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Why are negations driven inward before skolemisation?

  • A.Negations cannot be represented in clausal form at all
  • B.Skolemisation would otherwise introduce far too many functions
  • C.The conversion would produce a formula of exponential size
  • D.The quantifier a negation crosses is exchanged for its dual

Answer: D

Since the negation of a universal is an existential, and the reverse, a negation left outside a quantifier would cause the wrong quantifiers to be skolemised. Driving negations to the atoms settles which quantifiers are existential before skolemisation is applied. Negations on literals are fine, function counts follow from the formula, and the size issue arises at the distribution step. An ordering constraint between steps of a procedure, arising from an interaction between them, must be respected or the result is silently wrong.

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