An Order of Magnitude Calculus
This work addresses foundational issues in reasoning under uncertainty for AI and decision theory, but it appears incremental as it builds on existing concepts like kappa functions and Pearl's decision theory.
The paper tackles the problem of formalizing order of magnitude reasoning by developing a calculus with soundness and completeness results, and shows that order of magnitude probability functions are equivalent to kappa functions, leading to a decision theory that justifies an amended version of Pearl's theory.
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.