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What does refutation completeness mean?

  • A.Every entailed sentence can be derived directly by the rule
  • B.The procedure will terminate on every input it is given
  • C.Every satisfiable clause set can be shown to have a model
  • D.An unsatisfiable clause set will yield the empty clause

Answer: D

Resolution cannot derive every consequence directly, but if a clause set is unsatisfiable it will eventually produce the empty clause, and that suffices because entailment is converted into unsatisfiability by negating the goal. Direct completeness, termination and model construction are different properties. A weaker completeness that is enough for the question actually being asked is a common and useful pattern in proof theory.

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