A linear programming framework for logics of uncertainty

Several logics for reasoning under uncertainty distribute “probability mass” over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of...

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Bibliographic Details
Published in:Decision Support Systems Vol. 16; no. 1; pp. 39 - 53
Main Authors: Andersen, K.A., Hooker, J.N.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 1996
Elsevier Sequoia S.A
Subjects:
Decision support systems
Linear programming
Logic
Probability
Uncertainty
Logic
Linear programming
Uncertainty
ISSN:0167-9236, 1873-5797
Online Access:Get full text
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Summary:Several logics for reasoning under uncertainty distribute “probability mass” over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one “plugs in” a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic.
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ISSN:0167-9236
1873-5797
DOI:10.1016/0167-9236(94)00055-7