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Why is inference over Horn clauses efficient?

  • A.Horn clauses contain far fewer symbols than general clauses
  • B.Every Horn clause is automatically satisfiable
  • C.Resolution is unnecessary when clauses are Horn
  • D.Forward chaining derives every consequence in linear time

Answer: D

Applying each rule as soon as its conditions are satisfied derives the whole set of consequences in time linear in the size of the knowledge base, which is why deductive databases and Prolog are practical. Symbol counts are unrelated, satisfiability is not automatic since a set of Horn clauses may be contradictory, and resolution still applies. A restriction that converts an intractable problem into a linear one, at a stated cost in expressiveness, is the clearest possible illustration of the expressiveness against tractability trade.

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