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 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.