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. 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 restricts computational trajectories to states compatible with governing rules. This interpretation clarifies stability, convergence behaviour, and failure modes in computational systems including constraint solvers, distributed algorithms, and artificial intelligence architectures.