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What is the Herbrand universe of a set of clauses?

  • A.The domain of the intended interpretation of the clauses
  • B.The set of all atomic sentences appearing in the clauses
  • C.All ground terms built from its constants and function symbols
  • D.The set of all models satisfying the clauses

Answer: C

The Herbrand universe is the syntactic domain of all closed terms, and the Herbrand theorem shows that unsatisfiability may be established by considering only ground instances over it. That reduces first order refutation to a propositional question, though possibly an infinite one. Models, intended domains and atoms are different objects. Reducing a question about all interpretations to one about a single syntactic structure is what makes mechanical first order proof possible.

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