Semantic labelled tableaux for propositional BI⊥

Journal of Logic and Computation

Volumn 13, Issue 5, 2003, Pages 707-753

  Galmiche, Didier ^a   Méry, Daniel ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

BI logic; Intuitionistic logic; Labelled deduction; Semantics; Tableau method

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; DATA STRUCTURES; THEOREM PROVING;

INTUITIONISTIC LOGIC; SEMANTIC LABELLED TABLEAUX; TABLEAU METHOD;

SEMANTICS;

EID: 0344515285     PISSN: 0955792X     EISSN: None     Source Type: Journal    
DOI: 10.1093/logcom/13.5.707     Document Type: Article

References (38)

1. J. M. Andreoli, Logic programming with focusing proofs in linear logic. Journal of Logic and Computation, 2, 297-347, 1992.
2. P.A. Armelin and D. Pym. Bunched logic programming (extended abstract). In First International Joint Conference on Automated Reasoning, IJCAR 2001, Siena, Italy, pp. 289-304, volume 2083 of Lecture Notes in Computer Science, Springer-Verlag, 2001.
3. V. Balat and D. Galmiche, Labelled Deduction, volume 17 of Applied Logic Series, chapter Labelled proof systems for intuitionistic provability. Kluwer Academic Publishers, 2000.
4. A. Blass. A game semantics for linear logic. Annals of Pure and Applied Logic, 56, 183-220, 1992.
5. K. Broda, M. Finger, and A. Russo. Labelled natural deduction for substructural logics. Logic Journal of the IGPL, 7, 283-318, 1999.
6. W. Buszkowski. The finite model property for BCI and related systems. Studia Logica, 57, 303-323, 1996.
7. M. D'Agostino and D.M. Gabbay. A generalization of analytic deduction via labelled deductive systems. Part I: Basic substructural logics. Journal of Automated Reasoning, 13, 243-281, 1994.
8. R. Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic, 57, 795-807, 1992.
9. M. Fitting. First-Order Logic and Automated Theorem Proving. Texts and Monographs in Computer Science. Springer Verlag, 1990.
10. D.M. Gabbay. Labelled Deductive Systems, Volume I - Foundations. Oxford University Press, 1996.
11. D. Galmiche. Connection methods in linear logic and proof nets construction. Theoretical Computer Science, 232, 231-272, 2000.
12. D. Galmiche and D. Larchey-Wendling. Provability in intuitionistic linear logic from a New interpretation on Petri nets - extended abstract. Electronic Notes in Theoretical Computer Science, 17, 1998.
13. D. Galmiche and D. Larchey-Wendling. Structural sharing and efficient proof-search in propositional intuitionistic logic. In Asian Computing Science Conference, ASIAN'99, Phuket, Thailand, pp. 101-112, volume 1742 of Lecture Notes in Computer Science, Springer-Verlag, 1999.
14. D. Galmiche and D. Larchey-Wendling. Quantales as completions of ordered monoids: revised semantics for intuitionistic linear logic. Electronic Notes in Theoretical Computer Science, 35, 2000.
15. D. Galmiche and D. Méry. Connection-based proof search in propositional BI logic. In Eighteenth International Conference on Automated Deduction, CADE-18, Copenhagen, Denmark pp. 111-128, volume 2392 of Lecture Notes in Artificial Intelligence, Springer, 2002.
16. D. Galmiche, D. Méry, and D. Pym. Resource tableaux (extended abstract). In Sixteenth Internatinal Workshop on Computer Science Logic, CSL 2002, Edinburgh, Scotland, pp. 183-199, volume 2471 of Lecture Notes in Computer Science, Springer, 2002.
17. D. Galmiche and J.M. Notin. Calculi with dependency relations for mixed linear logic. In International Workshop on Logic and Complexity in Computer Science, LCCS'2001, pp. 81-102, Créteil, France, 2001.
18. D. Galmiche and G. Perrier. On proof normalization in linear logic. Theoretical Computer Science, 135, 67-110, 1994.
19. J.Y. Girard. Linear logic: its syntax and semantics. In Advances in Linear Logic, J.Y. Girard, Y. Lafont, and L. Regnier, eds, pp. 1-42. Cambridge University Press, 1995.
20. S. Ishtiaq and P. O'Hearn. BI as an assertion language for mutable data structures. In Twenty-eighth ACM Symposium on Principles of Programming Languages, POPL 2001, pp. 14-26, London, UK, 2001.
21. S. Ishtiaq and D. Pym. Kripke resources models of a dependently-typed bunched λ-calculus. In Thirteenth International Workshop on Computer Science Logic, CSL'99, Madrid, Spain, pp. 235-249, volume 1683 of Lecture Notes in Computer Science, springer, 1999.
22. C. Kreitz, H. Mantel, J. Otten, and S. Schmitt. Connection-based proof construction in Linear Logic. In Fourteenth Internatinal Conference on Automated Deduction, CADE-14, Townsville, Australia, pp. 207-221, volume 1249 of Lecture Notes in Computer Science, Springer, 1997.
23. Y. Lafont. The finite model property for various fragments of linear logic. Journal of Symbolic Logic, 62, 1202-1208, 1997.
24. D. Larchey-Wendling, D. Méry, and D. Galmiche. STRIP: Structural sharing for efficient proof-search. In First International Joint Conference on Automated Reasoning, IJCAR 2001, Siena, Italy, pp. 696-700, Volume 2083 of Lecture Notes in Computer Science, Springer, 2001.
25. H. Mantel and J. Otten. IinTAP: a tableau prover for linear logic. In International Conference on Analytic Tableaux and Related Methods, TABLEAUX'99, Saratoga Springs, NY, USA, pp. 216-231, volume 1617 of Lecture Notes in Computer Science, Springer, 1999.
26. R.K. Meyer, M.A. McRobbie, and N. Belnap. Linear analytic tableaux. In Fourth Workshop on Theorem Proving with Analytic Tableaux and Related Methods, St Goar am Rhein, Germany pp. 278-293, volume 918 of Lecture Notes in Computer Science, Springer, 1995.
27. P. O'Hearn. Resource interpretations, bunched implications and the αλ-calculus. In Fourth International Conference on Typed Lambda Calculi and Applications, TLCA'99, L'Aquila, Italy, pp. 258-279, volume 1581 of Lecture Notes in Computer Science, Springer, 1999.
28. P. O'Hearn, J. Reynolds, and H. Yang. Local reasoning about programs that alter data structures. In Fifteenth International Workshop on Computer Logic, CSL 2001, Paris, France, pp. 1-19, volume 2142 of Lecture Notes in Computer Science, Springer, 2001.
29. P.W. O'Hearn and D. Pym. The logic of bunched implications. Bulletin of Symbolic Logic, 5, 215-244, 1999.
30. M. Okada and K. Terui Completeness proofs for linear logic based on proof search method (preliminary report). In Type Theory and its Applications to Computer Systems, pp. 57-75, RIMS, Kyoto University, 1998.
31. M. Okada and K. Terui. The finite model property for various fragments of intuitionistic linear logic. Journal of Symbolic Logic, 64, 790-802, 1999.
32. H. Ono. Decidability and finite model property of substructural logics. In The Tbilisi Symposium on Logic, Language and Computation, pp. 262-274, CSLI Publications, 1997.
33. L. Pinto and R. Dyckhoff. Loop-free construction of counter-models for intuitionistic propositional logic. In Symposia Gaussiana, Behara, Fritsch, and Lintz, eds, pp. 225-232, 1995.
34. D. Pym. On bunched predicate logic. In Fourteenth Symposium on Logic in Computer Science, Trento, Italy, pp. 183-192, IEEE Computer Society Press, 1999.
35. D.J. Pym. The Semantics and Proof Theory of the Logic of Bunched Implications, volume 26 of of Applied Logic Series. Kluwer Academic Publishers, 2002.
36. K. Terui. Labelled tableau calculi generating simple models for substructural logics. Technical report, ILLC publications, University of Amsterdam, 1999.
37. A. Urquhart. Semantics for relevant logic. Journal of Symbolic Logic, 37, 159-169, 1972.
38. A. Voronkov. Proof-search in intuitionistic logic based on constraint satisfaction. In Fifth International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, Terrasini, Italy, pp. 312-327, volume 1071 of Lecture Notes in Artificial Intelligence, Springer, 1996.