Extending uncertainty formalisms to linear constraints and other complex formalisms
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Date
2008-08
Authors
Wilson, Nic
Journal Title
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Volume Title
Publisher
Elsevier
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Abstract
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.
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Keywords
Dempster-Shafer theory , Possibilistic logic , Lattice-valued possibilistic logic , Assumption-based reasoning , Linear constraints , Spatial and temporal reasoning , Networks
Citation
Wilson, N; (2008) 'Extending uncertainty formalisms to linear constraints and other complex formalisms'. International Journal of Approximate Reasoning, 49 (1): 83-98. doi: 10.1016/j.ijar.2007.08.007