Uncertain linear constraints

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying many AI uncertainty formalisms to this situation, as their representation of the underlying logic, either as a mutually exclusive and exhaustive set of possibilities, or with a propositional or a predicate logic, is inappropriate (or at least unhelpful). To overcome this, we express reasoning with linear constraints as a logic, and develop the formalisms based on this different underlying logic. We focus in particular on a possibilistic logic representation of uncertain linear constraints, a lattice-valued possibilistic logic, and a Dempster-Shafer representation