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 DempsterShafer theory other logics based on belief functions and secondorder 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 dierent column generation subroutine for each logic Several logics for reasoning under uncertainty are variations on a theme Numbers perhaps probabilities are assigned to propositions to indicate degrees of condence The object is to determine the degree of condence one can have in a conclusion inferred from the propositions Dependencie