Abstract
This is a survey of computational aspects of linear logic related to proof search.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Abramsky. Computational interpretations of linear logic. Theoretical Computer Science, 111: 3–57, 1993.
S. Abramsky and R. Jagadeesan. Games and full completeness for multiplicative linear logic. Accepted for publication in Journal of Symbolic Logic, 1994. Draft available using anonymous ftp from the host theory.Doc.Ic.Ac.Uk and the file theory /pap ers/Abramsky/gfc. Dvi.
J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. Workshop on Extensions of Logic Programming, Tuebingen. Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin, 1990.
J.-M. Andreoli and R. Pareschi. Linear objects: Logical processes with built-in inheritance. New Generation Computing, 9, 1991.
Jean-Marc Andreoli. Logic programming with focusing proofs in linear logic. Journal of Logic and Computation, 2 (3), 1992.
N. Benton, G. Bierman, V. de Paiva, and J.M.E. Hyland. Linear lambda-calculus and categorical models revisited. In Computer Science Logic’92, Selected Papers, pages 61–84. Springer LNCS, vol. 702, 1993.
A. Blass. A game semantics for linear logic. Annals of Pure and Applied Logic, 56:183–220, 1992. Special Volume dedicated to the memory of John Myhill.
S. Cerrito. A linear axiomatization of negation as failure. Journal of Logic Programming, 12: 1–24, 1992.
J. Chirimar, C. Gunter, and J. Riecke. Linear ML. In Proc. ACM Symposium on Lisp and Functional Programming, San Francisco. ACM Press, June 1992.
J. Chirimar, C. Gunter, and J. Riecke. Reference counting as a computational interpretation of linear logic. Manuscript, 1993. Available by anonymous ftp from the machine research att com in the file dist riecke linear logic journal.Ps.
V. Danos, J.-B. Joinet, and H. Schellinx. LKQ and LKT: sequent calculi for second order logic based upon dual linear decomposition of classical implication. Manuscript, October 1993.
V. Danos and L. Regnier. Local and asynchronous beta reduction. In Proc. 8-th IEEE Symp. on Logic in Computer Science, Montreal, pages 296–306. IEEE Computer Society Press, Los Alami- tos, California, June 1993.
R. Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic, 57: 795–807, 1992.
J.-Y. Girard. Linear logic. Theoretical Computer Science, 50: 1–102, 1987.
J.-Y. Girard. A new constructive logic: classical logic. Mathematical Structures in Computer Science, 1: 255–296, 1991.
J.-Y. Girard. On the unity of logic. Annals of Pure and Applied Logic, 59: 201–217, 1993.
G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proc. 19-th Annual ACM Symposium on Principles of Programming Languages, Albuquerque, New Mexico. ACM Press, New York, NY, January 1992.
G. Gonthier, M. Abadi, and J.-J. Levy. Linear logic without boxes. In Proc. 7-th Annual IEEE Symposium on Logic in Computer Science, Santa Cruz, California, pages 223–234. IEEE Com-puter Society Press, Los Alamitos, California, June 1992.
J.S. Hodas. Specifying filler-gap dependency parsers in a linear logic programming language. In K. Apt, editor, Proc. Joint International Conference and Symposium on Logic Programming, pages 622–636, 1992.
J.S. Hodas and D. Miller. Logic programming in a fragment of intuitionistic linear logic. In Proc. 6-th Annual IEEE Symposium on Logic in Computer Science, Amsterdam, pages 32–42. IEEE Computer Society Press, Los Alamitos, California, July 1991. Full paper to appear in Information and Computation. Draft available using anonymous ftp from host ftp.Cis.Upenn.Edu and the file pub/pap ers/miller/ic92. Dvi. Z.
J. Hudelmaier. Bounds for Cut Elimination in Intuitionistic Propositional Logic. PhD thesis, Universität Tübingen, 1989.
M. Kanovich. Horn programming in linear logic is NP-complete. In Proc. 7-th Annual IEEE Symposium on Logic in Computer Science, Santa Cruz, California, pages 200–210. IEEE Computer Society Press, Los Alamitos, California, June 1992. Full paper to appear in Annals of Pure and Applied Logic.
P. Lincoln, J. Mitchell, A. Scedrov, and N. Shankar. Decision problems for propositional linear logic. Annals of Pure and Applied Logic, 56:239–311, 1992. Special Volume dedicated to the memory of John Myhill.
P. Lincoln and A. Scedrov. First order linear logic without modalities is NEXPTIME-hard. Accepted for publication in Theoretical Computer Science, 1994. Available by anonymous ftp from host ftp.Cis.Upenn.Edu and the file pub papers scedrov malll.Dvi.
P. Lincoln, A. Scedrov, and N. Shankar. Linearizing intuitionistic implication. Annals of Pure and Applied Logic, 60: 151–177, 1993.
P. Lincoln and N. Shankar. Proof search in first order linear logic. Manuscript, October 1993.
P. Lincoln and T. Winkler. Constant-Only Multiplicative Linear Logic is NP-Complete. Manuscript, September 1992. Available using anonymous ftp from host ftp.Csl.Sri.Com and the file pub/lincoln/ comul t-np c. Dvi.
P.D.Lincoln. Computational A spects of Linear Logic. PhD thesis, Stanford University, 1992.
D. Miller. Abstractions in logic programming. In P. Odifreddi, editor, Logic and Computer Science, pages 329–359. APIC Studies in Data Processing, Vol. 31, Academic Press, 1990.
D. Miller. The π-calculus as a theory in linear logic: Preliminary results. In E. Lamma and P. Mello, editors, Proceedings of the 1992 Workshop on Extensions to Logic Programming, number 660 in Lecture Notes in Computer Science, pages 242–265. Springer-Verlag, 1993. Available using anonymous ftp from host ftp.Cis.Upenn.Edu and the file pub/papers/miller/pic.Dvi.Z.
D. Miller, G. Nadathur, F. Pfenning, and A. Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125–157, 1991. Special Issue on the 2-nd Annual IEEE Symposium on Logic in Computer Science, 1987.
A. Scedrov. A brief guide to linear logic. In G. Rozenberg and A. Salomaa, editors, Current Trends in Theoretical Computer Science, pages 377–394. World Scientific Publishing Co., 1993.
N. Shankar. Proof search in the intuitionistic sequent calculus. In Proc. of the 11th International Conference on Automated Deduction, pages 522–536. Springer LNAI, vol. 607, 1992.
E.Y. Shapiro. Alternation and the computational complexity of logic programs. Journal of Logic Programming, 1: 19–33, 1984.
L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52: 1–43, 1987.
A.S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes No. 29. Center for the Study of Language and Information, Stanford University, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Scedrov, A. (1995). Linear Logic and Computation: A Survey. In: Schwichtenberg, H. (eds) Proof and Computation. NATO ASI Series, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79361-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-79361-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-79363-9
Online ISBN: 978-3-642-79361-5
eBook Packages: Springer Book Archive