A logic for reasoning about coherent conditional probability: A modal fuzzy logic approach

Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)

Volumn 3229, Issue , 2004, Pages 213-225

  Marchioni, Enrico ^a,b   Godo, Lluís ^a  

^a ARTIFICIAL INTELLIGENCE RESEARCH INSTITUTE IIIA CSIC   (Spain)

^b UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; MANY VALUED LOGICS; PROBABILITY; ALGEBRA; FUZZY SETS; MATHEMATICAL MODELS; MODAL ANALYSIS; PROBLEM SOLVING; THEOREM PROVING;

COHERENT CONDITIONAL PROBABILITY; CONDITIONAL EVENTS; CONDITIONAL PROBABILITIES; FUZZY MODAL LOGIC; KRIPKE STRUCTURE; MODAL FUZZY LOGIC; PROBABILITY ASSESSMENTS; TRUTH VALUES;

FUZZY LOGIC; FORMAL LOGIC;

CONDITIONAL PROBABILITY; MODAL FUZZY LOGIC; PROBABILITY THEORY; REASONING;

EID: 22944455574     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-30227-8_20     Document Type: Conference Paper

References (24)

1. BACCHUS, F. Representing and Reasoning with Probabilistic Knowledge. MIT-Press, Cambridge Massachusetts, 1990.
2. BIAZZO V., GILIO A., LUKASIEWICZ T., AND SANFILIPPO G. Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning. In Proc. of ECSQARU-2001, 290-302, 2001.
3. CINTULA P. The ŁΠ and ŁΠ1/2 propositional and predicate logics. Fuzzy Sets and Systems 124, 289-302, 2001.
4. COLETTI, G. AND SCOZZAFAVA R. Probabilistic Logic in a Coherent Setting. Kluwer Academic Publisher, Dordrecht, The Netherlands, 2002.
5. ESTEVA F., GODO L. AND MONTAGNA F. The ŁΠ and ŁΠ1/2 logics: two complete fuzzy logics joining Łukasiewicz and Product logic. Archive for Mathematical Logic 40, 39-67, 2001.
6. FAGIN R., HALPERN J. Y. AND MEGIDDO N. A logic for reasoning about probabilities. Information and Computation 87(1/2), 78-128, 1990.
7. FATTAROSI-BARNABA M. AND AMATI G. Modal operators with probabilistic interpretations I. Studia Logica 48, 383-393, 1989.
8. FLAMINIO T. AND MONTAGNA F. A logical and algebraic treatment of conditional probability. To appear in Proc. of IPMU'04, Perugia, Italy, 2004.
9. GAIFMAN H. AND SNIR M. Probabilities over rich languages, testing and randomness The Journal of Symbolic Logic 47, No. 3, 495-548, 1982.
10. GERLA, G. Inferences in probability logic. Artificial Intelligence 70, 33-52, 1994.
11. GODO L., ESTEVA F. AND HÁJEK P. Reasoning about probability using fuzzy logic. Neural Network World 10, No. 5, 811-824, 2000.
12. HÁJEK P. Metamathematics of Fuzzy Logic. Kluwer 1998.
13. HÁJEK P., GODO L. AND ESTEVA F. Fuzzy logic and probability. In Proc. of UAI'95, Morgan Kaufmann, 237-244, 1995.
14. Halpern J. Y. An analysis of first-order logics of probability. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI'89), 1375-1381, 1989.
15. HALPERN J. Y. Reasoning about Uncertainty. The MIT Press, Cambridge Massachusetts, 2003.
16. KEISLER J. Probability quantifiers. In Model-theoretic Logics, J. Barwise and S. Feferman (eds.), Springer-Verlag, New York, 539-556, 1985.
17. KRAUSS P. H. Representation of conditional probability measures on Boolean algebras. In Acta Mathematica Academiae Scientiarum Hungaricae, Tomus 19(3-4), 229-241, 1969.
18. NILSSON N. J. Probabilistic logic Artificial Intelligence 28, No. 1, 71-87, 1986.
19. OGNJANOVIĆ Z., RAŠKOVIĆ M. Some probability logics with new types of probability operators. Journal of Logic and Computation, Vol. 9, Issue 2, 181-195, 1999.
20. RAŠKOVIĆ M., OGNJANOVIĆ Z. AND MARKOVIĆ Z. A probabilistic approach to default reasoning. In Proc. of NMR 2004, Whistler (Canada), 335-341, 2004.
21. RAŠKOVIĆ M., OGNJANOVIĆ Z. AND MARKOVIĆ Z. A logic with conditional probabilities. In Proc. of JELIA'2004, in this volume.
22. SCOTT D. AND KRAUSS P. Assigning probabilities to logical formulas In Aspects of Inductive Logic, J. Hintikka and P. Suppes (eds.), North-Holland, Amsterdam, 219-264, 1966
23. VAN DER HOEK, W. Some considerations on the logic PFD. Journal of Applied Non-Classical Logics Vol. 7, Issue 3, 287-307, 1997.
24. WILSON N. AND MORAL S. A logical view of probability In Proc. of the 11th European Conference on Artificial Intelligence (ECAI'94), 386-390, 1994.