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Why is a universal restriction satisfied by an individual with no such role?

  • A.The individual is excluded from the concept by default
  • B.The statement is vacuously true when there is nothing to check
  • C.The reasoner assumes the role exists unless told otherwise
  • D.Universal restrictions are interpreted under the closed world assumption

Answer: B

A claim that every child is a doctor holds trivially of someone with no children, exactly as a universally quantified statement over an empty set is true. Modellers intending to require a child must add an existential restriction as well. Assumed roles, closed world reading and default exclusion are misreadings. A logical convention that is correct and counter-intuitive will be a persistent source of error unless it is stated explicitly during training.

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