Logical questions behind the lottery and preface paradoxes: Lossy rules for uncertain inference

Synthese

Volumn 186, Issue 2, 2012, Pages 511-529

  Makinson, David ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Conjunction; Inconsistency; Lossy rules; Lottery paradox; Preface paradox; Rationality; Uncertain inference

Indexed keywords

EID: 84862261813     PISSN: 00397857     EISSN: 15730964     Source Type: Journal    
DOI: 10.1007/s11229-011-9997-2     Document Type: Article

References (25)

1. Adams E. W. (1966) Probability and the logic of conditionals. In: Hintikka J. K. K., Suppes P. (eds) Aspects of inductive logic. North-Holland, Amsterdam, pp 265-316.
2. Adams E. W. (1975) The logic of conditionals. Reidel, Dordrecht.
3. Adams E. W. (1996) Four probability-preserving properties of inferences. Journal of Philosophical Logic 25: 1-24.
4. Adams E. W. (1998) A primer of probability logic. CSLI, Stanford.
5. Boole G. (1854) Laws of thought. Dover, New York (Reprinted, 2003).
6. Hawthorne J. (1996) On the logic of nonmonotonic conditionals and conditional probabilities. Journal of Philosophical Logic 25: 185-218.
7. Hawthorne J., Makinson D. (2007) The quantitative/qualitative watershed for rules of uncertain inference. Studia Logica 86: 249-299.
8. Johnson M., Parikh R. (2008) Probabilistic conditionals are almost monotonic. The Review of Symbolic Logic 1: 73-80.
9. Kraus S., Lehmann D., Magidor M. (1990) Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44: 167-207.
10. Kyburg H. E. (1961) Probability and the logic of rational belief. Wesleyan University Press, Middletown, CT.
11. Kyburg, H. E. (1963). Probability and randomness. Theoria, 29, 27-55 (Reprinted from Kyburg, H. E. (1983). Epistemology and Inference (Minneapolis: Minnesota Press)).
12. Kyburg H. E. (1970a) Probability and inductive logic. Macmillan, London.
13. Kyburg H. E. (1970b) Conjunctivitis. In: Swain M. (eds) Induction, acceptance and rational belief. Reidel, Dordrecht, pp 55-82.
14. Kyburg H. E. (1997) The rule of adjunction and reasonable inference. The Journal of Philosophy 94: 109-125.
15. Makinson D. (1965) The paradox of the preface. Analysis 25: 205-207.
16. Makinson D. (2005) Bridges from classical to nonmonotonic logic. College Publications, London.
17. Makinson, D. (2011). Conditional probability in the light of qualitative belief change. Journal of Philosophical Logic, 40, 121-153. A preliminary version appeared in Hosni & Montagna (Eds.), Probability, Uncertainty and Rationality vol 10, Springer: CRM Series, Edizioni della Scuola Normale Superiore, Pisa, 2010.
18. Paris J., Simmonds R. (2009) O is not enough. Review of Symbolic Logic 2: 298-309.
19. Pearl J. (1988) Probabilistic reasoning in intelligent systems. Morgan Kaufmann, Los Altos, CA.
20. Pearl J. et al (1989) Probabilistic semantics for nonmonotonic reasoning: A survey. In: Brachman H. (eds) Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann, San Mateo, CA, pp 505-516.
21. Ramsey, F. P. (1929). Knowledge. Manuscript published posthumously in R. B. Braithwaite (Ed.), The Foundations of Mathematics and other Logical Essays (pp. 258-259). London: Routlege and Kegan Paul, 1931. Most recently republished in D. H. Mellor (Ed.), F. P. Ramsey: Philosophical papers (pp. 110-111). Cambridge: Cambridge University Press, 1990.
22. Schlechta K. (2004) Coherent systems. Elsevier, Amsterdam.
23. Shoham Y. (1988) Reasoning about change. MIT Press, Cambridge.
24. Venn, J. (1876). The logic of chance (2nd ed). London: Macmillan. The passage from chapter XIV section 36 cited in the first appendix above did not occur in the first edition of 1866; but it is preserved in the third edition of 1886 (reissued in 2006 by New York: Dover Publications), where it is moved to section 33 of the same chapter.
25. Wheeler G. (2007) A review of the lottery paradox. In: Harper W. L., Wheeler G. (eds) Probability and inference: Essays in honour of Henry E. Kyburg. Jr. College Publications, London, pp 1-31.