A Semantic Approach to Non-Monotonic Conditionals

In J. F. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 2. Elsevier (1988)
Any inferential system in which the addition of new premises can lead to the retraction of previous conclusions is a non-monotonic logic. Classical conditional probability provides the oldest and most widely respected example of non-monotonic inference. This paper presents a semantic theory for a unified approach to qualitative and quantitative non-monotonic logic. The qualitative logic is unlike most other non- monotonic logics developed for AI systems. It is closely related to classical (i.e., Bayesian) probability theory. The semantic theory for qualitative non-monotonic entailments extends in a straightforward way to a semantic theory for quantitative partial entailment relations, and these relations turn out to be the classical probability functions
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Richard Bradley (2006). Adams Conditionals and Non-Monotonic Probabilities. Journal of Logic, Language and Information 15 (1-2):65-81.
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