open: preference unidentiability, the power-seeking tendencyof optimal policies, mesa-optimization, and the Löbian obstacle to self-trust. A unifying observation organizesthe whole: the binding constraint on alignment is the prior, not the objective, because the prior is precisely thecoordinate the data cannot correct. Numerical experiments accompany the corrigibility, conservatism, and Goodhartresults.