A logic to reason about likelihood
Artificial Intelligence
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Foundations of deductive databases and logic programming
An introduction to possibilistic and fuzzy logics
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ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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Generic preferences over subsets of structured objects
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EDBT'06 Proceedings of the 2006 international conference on Current Trends in Database Technology
Acceptance, conditionals, and belief revision
WCII'02 Proceedings of the 2002 international conference on Conditionals, Information, and Inference
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Moral particularism in the light of deontic logic
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Actions, preferences, and logic programs
Canadian AI'12 Proceedings of the 25th Canadian conference on Advances in Artificial Intelligence
Cumulativity, Identity and Time in Deontic Logic
Fundamenta Informaticae - Deontic Logic in Computer Science
A simple logic for reasoning about incomplete knowledge
International Journal of Approximate Reasoning
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Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the context of studying counterfactuals, but he assumed a total preference order on worlds. Complications arise when examining partial orders that are not present for total orders. There are subtleties involving the exact approach to lifting the order on worlds to an order on sets of worlds. In addition, the axiomatization of the logic of relative likelihood in the case of partial orders gives insight into the connection between relative likelihood and default reasoning.