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ON SKOLEMIZATION AND PROOF COMPLEXITY
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The impact of Skolemization on the complexity of proofs in the sequent calculus is investigated. It is shown that prefix Skolemization may result in a nonelementary increase of Herbrand complexity (i. e. the minimal number of constituents in a Herbrand disjunction) versus structural Skolemization. Moreover it is shown that restricting the range of quantifiers never increases Herbrand complexity. The results provide a general mathematical justification for minimizing the range of quantifiers (by means of shifting) before Skolemization of formulas.
Title: ON SKOLEMIZATION AND PROOF COMPLEXITY
Description:
The impact of Skolemization on the complexity of proofs in the sequent calculus is investigated.
It is shown that prefix Skolemization may result in a nonelementary increase of Herbrand complexity (i.
e.
the minimal number of constituents in a Herbrand disjunction) versus structural Skolemization.
Moreover it is shown that restricting the range of quantifiers never increases Herbrand complexity.
The results provide a general mathematical justification for minimizing the range of quantifiers (by means of shifting) before Skolemization of formulas.
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