Seminar on Linear Logic and Applications (CS 359 - Winter 99) Suggested Topics

The seminar is based on student participation and initiative. The topics below and the number of lectures should be understood as suggestions, not as course outline. The references are mostly outdated. I am working on it.

Overview

Basic papers giving a taste of linear logic: Lin92b, Sce93, Sce94, Wad93,

Introductory papers including advanced topics: Gir87, Gal91, Laf88a, Tro93

Sequent Calculus [2]

Classical and intuitionistic sequent calculi; role of structural rules; interpretation from classical into intuitionistic logic; inversion principles; permutability of inference rules; normal and long normal forms; cut elimination.

Linear Sequent Calculus [2]

Additive, multiplicative, and exponential connectives; intuitionistic and classical versions; traditional and zonal presentations; interpretations from classical and intuitionistic into linear logic; cut-elimination; examples.

Proof Search [2]

Permutability of inference rules; inversion principles; dynamic Skolemization; basic complexity results Tam94, LS94b, GP94

Intuitionistic Logic Programming [2]

Goal-directed search and uniform derivations linear refinement; soundness and completeness; input-output model of resource management; lazy subcontexting; the Lolli language; applications of Lolli Mil95, MNPS91 Hod94, HM94, Cer97, Cer98

Classical Logic Programming [2]

Focussing derivations; linear objects; the LO language; multiset rewriting; implementation issues; examples; classical uniform derivations; the LYGON language AP91, And92, HP94

Logical Frameworks [2]

The Forum meta-language; applications; implementation issues; LU; the LLF logical framework; canonical forms; design and implementation issues; examples Mil94, Gir93, SH91, CP96, IP,

Natural Deduction [2]

Linear intuitionistic natural deductions; proof term assignments; reductions and equality; normal forms; normalization; relation to sequent calculi Bie94

Functional Programming [2]

Recursion; type checking; memory management; linear ML; linear Lisp; examples Bak92, CGRar, Laf88b, Mac93

Type Inference [2]

Intuitionistic type inference; linear decoration; classes of embeddings of classical and intuitionistic in linear logic Sch94, Dos92

Concurrency [3]

Petri-nets MOM89; pi-calculus Mil92, GN95; geometry of interaction GLR95

Mathematical Semantics [3]

Coherent spaces Gir87, Gal91; categorial semantics dP89, Laf88b; game semantics Bla92, LS91; Kripke models AD93

Proof Nets [2]

Classical proof nets; proof nets for multiplicative fragment of linear logic; general proof nets; normalization Gir87, Gir96, Gal91, Tro92

Decidability and Complexity [2]

Selection of decidability and complexity results for fragments of linear logic Kop94, Lin92a, LMSS92, LS94a, LW94

Non-Commutative Linear Logic [2]

Lambek calculus; applications in computational linguistics PP98, Abr90, Abr91, Lam95

References

Abr90

V. Michele Abrusci. Non-commutative intuitionistic linear propositional logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 36:297-318, 1990.

Abr91

V. Michele Abrusci. Lambek syntactic calculus and non-commutative linear logic. In G. Corsi and G. Sambin, editors, Nuovi problemi della logica e della filosofia della scienza, volume II, Viareggio, Italy, January 1991. CLUEB.

AD93

Gerard Allwein and Jon M. Dunn. Kripke models for linear logic. Journal of Symbolic Logic, 58(2):514-545, 1993.

And92

Jean-Marc Andreoli. Logic programming with focusing proofs in linear logic. Journal of Logic and Computation, 2(3):297-347, 1992.

AP91

Jean-Marc Andreoli and Remo Pareschi. Linear objects: Logical processes with built-in inheritance. New Generation Computing, 9:445-473, 1991.

Bak92

Henry Baker. Lively linear lisp - `Look Ma, no garbage!'. ACM SIGPLAN Notices, 27(8):89-98, August 1992.

Bie94

G. M. Bierman. On intuitionistic linear logic. Technical Report 346, University of Cambridge, Computer Laboratory, August 1994. Revised version of PhD thesis.

Bla92

Andreas 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.

Cer98

Iliano Cervesato. Proof-theoretic foundation of compilation in logic programming languages. In J. Jaffar, editor, Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming - JICSLP'98, pages 115-129, Manchester, UK, 16-19 June 1998. MIT Press.

CGRar

Jawahar L. Chirimar, Carl A. Gunter, and Jon G. Riecke. Reference counting as a computational interpretation of linear logic. Journal of Functional Programming, to appear.

CP96

Iliano Cervesato and Frank Pfenning. A linear logical framework. In E. Clarke, editor, Proceedings of the Eleventh Annual Symposium on Logic in Computer Science - LICS'96, pages 264-275, New Brunswick, New Jersey, 27-30 July 1996. IEEE Computer Society Press. This work also appeared as Preprint 1834 of the Department of Mathematics of Technical University of Darmstadt, Germany.

CP97

Iliano Cervesato and Frank Pfenning. Linear higher-order pre-unification. In Glynn Winskel, editor, Proceedings of the Twelfth Annual Sumposium on Logic in Computer Science (LICS'97), pages 422-433, Warsaw, Poland, June 1997. IEEE Computer Society Press.

Dos92

Kostas Dosen. Modal translations in substructural logics. Journal of Philosophical Logic, 21:283-336, 1992.

dP89

Valeria de Paiva. The Dialectica categories. In J. W. Gray and A. Scedrov, editors, Proceedings of the Conference on Categories in Computer Science and Logic, pages 47-62. American Mathematical Society, 1989. AMS-IMS-SIAM Joint Summer Research Conference, June 14-20, 1987, Boulder, Colorado; Contemporary Mathematics Volume 92.

Gal91

Jean Gallier. Constructive logics. Part II: Linear logic and proof nets. Research Report PR2-RR-9, Digital Equipment Corporation, Paris, 1991.

Gir87

Jean-Yves Girard. Linear logic. Theoretical Computer Science, 50:1-102, 1987.

Gir93

Jean-Yves Girard. On the unity of logic. Annals of Pure and Applied Logic, 59:201-217, 1993.

Gir96

Jean-Yves Girard. Proof-nets: The parallel syntax for proof-theory. In P. Agliano and A. Ursini, editors, Logic and Algebra, Marcel Dekker, New York, 1996.

GLR95

Jean-Yves Girard, Yves Lafont, and Laurent Regnier, editors. Geometry of Interaction III: accommodating the additives, number 222 in Advances in Linear Logic, London Mathematical Society Lecture Notes Series. Cambridge University Press, 1995.

GN95

Simon Gay and Rajagopal Nagarajan. A typed calculus of synchronous processes. In D. Kozen, editor, Proceedings of the Tenth Annual Symposium on Logic in Computer Science, San Diego, California, June 1995. To appear.

GP94

Didier Galmiche and Guy Perrier. Foundations of proof search strategies design in linear logic. In Symposium on Logical Foundations of Computer Science, pages 101-113, St. Petersburg, Russia, 1994. Springer-Verlag LNCS 813. Also available as Technical Report CRIN 94-R-112 from the Centre di Recherche en Informatique de Nancy.

HM94

Joshua S. Hodas and Dale Miller. Logic programming in a fragment of intuitionistic linear logic. Information and Computation, 110(2):327-365, 1994. Extended abstract in the Proceedings of the Sixth Annual Symposium on Logic in Computer Science, Amsterdam, July 15-18, 1991.

Hod94

Joshua S. Hodas. Logic Programming in Intuitionistic Linear Logic: Theory, Design and Implementation. PhD thesis, University of Pennsylvania, Department of Computer and Information Science, 1994.

HP94

James Harland and David Pym. A uniform proof-theoretic investigation of linear logic programming. Journal of Logic and Computation, 4(2):175-207, April 1994.

IP

Samin Ishtiaq and David Pym. A relevant analysis of natural deduction. Journal of Logic and Computation. To appear.

Kop95

Alexei P. Kopylov. Decidability of linear affine logic. In D. Kozen, editor, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 496-504, San Diego, California, June 1995.

Laf88a

Yves Lafont. Introduction to linear logic. Lecture notes for the Summer School on Constructive Logics and Category Theory, 1988.

Laf88b

Yves Lafont. The linear abstract machine. Theoretical Computer Science, 59:157-180, 1988. Some corrections in volume 62 (1988), pp. 327-328.

Lam95

Joachim Lambek. Bilinear logic in algebra and linguistics. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, pages 43-59. Cambridge University Press, 1995. Proceedings of the Workshop on Linear Logic, Ithaca, New York, June 1993.

Lin92a

Patrick Lincoln. Computational Aspects of Linear Logic. PhD thesis, Stanford Univeristy, 1992.

Lin92b

Patrick Lincoln. Linear logic. ACM SIGACT Notices, 23(2):29-37, Spring 1992.

LMSS92

Patrick Lincoln, John Mitchell, Andre Scedrov, and Natarajan Shankar. Decision problems for propositional linear logic. Annals of Pure and Applied Logic, 56:239-311, April 1992. Also in the Proceedings of the 31th Annual Symposium on Foundations of Computer Science, St Louis, Missouri, October 1990, IEEE Computer Society Press. Also available as Technical Report SRI-CSL-90-08 from SRI International, Computer Science Laboratory.

LS91

Yves Lafont and T. Streicher. Games semantics for linear logic. In Sixth Symposium on Logic in Computer Science, pages 43-50. IEEE Computer Society Press, July 1991. Amsterdam, The Netherlands.

LS94a

Patrick Lincoln and Andre Scedrov. First order linear logic without modalities is NEXPTIME-hard. Theoretical Computer Science, 135(1):139-154, 1994.

LS94b

Patrick Lincoln and Natarajan Shankar. Proof search in first-order linear logic and other cut-free sequent calculi. In S. Abramsky, editor, Ninth Annual Symposium on Logic in Computer Science, pages 282-291, Paris, France, 1994. IEEE Computer Society Press.

LW94

Patrick Lincoln and Timothy Winkler. Constant-only multiplicative linear logic is NP-complete. Theoretical Computer Science, 135:155-169, 1994.

Mac93

Ian Mackie. Lilac - a functional programming language based on linear logic. Journal of Functional Programming, 4(4):395-433, 1993.

Mil92

Dale Miller. The pi-calculus as a theory in linear logic: Preliminary results. In E. Lamma and P. Mello, editors, Proceedings of the Workshop on Extensions of Logic Programming, pages 242-265. Springer-Verlag LNCS 660, 1992.

Mil94

Dale Miller. A multiple-conclusion meta-logic. In S. Abramsky, editor, Ninth Annual Symposium on Logic in Computer Science, pages 272-281, Paris, France, July 1994. IEEE Computer Society Press.

Mil95

Dale Miller. A Survey of Linear Logic Programming. In Computational Logic: The Newsletter of the European Network in Computational Logic, Volume 2, No. 2, December 1995, pp. 63-67

MNPS91

Dale Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125-157, 1991.

MOM89

N. Marti-Oliet and J. Meseguer. From Petri nets to linear logic. In P. Dybjer, A. M. Pitts, D. H. Pitt, A. Poigne, and D. E. Rydeheard, editors, Proceedings of the Conference on Category Theory and Computer Science, Springer-Verlag LNCS 389, pages 313-340, Manchester, United Kingdom, September 1989.

PP98

Jeff Polakow and Frank Pfenning. Natural deduction for intuitionistic non-commutative linear logic. Preliminary version. Final version to appear at TLCA'99, October 1998.

Sce93

Andre 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 Company, 1993. Also in Bulletin of the European Association for Theoretical Computer Science, volume 41, pages 154-165.

Sce94

Andre Scedrov. Linear logic and computation: A survey. In L. F. Bauer, W. Brauer, and H. Schwichtenberg, editors, Proceedings of the International Summer School of Marktoberdorf, NATO Advanced Science Institutes, series F94, pages ??-?? Springer-Verlag, 1994.

Sch94

Harold Schellinx. The Noble Art of Linear Decorating. PhD thesis, Institute for Logic, Language and Computation, University of Amsterdam, 1994.

SH91

P. Schröder-Heister. Structural frameworks, substructural logics, and the role of elimination inferences. In G. Huet and G. Plotkin, editors, Logical Frameworks, pages 385-403. Cambridge University Press, 1991.

Tam94

T. Tammet. Proof strategies in linear logic. Journal of Automated Reasoning, 12:273-304, 1994. Also available as Programming Methodology Group Report 70, Chalmers University, 1993.

Tro92

Anne S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes 29, Center for the Study of Language and Information, Stanford, California, 1992.

Tro93

Anne S. Troelstra. Natural deduction for intuitionistic linear logic. Prepublication Series for Mathematical Logic and Foundations ML-93-09, Institute for Language, Logic and Computation, University of Amsterdam, 1993.

Wad93

Philip Wadler. A taste of linear logic. In A. M. Borzyszkowski and S. Sokolowski, editors, Mathematical Foundations of Computer Science, pages 185-210, Gdansk, Poland, 1993. Springer-Verlag LNCS 781.