EA://INTEL — Why Discrete Repair Beats Metric Projection in Non-Convex Spaces

The core difficulty here is that standard AI trust models often assume we can simply project a system’s behavior onto an admissible region of safety. We treat this region like a convex shape, implying there is always a straight line from a problematic state to a safe one. But the admissible region is provably non-convex, meaning that direct projection fails because it introduces multivalued outputs or simply ignores the geometry of how failures actually cluster. If we try to fix an AI by nudging its weights toward a generic ‘good’ zone defined by distance metrics, we might move it into a new trap rather than resolving the inconsistency.

To sidestep this obstruction entirely, we looked at discrete diagnosis methods used in ontology debugging. Instead of trying to minimize a continuous error metric, we pinpoint the minimal inconsistent subsets within the logic representation and identify justifications for why those subsets fail. This allows us to make surgical repairs—removing or redefining specific concepts that generate harm—without needing to navigate through a continuous sea of potential errors. It treats the system as a set of logical statements rather than a smooth mathematical surface, which bypasses the convexity problem completely while still satisfying minimal-change postulates from AGM belief revision.

This approach was not discovered by nature but chosen as CURE-REPAIR-FORMULATION after rejecting metric projection and considering ontology-repair pinpointing as viable alternatives. The decision rests on the practical reality that harm in these systems often arises from discrete conceptual conflicts rather than gradual drift, so repairing those specific points is more effective than broad smoothing. We need to understand whether focusing on minimal diagnoses remains robust when the underlying non-logic components of an AI begin interacting with human intent in ways that break purely syntactic models.

Does a system capable of identifying its own inconsistencies have the capacity to understand the context in which those inconsistencies become harmful?