Conditional probability and defeasible inference

Journal of Philosophical Logic

Volumn 34, Issue 1, 2005, Pages 97-119

  Costa, Horacio Arló ^a   Parikh, Rohit ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Belief revision; Conditional probability; Conditionals; Countable additivity; Non monotonic logic

Indexed keywords

EID: 35348859879     PISSN: 00223611     EISSN: 15730433     Source Type: Journal    
DOI: 10.1007/s10992-004-5553-6     Document Type: Article

References (36)

1. Adams, E. (1975) The Logic of Conditionals, Reidel, Dordrecht.
2. Arló-Costa, H. and Shapiro, S. (1992) Maps between nonmonotonic and conditional logics, in B. Nebel, C. Rich and W. Swar tout (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference, pp. 553-564.
3. Arló-Costa, H. (1999) Qualitative and probabilistic models of full belief, in S. Buss, P. Hajek and P. Pudlak (eds.), Proceedings of Logic Colloquim'98, Lecture Notes on Logic 13, ASL, A. K. Peters.
4. Arló-Costa, H. and Thomason, R. (2001) Iterative probability kinematics, J. Philos. Logic 46,479-524.
5. Arló-Costa, H. (2001) Bayesian epistemology and epistemic conditionals: On the status of the export-import laws, J. Philosophy XCVIII(11), 555-598.
6. Blume, L., Brandenburger, A. and Dekel, E. (1991) Lexicographic probabilities and choice under uncertainty, Econometrica 59(1), 61-79.
7. Cross, C. and Nute, D. (1998) Conditional logic, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd edn, Extensions of Classical Logic III, Reidel, Dordrecht.
8. De Finetti, B. (1936) Les probabilités nulls, Bull. Sci. Math. (premiere partie) 60, 275-288.
9. Delgrande, J. (1987) A first-order logic for prototypical properties, Artificial Intelligence 33,105-130.
10. Dubins, L. E. (1975) Finitely additive conditional probabilities, conglomerability, and disintegrations, Ann. Probab. 3, 89-99.
11. Gabbay, D. M. (1985) Theoretical foundations for nonmonotonic reasoning in expert systems, in K. R. Apt (ed.), Proceedings NATO Advanced Study Institute on Logics and Models of Concurrent Systems, pp. 439-457.
12. Gärdenfors, P. (1993) The role of expectations in reasoning, Lund University Cognitive Studies, 21.
13. Gärdenfors, P. and Makinson, D. (1994) Nonmonotonic inference based on expectations, Artificial Intelligence 65, 197-245.
14. Ginsberg, M. (1986) Counterfactuals, Artificial Intelligence 30, 35-79.
15. Grove, A. (1988) Two modelings for theory change, J. Philos. Logic 17, 157-170.
16. Halpern, J. (2000) Lexicographic probability, conditional probability and nonstandrad probability, Manuscript, Cornell University, November 14.
17. Hammond, P. J. (1994) Elementary non-Archimedean representations of probability for decision theory and games, in Humphreys (ed.), Patrick Suppes: Scientific Philosopher, Vol. 1, Kluwer.
18. Hawthorne, J. (1998) On the logic of nonmonotonic conditionals and conditional probabilities: Predicate logic, J. Philos. Logic 27, 1-34.
19. Jeffreys, H. (1961) Theory of Probability, 3rd edn, New York, Oxford, p. 25.
20. Katsuno, H. and Satoh, K. (1996) A unified view of consequence relation, belief re-vision and conditional logic, in G. Crocco, L. Fariñas del Cerro and H. Herzig (eds.), Conditionals from Philosophy to Computer Science, Oxford University Press, pp. 33-65.
21. Kraus, S., Lehmann, D. and Magidor, M. (1990) Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence 44, 167-207.
22. Kyburg, H. E., Jr. (1961) Probability and the Logic of Rational Belief, Wesleyan University Press, Middletown.
23. Lehmann, D. and Magidor, M. (1992) What does a conditional base entails? Artificial Intelligence 55, 1-60.
24. Levi, I. (1988) Iteration of conditionals and the Ramsey test, Synthese 76, 49-81.
25. Levi, I. (1996) For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference, and Nonmonotonic Reasoning, Cambridge University Press, Cambridge.
26. Lewis, D. (1976) Propoabilities of conditionals and conditional probabilities, The Philosophical Review 85, 297-315.
27. Makinson, D. (1989) General theory of cumulative inference, in M. Reinfrank (ed.), Proceedings Second International Workshop on Nonmonotonic Reasoning, Lecture Notes in Comput. Sci., Springer-Verlag, Berlin.
28. McGee, V. (1994) Learning the impossible, in Ellery Eells and Brian Skyrms (eds.), Probability and Conditionals: Belief Revision and Rational Decision, Cambridge University Press, Cambridge, England, pp. 179-199.
29. Parikh, R. and Parnes, M. (1972) Conditional probability can be defined for arbitrary pairs of sets of reals, Advances in Math. 9, 520-522.
30. Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, Monterrey, CA.
31. Popper, K. (1968) The Logic of Scientific Discovery, revised edn, Hutchinson, London.
32. Renyi, A. (1970) Foundations of Probability, Holden-Day, San Francisco.
33. Seidenfeld, T. (2001) Remarks on the theory of conditional probability: Some issues of finite versus countable additivity, in V. F. Hendricks, S. A. Pedersen and K. F. Jorgensen (eds.), Probability Theory: Philosophy, Recent History and Relations to Science, Kluwer Academic Publishers, Dordrecht, pp. 167-178.
34. Shoham, Y. (1987) Reasoning About Change, MIT Press, Cambridge, MA.
35. Spohn, W. (1988) A general non-probabilistic theory of inductive inference, in W. Harper and B. Skyrms (eds.), Causation in Decision, Belief Change and Statistics, Reidel, Dordrecht, pp. 105-134.
36. van Fraassen, B. (1995) Fine-grained opinion, probability, and the logic of full belief, J. Philos. Logic 24, 349-377.