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)|
References found in this work BETA
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Citations of this work BETA
Reducing Belief Simpliciter to Degrees of Belief.Hannes Leitgeb - 2013 - Annals of Pure and Applied Logic 164 (12):1338-1389.
Conditionals and Consequences.Gregory Wheeler, Henry E. Kyburg & Choh Man Teng - 2007 - Journal of Applied Logic 5 (4):638-650.
A Geo-Logical Solution to the Lottery Paradox, with Applications to Conditional Logic.Hanti Lin & Kevin T. Kelly - 2012 - Synthese 186 (2):531-575.
Nonmonotonic Conditionals That Behave Like Conditional Probabilities Above a Threshold.James Hawthorne - 2007 - Journal of Applied Logic 5 (4):625-637.
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