Path consistency

A consistency property that is similar to arc consistency but that considers pairs of variables instead of just one. A pair of variables $LaTeX: (x,y)$ is path-consistent with another variable $LaTeX: z$ if for every consistent value pair for the binary constraint on $LaTeX: x$ and $LaTeX: y$ there exists a value for $LaTeX: z$ such that all binary constraints between $LaTeX: ({x},z)$ and $LaTeX: (y,z)$ are satisfied.