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Reports (Research Report) Year : 1990

A logic program for transforming sequent proofs to natural deduction proofs

Abstract

In this paper, we show that an intuitionistic logic with second-order function quantification, called hh² 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 hh² 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 deductions proofs. The logic of hh² can be implemented using such logic programming techniques as providing operational interpretations to the connectives and implementing unification on lambda-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 natural deduction proof corresponding to each sequent proof. Our specification, in fact, provides a direct implementation of the transformation in this direction.

Domains

Other [cs.OH]
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Dates and versions

inria-00075258 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00075258 , version 1

Cite

Amy Felty. A logic program for transforming sequent proofs to natural deduction proofs. [Research Report] RR-1301, INRIA. 1990, pp.21. ⟨inria-00075258⟩
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