Algorithmic Constraint Propagation

Constraint propagation is a fundamental mechanism in computational systems. It appears in constraint satisfaction problems, logic programming, optimisation algorithms, and artificial intelligence systems. Traditional treatments describe propagation as a procedural mechanism that reduces search space by eliminating inconsistent states. This paper interprets algorithmic constraint propagation through the admissibility framework of the Paton System. Within this interpretation, constraint propagation functions as a structural mechanism that preserves admissibility across computational state evolution. Computational systems evolve only through states compatible with governing logical, structural, and resource constraints. Constraint propagation therefore acts as an admissibility-preserving operator that ensures computational trajectories remain within permitted regions of system state space. By framing constraint propagation in this structural way, the Paton System clarifies stability, convergence behaviour, and failure modes in computational systems such as constraint solvers, distributed algorithms, and artificial intelligence systems. This paper forms part of the Paton System Tier-7 Domain Instantiation for Computational Systems, which applies the admissibility framework to distributed computation, artificial intelligence, and algorithmic stability.