David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 34 (1):97 - 119 (2005)
We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability
|Keywords||belief revision conditional probability conditionals countable additivity non-monotonic logic|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Horacio Arló Costa & Rohit Parikh (2005). Conditional Probability and Defeasible Inference. Journal of Philosophical Logic 34 (1):97 - 119.
Robert C. Stalnaker (1970). Probability and Conditionals. Philosophy of Science 37 (1):64-80.
Alexandru Baltag & Sonja Smets (2008). Probabilistic Dynamic Belief Revision. Synthese 165 (2):179 - 202.
Horacio Arló-Costa & Richmond H. Thomason (2001). Iterative Probability Kinematics. Journal of Philosophical Logic 30 (5):479-524.
James Hawthorne (1996). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities. Journal of Philosophical Logic 25 (2):185-218.
Teddy Seidenfeld, Remarks on the Theory of Conditional Probability: Some Issues of Finite Versus Countable Additivity.
Angelo Gilio (2005). Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning. Synthese 146 (1-2):139 - 152.
Niki Pfeifer & G. D. Kleiter (2006). Inference in Conditional Probability Logic. Kybernetika 42 (2):391--404.
Charles G. Morgan (1999). Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language. Topoi 18 (2):97-116.
James Hawthorne (1988). A Semantic Approach to Non-Monotonic Conditionals. In J. F. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 2. Elsevier.
Niki Pfeifer & G. D. Kleiter (2011). Uncertain Deductive Reasoning. In K. Manktelow, D. E. Over & S. Elqayam (eds.), The Science of Reason: A Festschrift for Jonathan St B.T. Evans. Psychology Press. 145--166.
Richard Bradley (2006). Adams Conditionals and Non-Monotonic Probabilities. Journal of Logic, Language and Information 15 (1-2):65-81.
Sorry, there are not enough data points to plot this chart.
Added to index2010-12-22
Total downloads1 ( #301,481 of 1,005,729 )
Recent downloads (6 months)0
How can I increase my downloads?