Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive Datalog

Logical Methods in Computer Science

Volumn 8, Issue 1, 2012, Pages

  Rudolph, Sebastian ^a   Krötzsch, Markus ^b   Hitzler, Pascal ^c  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c WRIGHT STATE UNIVERSITY   (United States)

Author keywords

Datalog; Decision diagrams; Description logics; Type elimination

Indexed keywords

EID: 84860014850     PISSN: None     EISSN: 18605974     Source Type: Journal    
DOI: 10.2168/LMCS-8(1:12)2012     Document Type: Article

References (36)

1. Pablo Arrighi and Gilles Dowek. A computational definition of the notion of vectorial space. In Narciso Martí-Oliet, editor, Proceedings of WRLA-2004, volume 117 of Electronic Notes in Theoretical Computer Science, pages 249-261. Elsevier, 2004.
2. Pablo Arrighi and Gilles Dowek. Linear-algebraic lambda-calculus: higher-order, encodings, and confluence. In Andrei Voronkov, editor, Proceedings of RTA-2008, volume 5117 of Lecture Notes in Computer Science, pages 17-31. Springer, 2008.
3. Pablo Arrighi and Alejandro Díaz-Caro. Scalar System F for linear-algebraic?-calculus: Towards a quantum physical logic. In Bob Coecke, Prakash Panangaden, and Peter Selinger, editors, Proceedings of QPL-2009, volume 270/2 of Electronic Notes in Theoretical Computer-Science, pages 219-229. Elsevier, 2011.
4. Pablo Arrighi, Alejandro Díaz-Caro, and Benoît Valiron. A type system for the vectorial aspects of the linear-algebraic lambda-calculus. In Proceedings of the 7th International Workshop on Developments of Computational Methods (DCM 2011), Zurich, Switzerland, 2011. To appear in EPTCS. Draft at http: //www.diaz-caro.info/vectorial.pdf.
5. Ariel Arbiser, Alexandre Miquel, and Alejandro Ríos. The?-calculus with constructors: Syntax, confluence and separation. Journal of Functional Programming, 19(5): 581-631, 2009.
6. Henk P. Barendregt. Lambda calculi with types. Handbook of Logic in Computer Science: Volume 2. Oxford University Press, 1992.
7. Olivier Bournez and Mathieu Hoyrup. Rewriting logic and probabilities. In Robert Nieuwenhuis, editor, Proceedings of RTA-2003, volume 2706 of Lecture Notes in Computer Science, pages 61-75. Springer, 2003.
8. Gerard Boudol. Lambda-calculi for (strict) parallel functions. Information and Computation, 108(1): 51-127, 1994.
9. Horatiu Cirstea, Claude Kirchner, and Luigi Liquori. The Rho Cube. In Furio Honsell and Marino Miculan, editors, Proceedings of FOSSACS-2001, volume 2030 of Lecture Notes in Computer Science, pages 168-183. Springer, 2001.
10. Coq Dev. Team. The Coq proof assistant reference manual. INRIA, 8.2 edition, February 2009.
11. Alejandro Díaz-Caro, Simon Perdrix, Christine Tasson, and Benoît Valiron. Equivalence of algebraic?-calculi. In Informal Proceedings of the 5th International Workshop on Higher-Order Rewriting, HOR-2010, pages 6-11, Edinburgh, UK, July 14, 2010.
12. Alessandra Di Pierro, Chris Hankin, and Herbert Wiklicky. Probabilistic?-calculus and quantitative program analysis. Journal of Logic and Computation, 15(2): 159-179, 2005.
13. Daniel J. Dougherty. Adding algebraic rewriting to the untyped lambda calculus. Information and Computation, 101(2): 251-267, 1992.
14. Ugo de'Liguoro and Adolfo Piperno. Non deterministic extensions of untyped ?-calculus. Information and Computation, 122(2): 149-177, 1995.
15. Ugo Dal Lago and Margherita Zorzi. Probabilistic operational semantics for the lambda calculus. Preprint at arXiv: 1104.0195, April 2011.
16. Thomas Ehrhard. Finiteness spaces. Mathematical Structures in Computer Science, 15(4): 615-646, 2005.
17. Thomas Ehrhard. A finiteness structure on resource terms. In Proceedings of LICS-2010, pages 402-410. IEEE Computer Society, 2010.
18. Thomas Ehrhard and Laurent Regnier. The differential lambda-calculus. Theoretical Computer-Science, 309(1): 1-41, 2003.
19. Jean-Yves Girard. Une extension de l'interpretation de Gödel à l'analyse, et son application à l'élimination des coupures dans l'analyse et la théorie des types. In Jens Erik Fenstad, editor, Proceedings of the 2nd Scandinavian Logic Symposium, volume 63 of Studies in Logic and the Foundations of Mathematics, pages 63-92. North-Holland, 1971.
20. Jean-Yves Girard. Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieure. PhD thesis, Universite Paris Diderot, Paris, France, 1972.
21. Lov K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on Theory of computing, STOC-96, pages 212-219. ACM, 1996.
22. Oltea Mihaela Herescu and Catuscia Palamidessi. Probabilistic asynchronous p-calculus. In Jerzy Tiuryn, editor, Proceedings of F0SSACS-2000, volume 1784 of Lecture Notes in Computer-Science, pages 146-160. Springer, 2000.
23. Jean-Pierre Jouannaud and Hélène Kirchner. Completion of a set of rules modulo a set of equations. SIAM Journal on Computing, 15(4): 1155-1194, 1986.
24. Jean-Louis Krivine. Lambda-calcul: types et modèles. Etudes et recherches en informatique. Masson, 1990.
25. F: raising ML to the power of System F. In Proceedings of the eighth ACM SIGPLAN international conference on Functional programming, ICFP'03, pages 27-38, New York, NY, USA, 2003. ACM.
26. Barbara Petit. A polymorphic type system for the lambda-calculus with constructors. In Pierre-Louis Curien, editor, Proceedings of TLCA-2009, volume 5608 of Lecture Notes in Computer Science, pages 234-248. Springer, 2009.
27. Gerald E. Peterson and Mark E. Stickel. Complete set of reductions for some equational theories. Journal of the ACM, 28(2): 233-264, 1981.
28. John C. Reynolds. Towards a theory of type structure. In Bernard Robinet, editor, Programming Symposium: Proceedings of the Colloque sur la Programmation, volume 19 of Lecture Notes in Computer Science, pages 408-425. Springer, 1974.
29. Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5): 1484-1509, 1997.
30. William W. Tait. Intensional interpretations of functionals of finite type I. The Journal of Symbolic Logic, 32(2): 198-212, 1967.
31. Christine Tasson. Algebraic totality, towards completeness. In Pierre-Louis Curien, editor, Proceedings of TLCA-2009, volume 5608 of Lecture Notes in Computer Science, pages 325-340. Springer, 2009.
32. TeReSe. Term Rewriting Systems, volume 55 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 2003.
33. Benoît Valiron. Semantics of a typed algebraic lambda-calculus. In S. Barry Cooper, Prakash Panangaden, and Elham Kashefi, editors, Proceedings DCM-2010, volume 26 of Electronic Proceedings in Theoretical Computer Science, pages 147-158. Open Publishing Association, 2010.
34. Benoît Valiron. Coq proof. www.monoidal.net/vectorial-lvec-coqproof.tar.bz2, 2011.
35. Lionel Vaux. On linear combinations of lambda-terms. In Franz Baader, editor, Proceedings of RTA-2007, volume 4533 of Lecture Notes in Computer Science, pages 374-388. Springer, 2007.
36. Lionel Vaux. The algebraic lambda calculus. Mathematical Structures in Computer Science, 19(5): 1029-1059, 2009.