Local consistency
（重定向自Arc consistency）
![x2 is arc-consistent with x3 but not with x1, as the value x2=1 does not correspond to any value for x1.](/Images/godic/202412/21/Arc-consistency-1.svg1833.png")
![Arc consistency enforced by removing 1 as a value for x2. As a result, x3 is no longer arc-consistent with x2 because x3=2 does not correspond to a value for x2.](/Images/godic/202412/21/Arc-consistency-2.svg1833.png")
![](/Images/godic/202412/21/Path-consistency-1.svg1833.png")
![](/Images/godic/202412/21/Path-consistency-2.svg1833.png")
In constraint satisfaction, local consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints. Several such conditions exist, the most known being node consistency, arc consistency, and path consistency. Local consistency can be enforced via transformations of the problem called constraint propagation.