Abstract
Proof search often involves a choice between alternatives which may result in redundant information once the search is complete. This behavior can manifest itself in proof search for sequent systems by the presence of redundant formulae or subformulae in a sequent for which a proof has been found. In this paper we investigate the detection and elimination of redundant parts of a provable sequent by using labels and Boolean constraints to keep track of usage information. We illustrate our ideas in propositional linear logic, but we believe the general approach is applicable to a variety of sequent systems, including other resource-sensitive logics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cervesato, I., Hodas, J., Pfenning, F.: Efficient Resource Management for Linear Logic Proof Search. In: Herre, H., Dyckhoff, R., Schroeder-Heister, P. (eds.) ELP 1996. LNCS (LNAI), vol. 1050, pp. 67–82. Springer, Heidelberg (1996)
Galmiche, D., Méry, D.: Resource Graphs and Countermodels in Resource Logics. In: Proceedings of the IJCAR 2004 Workshop on disproving: Non-Theorems, Non-Validity, Non-Provability, Cork, Ireland, pp. 59–75 (2004)
Galmiche, D., Perrier, G.: On Proof Normalisation in Linear Logic. Theoretical Computer Science 135, 67–110 (1994)
Harland, J.: An Algebraic Approach to Proof Search in Sequent Calculi. Short paper presented at the International Joint Conference on Automated Reasoning, Siena (July 2001)
Harland, J., Pym, D.: Resource-distribution via Boolean constraints. ACM Transactions on Computational Logic 4(1), 56–90 (2003)
Hodas, J., Lopez, P., Polakow, J., Stoilova, L., Pimentel, E.: A Tag-Frame System of Resource Management for Proof Search in Linear Logic Programming. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002, vol. 2471, pp. 167–182. Springer, Heidelberg (2002)
Lopez, P., et al.: Isolating Resource Consumption in Linear Logic Proof Search (extended abstract). Electronic Notes in Theoretical Computer Science 70(2) (2002)
Lutovac, T., Harland, J.: Issues in the Analysis of Proof-search Strategies in Sequential Presentations of Logics. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS, vol. 3097, pp. 115–147. Springer, Heidelberg (2004)
Massacci, F.: Efficient Approximate Deduction and an Application to Computer Security, PhD thesis, Università degeli Studi di Roma ’La Sapienza’ (1998)
Marriot, K., Stuckey, P.: Programming with Constraints. MIT Press, Cambridge (1998)
Pfenning, F., Schürmann, C.: Twelf — a meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)
Polakov, J.: Linear Logic Programming with an Ordered Context. In: Proceedings of the Second International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP 2000), Montreal, pp. 68–79 (2000)
Polakov, J.: Linearity Constraints as Bounded Intervals in Linear Logic Programming. In: Galmiche, D., Pym, D., O’Hearn, P. (eds.) Proceedings of the LICS 2004 Workshop on Logic for Resources, Process and Programs (LRPP), pp. 173–182 (2004)
Schmitt, S., Kreitz, C.: Deleting Redundancy in Proof Reconstruction. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS, vol. 1397, pp. 262–277. Springer, Heidelberg (1998)
Wallen, L.: Automated Proof Search in Non-classical Logic. MIT Press, Cambridge (1990)
Winikoff, M., Harland, J.: Implementing the Linear Logic Programming Language Lygon. In: Proceedings of the International Logic Programming Symposium, Portland, December 1995, pp. 66–80 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lutovac, T., Harland, J. (2005). A Redundancy Analysis of Sequent Proofs. In: Beckert, B. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2005. Lecture Notes in Computer Science(), vol 3702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554554_15
Download citation
DOI: https://doi.org/10.1007/11554554_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28931-9
Online ISBN: 978-3-540-31822-4
eBook Packages: Computer ScienceComputer Science (R0)