From classical description logic to n-graded fuzzy description logic

2010 IEEE World Congress on Computational Intelligence, WCCI 2010

Volumn , Issue , 2010, Pages

  Cerami, Marco ^a   García Cerdaña, Àngel ^a   Esteva, Francesc ^a  

^a ARTIFICIAL INTELLIGENCE RESEARCH INSTITUTE IIIA CSIC   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL LOGIC; DESCRIPTION LANGUAGES; DESCRIPTION LOGIC; FINITE CHAINS; FUZZY DESCRIPTION LOGIC; KNOWLEDGE BASIS; KNOWLEDGE REPRESENTATION LANGUAGE; NATURAL EXTENSION; REAL APPLICATIONS; REASONING TASKS; RESIDUATED LATTICES; T - NORM;

ARTIFICIAL INTELLIGENCE; DATA DESCRIPTION; FUZZY SYSTEMS; KNOWLEDGE REPRESENTATION;

FUZZY LOGIC;

EID: 78549251724     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FUZZY.2010.5584114     Document Type: Conference Paper

References (29)

1. P. Aglianò and F. Montagna. Varieties of BL-algebras I. General properties. Journal of Pure and Applied Algebra, 181(2-3):105-129, 2003.
2. F. Baader and W. Nutt. Basic Description Logics. In F. Baader, D. Calvanese, D. L. McGuinness, D. Nardi, and P. F. Patel-Schneider, editors, The Description Logic Handbook: Theory, Implementation, and Applications, pages 47-100. Cambridge University Press, 2003.
3. M. Baaz. Infinite-valued Gödel Logics with 0-1-Projections and Relativizations. In P. Hájek, editor, Proc. Gödel'96, Logic Foundations of Mathematics, Computer Science and Physics - Kurt Gödel's Legacy, volume 6 of Lecture Notes in Logic, pages 23-33. Springer, 1996.
4. M. Baaz, C. G. Fermüller, G. Salzer, and R. Zach. MUltlog 1.0: Towards an Expert System for Many-Valued Logics. In CADE-13: Proceedings of the 13th International Conference on Automated Deduction, pages 226-230, London, UK, 1996. Springer-Verlag.
5. M. Baaz, C. G. Fermüller, and R. Zach. Systematic Construction of Natural Deduction Systems for Many-Valued Logics. In Proceedings of ISMVL, pages 208-213, 1993.
6. F. Bobillo, M. Delgado, and J. Gómez-Romero. A crisp representation for fuzzy SHOIN with fuzzy nominals and general concept inclusions. In Proc. of the 2nd International Workshop on Uncertainty Reasoning for the Semantic Web (URSW 06), 2006.
7. F. Bobillo, M. Delgado, J. Gómez-Romero, and U. Straccia. Fuzzy description logics under Gödel semantics. International Journal of Approximate Reasoning, 50(3):494-514, 2009.
8. F. Bobillo and U. Straccia. Fuzzy description logics with general tnorms and datatypes. Fuzzy Sets and Systems, 160(23):3382-3402, 2009.
9. F. Bou, F. Esteva, L. Godo, and R. Rodríguez. On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice. Journal of Logic and Computation, doi: 10.1093/logcom/exp062, 2009.
10. M. Cerami, F. Esteva, and F. Bou. Decidability of a description logic over infinite-valued product logic. Accepted in the Knowledge Representation and Reasoning Conference 2010.
11. P. Cintula and P. Hájek. Triangular norm based predicate fuzzy logics. Fuzzy Sets and Systems., 161:311-346, 2010.
12. F. Esteva, J. Gispert, L. Godo, and C. Noguera. Adding truth-constants to logics of continuous t-norms: axiomatization and completeness results. Fuzzy Sets and Systems, 158(6):597-618, 2007.
13. F. Esteva, L. Godo, P. Hájek, and M. Navara. Residuated fuzzy logics with an involutive negation. Archive for Mathematical Logic, 39(2):103-124, 2000.
14. F. Esteva, L. Godo, and M. Montagna. Equational Characterization of the Subvarieties of BL Generated by t-norm Algebras. Studia Logica, 76(2):161-200, 2004.
15. À. García-Cerdaña, E. Armengol, and F. Esteva. Fuzzy description logics and t-norm based fuzzy logics. International Journal of Approximate Reasoning, doi:10.1016/j.ijar.2010.01.001, 2010.
16. P. Hájek. Metamathematics of Fuzzy Logic, volume 4 of Trends in Logic. Studia Logica Library. Kluwer Academic Publishers, Dordrecht, 1998.
17. P. Hájek. Making fuzzy description logic more general. Fuzzy Sets and Systems, 154(1):1-15, 2005.
18. P. Hájek. Computational complexity of t-norm based propositional fuzzy logics with rational truth constants. Fuzzy Sets and Systems, 157(5):677-682, 2006.
19. P. Hájek. What does mathematical fuzzy logic offer to description logic? In Elie Sanchez, editor, Fuzzy Logic and the Semantic Web, Capturing Intelligence, chapter 5, pages 91-100. Elsevier, 2006.
20. P. Hájek and P. Cintula. On theories and models in fuzzy predicate logics. Journal of Symbolic Logic, 71(3):863-880, 2006.
21. T. Lukasiewicz and U. Straccia. Managing uncertainty and vagueness in Description Logics for the Semantic Web. Journal of Web Semantics, 6(4):291-308, 2008.
22. G. Mayor and J. Torrens. On a class of operators for expert systems. International Journal of Intelligent Systems, 8:771-778, 1993.
23. G. Mayor and J. Torrens. Triangular norms in discrete settings. In E.P. Klement and R. Messiar, editors, Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pages 189-230. Elsevier, Amsterdam, 2005.
24. A. Monteiro. Sur les algèbres de Heyting simétriques. Portugaliae Mathematica, 39:1-237, 1980.
25. D. Sánchez and A.G.B. Tettamanzi. Fuzzy quantification in fuzzy description logics. In E. Sanchez, editor, Fuzzy Logic and the Semantic Web (Capturing Intelligence), chapter 8, pages 135-159. Elsevier, 2006.
26. U. Sattler, D. Calvanese, and R. Molitor. Relationship with other formalisms. In The Description Logic Handbook: Theory, Implementation and Applications, pages 137-177. Cambridge University Press, 2003.
27. G. Stoilos, G. Stamou, J.Z. Pan, V. Tzouvaras, and I. Horrocks. Reasoning with very expressive Fuzzy Description Logics. Journal of Artificial Intelligence Research, 30(8):273-320, 2007.
28. U. Straccia. Reasoning within Fuzzy Description Logics. Journal of Artificial Intelligence Research, 14:137-166, 2001.
29. U. Straccia and F. Bobillo. Mixed Integer Programming, General Concept Inclusions and Fuzzy Description Logics. Mathware and Soft Computing, 14(3):247-259, 2007.