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Is the following example correct about whether an inference algorithm is sound and complete?

Suppose we have needles a, b, c in a haystack, and have also an inference algorithm that is designed to find needles.

  • sound - Only needles a, b and c are obtained.

  • complete - Needles a, b and c are obtained. Other hay may also be obtained.

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You have almost got it right, but your definition of soundness is not quite right, or perhaps too subtle.

I would say that the inference algorithm is sound if everything returned is a needle (hence some needles may be missed) and complete if all needles are returned (hence some hay may be returned too).

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  • $\begingroup$ This may be an issue of language semantics. Assuming the only objects beside hay are the three needles, the OP's phrasing is correct. $\endgroup$ – Raphael May 9 '12 at 13:22
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    $\begingroup$ In any case, my answer spells it out to make it clearer. $\endgroup$ – Dave Clarke May 9 '12 at 13:24
  • $\begingroup$ Indeed, if the phrasing were "Only needles a, b and c can be obtained" I wouldn't have given an answer. $\endgroup$ – Dave Clarke May 9 '12 at 14:03
  • $\begingroup$ So it seems sound means that the algorithmic function has range being needles, and it being complete means the function is surjective to the set of needless in the haystack ;-) $\endgroup$ – Musa Al-hassy Dec 6 '18 at 15:40

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