Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
Proofs and types
Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
Relative complexities of first order calculi
Relative complexities of first order calculi
On different structure-preserving translations to normal form
Journal of Symbolic Computation
Gentzen-type systems and resolution rules. Part I. Propositional logic
COLOG '88 Proceedings of the International Conference on Computer Logic
On Skolemization And Proof Complexity
Fundamenta Informaticae
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In this paper, we examine different definitional transformations into normal form for intuitionistic logic. In contrast to the classical case, “intuitionistic clauses” may contain implications and quantifiers. Usually, such definitional transformations introduce labels defining subfor-mulae. An obvious optimization is the use of implications instead of equivalences whenever possible, which can reduce the size of the resulting normal form. We compare the optimized transformation with the unoptimized transformation with respect to the shortest cut-free LJ-derivation of the resulting normal forms. The comparison is based on a sequence (H k) k∈N of formulae for which the following hold: (i) there exist cut-free LJ-proofs of the unoptimized normal form of H k with length double-exponential in k, and (ii) any cut-free LJ-proof of the optimized normal form of H k has length non-elementary in k. The reason for the different behaviour is the simulation of analytic cuts by the unoptimized translation, which is not possible when the optimization is applied.