A Logic Program for Transforming Sequent Proofs to Natural Deduction Proofs (1991)
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@MISC{Felty91alogic,
author = {Amy Felty},
title = {A Logic Program for Transforming Sequent Proofs to Natural Deduction Proofs},
year = {1991}
}
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Abstract
In this paper, we show that an intuitionistic logic with second-order function quantification, called hh 2 here, can serve as a meta-language to directly and naturally specify both sequent calculi and natural deduction inference systems for first-order logic. For the intuitionistic subset of first-order logic, we present a set of hh 2 formulas which simultaneously specifies both kinds of inference systems and provides a direct and concise account of the correspondence between cut-free sequential proofs and normal natural deduction proofs. The logic of hh 2 can be implemented using such logic programming techniques as providing operational interpretations to the connectives and implementing unification on -terms. With respect to such an interpreter, our specification provides a description of how to convert a proof in one system to a proof in the other. The operation of converting a sequent proof to a natural deduction proof is functional in the sense that there is always one na...
