THE ALGORITHMS THAT achieve local consistency are called constraint propagation algorithms. In the literature, perhaps to confuse newcomers entering the field, several other names have also been used. In fact, we found the following alternative names for these algorithms: consistency, local consistency, local propagation, consistency enforcing, Waltz, filtering and narrowing algorithms. The aim of this chapter is to discuss various constraint propagation algorithms. These algorithms form a crucial ingredient of the generic procedure Solve of Figure 3.1 from Section 3.2 that can be used to solve a given CSP.

Sometimes a CSP can already be solved solely by means of a constraint propagation algorithm. Examples are furnished by some of the results proved in Chapter 5, namely the Consistency 2 Theorem 5.48, the Directional Arc Consistency Theorem 5.49, and the Directional Path Consistency Theorem 5.50. Another example is provided by the crossword puzzle of Example 2.8. We saw at the end of Section 5.2 that the CSP that represents this puzzle can be solved by transforming it to an equivalent arc consistent CSP. So arc consistency turned out to be sufficient to find a solution to this CSP.

When introducing in Chapter 5 several local consistency notions we characterised them by means of proof rules of the proof theoretic framework of Section 4.1. Also in Chapter 6 we defined some incomplete constraint solvers using rules.