Extending uncertainty formalisms to linear constraints and other complex formalisms Original Research Article

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying 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 difficulty, 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, an assumption-based reasoning formalism and a Dempster–Shafer representation, proving some fundamental results for these extended systems. Our results on extending uncertainty formalisms also apply to a very general class of underlying monotonic logics.