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Three of the following are syntactic notions. Which is the odd one out?

Entailment

Conjunctive normal form

Literal

Clause

  • A.Conjunctive normal form
  • B.Literal
  • C.Clause
  • D.Entailment

Answer: D

Normal forms, literals and clauses are all defined by the shape of an expression and can be checked by inspection. Entailment is semantic, defined by quantifying over models, and cannot be read off the syntax. Keeping the syntactic and semantic vocabularies apart is what allows soundness and completeness to be stated as a relationship between them rather than as a tautology.

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