This paper identifies a structural limitation in contemporary statistical AI systems: the absence of an explicit termination condition for dependency resolution. Within the framework of the Modal–Dependence Calculus (MDC), probabilistic generative models are analyzed as inducing open-ended dependency paths that are not guaranteed to terminate. This condition, formalized as the Taxicab Condition, explains how systems can achieve high local coherence while lacking structural evaluability. To address this limitation, the paper introduces the τ-operator as a binary admissibility function defined over candidate outputs, where evaluability depends on the existence of a terminating dependency path to an invariant anchor. Building on this formulation, the Semantic AI Reactor is proposed as a constraint-based architecture that enforces termination as a structural requirement on inference. The analysis establishes a fundamental distinction between generative systems that optimize probabilistic breadth and reactor systems that enforce finite dependency depth, positioning termination as a necessary condition for semantically grounded computation.
Austin Jacobs (Tue,) studied this question.