An Order of Magnitude Calculus
This paper develops a simple calculus for order of magnitude reasoning. A semantics is given with soundness and completeness results. Order of magnitude probability functions are easily defined and turn out to be equivalent to kappa functions, which are slight generalizations of Spohn's Natural Conditional Functions. The calculus also gives rise to an order of magnitude decision theory, which can be used to justify an amended version of Pearl's decision theory for kappa functions, although the latter is weaker and less expressive.
Keywords: Order of magnitude reasoning, kappa functions, natural conditional
PDF Link: /papers/95/p548-wilson.pdf
AUTHOR = "Nic Wilson
TITLE = "An Order of Magnitude Calculus",
BOOKTITLE = "Proceedings of the Eleventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-95)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1995",
PAGES = "548--555"