Defining Relative Likelihood in Partially-Ordered Preferential Structures
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 (1973) 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.
PS Link: HTTP://www.cs.cornell.edu/home/halpern/papers/prec.ps
PDF Link: /papers/96/p299-halpern.pdf
AUTHOR = "Joseph Halpern
TITLE = "Defining Relative Likelihood in Partially-Ordered Preferential Structures",
BOOKTITLE = "Proceedings of the Twelfth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-96)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1996",
PAGES = "299--306"