Abstract
Linear logic is increasingly being used as a tool for communicating reasoning agents in domains such as authorization, access control, electronic voting, etc., where proof certificates represent evidence that must be verified by proof consumers as part of higher protocols. Controlling the size of these certificates is critical. We assume that the proof consumer is allowed to do some search to reconstruct details of the full proof that are omitted from the certificates. Because the decision problem for linear logic is unsolvable, the certificate must contain at least enough information to bound the search: we show how to use the sequence of contractions in the sequent proof for this bound. The remaining content of the proof, in particular the information about resource divisions, can then be omitted from the certificate. We also describe a technique for giving a variable amount of additional search hints to the proof consumer to limit its non-determinism.
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
Andreoli, J.-M.: Logic programming with focusing proofs in linear logic. J. of Logic and Computation 2(3), 297–347 (1992)
Boespflug, M.: Conception d’un noyau de vérification de preuves pour le λΠ-calcul modulo. PhD thesis, Ecole Polytechnique (2011)
Brock-Nannestad, T., Schürmann, C.: Focused Natural Deduction. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 157–171. Springer, Heidelberg (2010)
Chaudhuri, K.: The Focused Inverse Method for Linear Logic. PhD thesis, Carnegie Mellon University, Technical report CMU-CS-06-162 (December 2006)
Chaudhuri, K.: Focusing Strategies in the Sequent Calculus of Synthetic Connectives. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 467–481. Springer, Heidelberg (2008)
Chaudhuri, K.: Magically Constraining the Inverse Method Using Dynamic Polarity Assignment. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 202–216. Springer, Heidelberg (2010)
Chaudhuri, K., Guenot, N., Straßburger, L.: The Focused Calculus of Structures. In: Computer Science Logic: 20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), pp. 159–173. Schloss Dagstuhl–Leibniz-Zentrum für Informatik (September 2011)
Chaudhuri, K., Pfenning, F., Price, G.: A logical characterization of forward and backward chaining in the inverse method. J. of Automated Reasoning 40(2-3), 133–177 (2008)
Dyckhoff, R.: Contraction-free sequent calculi for intuitionistic logic. J. of Symbolic Logic 57(3), 795–807 (1992)
Hodas, J., Miller, D.: Logic programming in a fragment of intuitionistic linear logic. Information and Computation 110(2), 327–365 (1994)
Hodas, J., Watkins, K., Tamura, N., Kang, K.-S.: Efficient implementation of a linear logic programming language. In: Jaffar, J. (ed.) Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming, pp. 145–159 (1998)
Laurent, O.: Etude de la polarisation en logique. PhD thesis, Université Aix-Marseille II (March 2002)
Laurent, O.: A proof of the focalization property of linear logic (May 2004) (unpublished note)
Liang, C., Miller, D.: Focusing and polarization in linear, intuitionistic, and classical logics. Theoretical Computer Science 410(46), 4747–4768 (2009)
Lincoln, P., Mitchell, J., Scedrov, A., Shankar, N.: Decision problems for propositional linear logic. Annals Pure Applied Logic 56, 239–311 (1992)
Miller, D.: A Proposal for Broad Spectrum Proof Certificates. In: Jouannaud, J.-P., Shao, Z. (eds.) CPP 2011. LNCS, vol. 7086, pp. 54–69. Springer, Heidelberg (2011)
Miller, D., Saurin, A.: From Proofs to Focused Proofs: A Modular Proof of Focalization in Linear Logic. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 405–419. Springer, Heidelberg (2007)
Necula, G.C.: Proof-carrying code. In: Conference Record of the 24th Symposium on Principles of Programming Languages 1997, Paris, France, pp. 106–119. ACM Press (1997)
Straßburger, L.: Linear Logic and Noncommutativity in the Calculus of Structures. PhD thesis, Technische Universität Dresden (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chaudhuri, K. (2012). Compact Proof Certificates for Linear Logic. In: Hawblitzel, C., Miller, D. (eds) Certified Programs and Proofs. CPP 2012. Lecture Notes in Computer Science, vol 7679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35308-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-35308-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35307-9
Online ISBN: 978-3-642-35308-6
eBook Packages: Computer ScienceComputer Science (R0)