Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/association-for-computing-machinery/a-system-of-interaction-and-structure-nEqexgNZNw
References (49)
-
Greg Restall (2000)
An Introduction to Substructural Logics -
D. Miller (1996)
Forum: A Multiple-Conclusion Specification LogicTheor. Comput. Sci., 165
-
Alwen Tiu (2005)
A System of Interaction and Structure II: The Need for Deep InferenceArXiv, abs/cs/0512036
-
N. Belnap (1982)
Display logicJournal of Philosophical Logic, 11
-
Alessio Guglielmi, Lutz Straßburger (2001)
Non-commutativity and MELL in the Calculus of Structures -
C. Retoré (1993)
Réseaux et séquents ordonnés -
J. Hodas, D. Miller (1991)
Logic programming in a fragment of intuitionistic linear logic[1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
-
Lutz Straßburger (2003)
Linear logic and noncommutativity in the calculus of structures -
(1970)
Investigations into Logical Deduction -
R. Milner (1989)
Communication and concurrency -
J. Lambek (1958)
The Mathematics of Sentence StructureAmerican Mathematical Monthly, 65
-
Kai Brünnler, Alwen Tiu (2001)
A Local System for Classical Logic -
C. Retoré (1999)
Pomset Logic as a Calculus of Directed Cographs -
P. Ruet (2000)
Non-commutative logic II: sequent calculus and phase semanticsMathematical Structures in Computer Science, 10
-
Kai Bruennler, Alessio Guglielmi (2004)
A First Order System with Finite Choice of Premises -
Francis Pelletier (2000)
The Journal of Symbolic Logic -
D. Miller (1992)
The pi-Calculus as a Theory in Linear Logic: Preliminary Results -
Alessio Guglielmi, Lutz Straßburger (2002)
A Non-commutative Extension of MELL -
copar' structural relation of S, 10 |α|, cardinality of set α -
P. Bruscoli (2002)
A Purely Logical Account of Sequentiality in Proof Search -
Ozan Kahramanoğulları (2004)
System BV without the Equalities for Unit -
Ozan Kahramanoù (2004)
Implementing System BV of the Calculus of Structures in Maude -
J. Andreoli (1992)
Logic Programming with Focusing Proofs in Linear LogicJ. Log. Comput., 2
-
Pietro Gianantonio (2004)
Structures for Multiplicative Cyclic Linear Logic: Deepness vs Cyclicity -
P. Brézillon, Paolo Bouquet (1999)
Lecture Notes in Artificial Intelligence -
Michele Abrusci, P. Ruet (1999)
Non-Commutative Logic I: The Multiplicative FragmentAnn. Pure Appl. Log., 101
-
(2002)
Received August -
A note on algebraic terms and their representation by the means of relations. In preparation -
Kai Brünnler (2003)
Atomic Cut Elimination for classical Logic -
=, syntactic equivalence on structures -
Lutz Straßburger (2003)
MELL in the calculus of structuresTheor. Comput. Sci., 309
-
R. Möhring (1989)
Computationally Tractable Classes of Ordered Sets -
Kai Brünnler (2003)
Two Restrictions on ContractionLog. J. IGPL, 11
-
M. Fisher (2004)
C and C -
P. Lincoln (1992)
Linear logicSIGACT News, 23
-
H. Reichel, D. Miller (2003)
Deep Inference and Symmetry in Classical Proofs -
(2007)
Article 1, Publication date -
Alwen Tiu, Steffen Hölldobler, Alessio Guglielmi (2001)
Properties of a Logical System in the Calculus of Structures -
Lutz Straßburger (2003)
System NEL is Undecidable -
J. Polokow, F. Pfenning (1999)
Relating Natural Deduction and Sequent Calculus for Intuitionistic Non-Commutative Linear Logic -
C. Retoré (1997)
Pomset Logic: A Non-commutative Extension of Classical Linear Logic -
Lutz Straßburger (2002)
A Local System for Linear Logic -
S , 'seq' structural relation of S -
M. Amblard, Christian Retoré (2007)
Natural Deduction and Normalisation for Partially Commutative Linear Logic and Lambek Calculus with Product -
A. Troelstra, H. Schwichtenberg (1996)
Basic proof theory, 43
-
S. Abramsky, R. Jagadeesan (1992)
Games and full completeness for multiplicative linear logicJournal of Symbolic Logic, 59
-
B. Herwig, H. Macpherson, G. Martin, A. Nurtazin (2000)
Abrusci, VM and Ruet, P., Non-commutative logic I: the multiplicative fragment (1) 29} 64 Bridges, D., Richman, F. and Schuster, P., Linear independence without choice (1) 95} 102 Creed, P. and Truss, JK, On o-amorphous sets (2} 3) 185} 226 -
Charles Stewart, P. Stouppa (2004)
A Systematic Proof Theory for Several Modal Logics -
WV-03-08, Technische UniversitUniversit¨Universität Dresden
- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2007 by ACM Inc.
- ISSN
- 1529-3785
- DOI
- 10.1145/1182613.1182614
- Publisher site
- See Article on Publisher Site
Abstract
This article introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far, it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures , which is the main contribution of this work. Structures are formulas subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalizing the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allowing the design of BV, yield a modular proof of cut elimination.
Journal
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Jan 1, 2007