Elementary Elimination of Prenex Cuts in Disjunction-free Intuitionistic Logic
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چکیده
The size of shortest cut-free proofs of first-order formulas in intuitionistic sequent calculus is known to be non-elementary in the worst case in terms of the size of given sequent proofs with cuts of the same formulas. In contrast to that fact, we provide an elementary bound for the size of cut-free proofs for disjunction-free intuitionistic logic for the case where the cut-formulas of the original proof are prenex. To emphasize the non-triviality of our result, we establish non-elementary lower bounds for classical disjunction-free proofs with prenex cut-formulas and intuitionistic disjunction-free proofs with non-prenex cut-formulas. 1998 ACM Subject Classification F.4.1 Mathematical Logic (Proof Theory)
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تاریخ انتشار 2015