Reasoning about Uncertainty in Metric Spaces
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as a measure of uncertainty. A formal logical system is constructed for the reasoning about expected distance. Soundness and completeness are shown for this logic. For reasoning on product metric space with uncertainty, a new metric is defined and shown to have good properties.
PDF Link: /papers/06/p289-lee.pdf
AUTHOR = "Seunghwan Lee
TITLE = "Reasoning about Uncertainty in Metric Spaces",
BOOKTITLE = "Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "289--297"