Abstract
In this paper, we present a new system for proof-search in propositional intuitionistic logic from which an efficient implementation based on structural sharing is naturally derived. The way to solve the problem of formula duplication is not based on logical solutions but on an appropriate representation of sequents with a direct impact on sharing and therefore on the implementation. Then, the proof-search is based on a finer control of the resources and has a O(n log n)-space complexity. The system has the subformula property and leads to an algorithm that, for a given sequent, constructs a proof or generates a counter-model.
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References
R. Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic, 57:795–807, 1992.
D. Galmiche and D. Larchey-Wendling. Formulae-as-resources management for an intuitionistic theorem prover. In 5th Workshop on Logic, Language, Information and Computation, WoLLIC’98, Sao Paulo, Brazil, July 1998.
J. Hudelmaier. An O(n log n)-space decision procedure for intuitionistic propositional logic. Journal of Logic and Computation, 3(1):63–75, 1993.
M. Ornaghi P. Miglioli, U. Moscato. Avoiding duplications in tableaux systems for intuitionistic and Kuroda logic. Logic Journal of the IGPL, 5(1):145–167, 1997.
L. Pinto and R. Dyckhoff. Loop-free construction of counter-models for intuitionistic propositional logic. In Behara and al., editors, Symposia Gaussiana, pages 225–232, 1995.
N. Shankar. Proof search in the intuitionistic sequent calculus. In 11th Conference on Automated DEduction, LNAI 607, pages 522–536, Saratoga Springs, June 1992.
T. Tammet. A resolution theorem prover for intuitionistic logic. In 13th Conference on Automated Deduction, LNAI 1104, pages 2-16, NJ, USA, 1996.
C. Urban. Implementation of proof search in the imperative programming language pizza. In Int. Conference TABLEAUX’98, LNAI 1397, pages 313–319, Oisterwijk, The Netherlands, May 1998.
A. Voronkov. Proof-search in intuitionistic logic based on constraint satisfaction. In Int. Workshop TABLEAUX’96, LNAI 1071, pages 312–327, Italy, 1996.
K. Weich. Decisions procedures for intuitionistic logic by program extraction. In Int. Conference TABLEAUX’98, LNAI 1397, pages 292–306, Oisterwijk, The Netherlands, May 1998.
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© 1999 Springer-Verlag Berlin Heidelberg
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Galmiche, D., Larchey-Wendling, D. (1999). Structural Sharing and Efficient Proof-Search in Propositional Intuitionistic Logic. In: Thiagarajan, P.S., Yap, R. (eds) Advances in Computing Science — ASIAN’99. ASIAN 1999. Lecture Notes in Computer Science, vol 1742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46674-6_10
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DOI: https://doi.org/10.1007/3-540-46674-6_10
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