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. It is shown that these logics are instances of a certain type of linear programming model, typically with exponentially many variables, and how a single linear program package can implement these logics computationally if one plugs in a different column generation subroutine for each logic