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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Judea Pearl (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.
Ernest W. Adams (1975). The Logic of Conditionals: An Application of Probability to Deductive Logic. D. Reidel Pub. Co..
Henry E. Kyburg Jr (1961). Probability and the Logic of Rational Belief. Wesleyan University Press.
Adam Grove (1988). Two Modellings for Theory Change. Journal of Philosophical Logic 17 (2):157-170.
Citations of this work BETA
David Makinson (2011). Conditional Probability in the Light of Qualitative Belief Change. Journal of Philosophical Logic 40 (2):121 - 153.
Eleonora Cresto (2010). Belief and Contextual Acceptance. Synthese 177 (1):41-66.
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
Frederik Herzberg (2014). A Graded Bayesian Coherence Notion. Erkenntnis 79 (4):843-869.
Similar books and articles
Niki Pfeifer & G. D. Kleiter (2006). Inference in Conditional Probability Logic. Kybernetika 42 (2):391--404.
James Hawthorne (1988). A Semantic Approach to Non-Monotonic Conditionals. In J. F. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 2. Elsevier
Angelo Gilio (2005). Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning. Synthese 146 (1-2):139 - 152.
Teddy Seidenfeld, Remarks on the Theory of Conditional Probability: Some Issues of Finite Versus Countable Additivity.
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.
Robert C. Stalnaker (1970). Probability and Conditionals. Philosophy of Science 37 (1):64-80.
Rohit Parikh (2005). Conditional Probability and Defeasible Inference. Journal of Philosophical Logic 34 (1):97 - 119.
Added to index2009-01-28
Total downloads25 ( #118,812 of 1,724,879 )
Recent downloads (6 months)4 ( #167,173 of 1,724,879 )
How can I increase my downloads?