Some Remarks on Boolean Constraint Propagation

TL;DR

This paper analyzes Boolean constraint propagation rules, establishing their completeness, equivalence to unit propagation, and characterizing rule sets via hyper-arc consistency, clarifying their theoretical foundations.

Contribution

It introduces a notion of completeness for Boolean constraint propagation rules, proves their equivalence to unit propagation, and characterizes rule sets using hyper-arc consistency.

Findings

Proposes a simple completeness notion for Boolean constraint rules

Establishes equivalence between Boolean constraint propagation and unit propagation

Characterizes rule sets using hyper-arc consistency

Abstract

We study here the well-known propagation rules for Boolean constraints. First we propose a simple notion of completeness for sets of such rules and establish a completeness result. Then we show an equivalence in an appropriate sense between Boolean constraint propagation and unit propagation, a form of resolution for propositional logic. Subsequently we characterize one set of such rules by means of the notion of hyper-arc consistency introduced in (Mohr and Masini 1988). Also, we clarify the status of a similar, though different, set of rules introduced in (Simonis 1989a) and more fully in (Codognet and Diaz 1996).