A linear programming framework for logics of uncertainty

Several logics for reasoning under uncertainty distribute probabil ity 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 in stances of a certain type of linear programming model typically with exponentially many variables We also show how a single linear pro gramming package can implement these logics computationally if one plugs in a di erent column generation subroutine for each logic