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Which consistency condition considers triples of variables?

  • A.Every variable lies on a path to every other variable
  • B.Every arc along a path has been made consistent in both directions
  • C.Every consistent pair extends consistently to any third variable
  • D.Every path in the constraint graph can be traversed consistently

Answer: C

Path consistency looks at triples: for every consistent assignment to two variables there must be a value for a third consistent with both, which prunes more than arc consistency and costs considerably more. It is the k equal to three case of k consistency. Graph paths and traversal are different notions. Each step up the hierarchy considers one more variable and costs an order more work, which is why the higher levels are rarely enforced in full.

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