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What is a proof?

  • A.A finite sequence of sentences each justified by a rule
  • B.A demonstration that a sentence is true in the intended interpretation of the domain
  • C.An argument persuading a reader that a conclusion follows from the premises
  • D.A record of the search a prover performed before finding the conclusion

Answer: A

A proof is a syntactic object whose steps can be checked mechanically, which is why a machine derived proof can be verified independently of the machine that found it. Truth in an interpretation is semantic, persuasion is informal, and the search record is usually far larger than the proof. That finding a proof is hard and checking one is easy is the asymmetry the whole enterprise rests on.

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