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Proof search in the intuitionistic sequent calculus

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Automated Deduction—CADE-11 (CADE 1992)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 607))

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Abstract

The use of Ilerbrand functions (sometimes called Skolemization) plays an important role in classical theorem proving and logic programming. We define a notion of Herbrand functions for the full intuitionistic predicate calculus. This definition is based on the view that the proof-theoretic role of Herbrand functions (to replace universal quantifiers), and of unification (to find instances corresponding to existential quantifiers), is to ensure the eigenvariable conditions on a sequent proof. The propositional impermutabilities that arise in the intuitionistic but not the classical sequent calculus motivate a generalization of the classical notion of Ilerbrand functions. This generalization of Herbrand functions also applies to the sequent calculus formalizations of logics other than intuitionistic predicate calculus.

The main part of this work was performed during 1987–88 at Stanford University, where it was funded by NSF Grant No. CCR-8718605. The preparation of this paper has been supported by the SRI International Computer Science Laboratory.

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Deepak Kapur

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© 1992 Springer-Verlag Berlin Heidelberg

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Shankar, N. (1992). Proof search in the intuitionistic sequent calculus. In: Kapur, D. (eds) Automated Deduction—CADE-11. CADE 1992. Lecture Notes in Computer Science, vol 607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55602-8_189

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  • DOI: https://doi.org/10.1007/3-540-55602-8_189

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55602-2

  • Online ISBN: 978-3-540-47252-0

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