Possibilistic conditioning framed in fuzzy logics

International Journal of Approximate Reasoning

Volumn 43, Issue 2, 2006, Pages 133-165

  Marchioni, Enrico ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

Coherence; Compactness; Comparative conditional possibility; Conditional possibility; Fuzzy logics; Possibility theory

Indexed keywords

COMPUTATION THEORY; FORMAL LOGIC; MATHEMATICAL OPERATORS; MODAL ANALYSIS; OPTIMIZATION; PROBABILISTIC LOGICS;

COMPACTNESS; COMPARATIVE CONDITIONAL POSSIBILITY; CONDITIONAL POSSIBILITY; POSSIBILITY THEORY;

FUZZY SETS;

EID: 33748439968     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2006.03.002     Document Type: Article

References (46)

1. B. Bouchon-Meunier, G. Coletti, C. Marsala, Possibilistic conditional events, in: Proceedings of IPMU 2000, Madrid, Spain, 2000, pp. 1561-1566.
2. Bouchon-Meunier B., Coletti G., and Marsala C. Independence and possibilistic conditioning. Annals of Mathematics and Artificial Intelligence 35 (2002) 107-123
3. Bouchon-Meunier B., Coletti G., and Marsala C. Conditional possibility and necessity. Technologies for Constructing Intelligent Systems (2002), Physica Verlag, Heidelberg 59-71
4. Butnariu E., Klement E.P., and Zafrany S. On triangular norm-based propositional fuzzy logics. Fuzzy Sets and Systems 69 (1995) 241-255
5. Cignoli R., Esteva F., Godo L., and Torrens A. Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Computing 4 (2000) 106-112
6. Cintula P. The ŁΠ and Ł Π frac(1, 2) propositional and predicate logics. Fuzzy Sets and Systems 124 (2001) 21-34
7. Cintula P. Advances in the ŁΠ and Ł Π frac(1, 2) logics. Archive for Mathematical Logic 42 (2003) 449-468
8. Cintula P., and Navara M. Compactness of fuzzy logics. Fuzzy Sets and Systems 143 (2004) 59-73
9. Coletti G., and Scozzafava R. Probabilistic Logic in a Coherent Setting (2002), Kluwer Academic Publisher, Dordrecht, The Netherlands
10. G. Coletti, B. Vantaggi, Independence in conditional possibility theory, in: Proceedings of the 10th IPMU International Conference, Perugia, Italy, 2004, pp. 849-856.
11. G. Coletti, B. Vantaggi, Representability of ordinal relations on a set of conditional events, Theory and Decision, in press.
12. Coletti G., and Vantaggi B. Comparative conditional possibilities. In: Godo L. (Ed). ECSQARU'05. Lecture Notes in Artificial Intelligence (2005), Springer-Verlag, Berlin, Heidelberg 872-883
13. De Baets B., and Kerre E. A primer on solving fuzzy relational equations on the unit interval. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2 (1994) 205-225
14. De Baets B., Tsiporkova E., and Mesiar R. Conditioning in possibility theory with strict order norms. Fuzzy Sets and Systems 106 (1999) 121-129
15. Dubois D., Lang J., and Prade H. Possibilistic Logic. In: Gabbay D.M., et al. (Ed). Handbook of Logic in Artificial Intelligence and Logic Programming vol. 3 (1994), Oxford University Press 439-513
16. Dubois D., and Prade H. Possibility Theory (1988), Plenum Press, New York
17. Dubois D., and Prade H. The logical view of conditioning and its application to possibility and evidence theories. International Journal of Approximate Reasoning 4 (1990) 23-46
18. Dubois D., and Prade H. Possibility theory: Qualitative and quantitative aspects. In: Gabbay D.M., and Smets Ph. (Eds). Handbook of Defeasible Reasoning and Uncertainty Management Systems vol. 1 (1998), Kluwer Academic Publisher, Dordrecht, The Netherlands 169-226
19. Esteva F., and Godo L. Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Sets and Systems 124 (2001) 271-288
20. Esteva F., Godo L., Hájek P., and Navara M. Residuated fuzzy logics with an involutive negation. Archive for Mathematical Logic 39 (2000) 103-124
21. Esteva F., Godo L., and Montagna F. The ŁΠ and Ł Π frac(1, 2) logics: two complete fuzzy logics joining Łukasiewicz and product logic. Archive for Mathematical Logic 40 (2001) 39-67
22. F. Esteva, L. Godo, C. Noguera, On rational Weak Nilpotent Minimum logics, Journal of Multiple-Valued Logic and Soft Computing, in press.
23. Ferracuti L., and Vantaggi B. Independence and conditional possibility for strictly monotone triangular norms. International Journal of Intelligent Systems 21 (2006) 299-323
24. T. Flaminio, NP-containment for the coherence test of an assessment of conditional probability: a fuzzy logic approach, Archive for Mathematical Logic, in press.
25. T. Flaminio, E. Marchioni, Extending the Monoidal T-norm based Logic with an independent involutive negation, in: Proceedings of EUSFLAT'05, 2005, pp. 860-865.
26. T. Flaminio, E. Marchioni, T-norm based logics with an independent involutive negation, submitted for publication.
27. Flaminio T., and Montagna F. A logical and algebraic treatment of conditional probability. Archive for Mathematical logic 44 2 (2005) 245-262
28. Godo L., Esteva F., and Hájek P. Reasoning about probability using fuzzy logic. Neural Network World 10 5 (2000) 811-824
29. L. Godo, E. Marchioni, Coherent conditional probability in a fuzzy logic setting, Logic Journal of the IGPL, in press.
30. Hájek P. Basic fuzzy logic and BL-algebras. Soft Computing 2 3 (1998) 124-128
31. Hájek P. Metamathematics of Fuzzy Logic (1998), Kluwer Academic Publisher, Dordrecht, The Netherlands
32. P. Hájek, L. Godo, F. Esteva, Fuzzy logic and probability, in: Proceedings of UAI'95, 1995, pp. 237-244.
33. Hájek P., and Tulipani S. Complexity of fuzzy probability logics. Fundamenta Informaticae 45 (2001) 1-7
34. Halpern J.Y. Reasoning about Uncertainty (2003), The MIT Press, Cambridge, Massachusetts
35. Hisdal E. Conditional possibilities independence and noninteraction. Fuzzy Sets and Systems 1 (1978) 283-297
36. Horčík R., and Cintula P. Product Łukasiewicz logic. Archive for Mathematical Logic 43 4 (2004) 477-503
37. Jenei S., and Montagna F. A proof of standard completeness for Esteva and Godo's logic MTL. Studia Logica 70 (2002) 183-192
38. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer Academic Publisher, Dordrecht, The Netherlands
39. Marchioni E. A logical treatment of possibilistic conditioning. In: Godo L. (Ed). ECSQARU'05. Lecture Notes in Artificial Intelligence (2005), Springer-Verlag, Berlin Heidelberg 701-713
40. Marchioni E., and Godo L. A logic for reasoning about coherent conditional probability: a modal fuzzy logic approach. In: Alferes J.J., and Leite J.A. (Eds). Logics in Artificial Intelligence. Lecture Notes in Artificial Intelligence (2004), Springer-Verlag, Berlin, Heidelberg 213-225
41. E. Marchioni, F. Montagna, A note on definability in Ł Π frac(1, 2), in: Proceedings of the 11th IPMU International Conference, Paris, France, in press.
42. Nguyen L. On conditional possibility distributions. Fuzzy Sets and Systems 1 (1978) 299-309
43. Pavelka J. On fuzzy logic I, II, III. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 25 (1979) 45-52 119-134, 447-464
44. P. Savický, R. Cignoli, F. Esteva, L. Godo, C. Noguera, On product logic with truth-constants, Journal of Logic and Computation, in press.
45. Trillas E. Sobre funciones de negación en teoría de conjuntos difusos. Stochastica 3 1 (1979) 47-59
46. Zadeh L. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28