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Algorithms for dempstershafer theory
 Algorithms for Uncertainty and Defeasible Reasoning
, 2000
"... The method of reasoning with uncertain information known as DempsterShafer theory arose from the reinterpretation and development of work of Arthur Dempster [Dempster, 67; 68] by Glenn Shafer in his book a mathematical theory of evidence [Shafer, 76], and further publications e.g., [Shafer, 81; 90] ..."
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Cited by 20 (3 self)
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The method of reasoning with uncertain information known as DempsterShafer theory arose from the reinterpretation and development of work of Arthur Dempster [Dempster, 67; 68] by Glenn Shafer in his book a mathematical theory of evidence [Shafer, 76], and further publications e.g., [Shafer, 81; 90]. More recent
Inner And Outer Approximation Of Belief Structures Using A Hierarchical Clustering Approach
, 2001
"... ..."
Resourcebounded and anytime approximation of belief function computations
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2002
"... This papers proposes a new approximation method for DempsterShafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resourcebounded propa ..."
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This papers proposes a new approximation method for DempsterShafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resourcebounded propagation scheme, in which the user determines in advance the maximal time available for the computation. This leads then to convenient, interruptible anytime algorithms giving progressively better solutions as execution time goes on, thus offering to trade the quality of results against the costs of computation. The paper demonstrates the usefulness of these new methods and shows its advantages and drawbacks compared to existing techniques.
Fast Markov chain algorithms for calculating DempsterShafer belief
 IN PROCEEDINGS OF THE 12TH EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1996
"... We present a new type of Markov Chain algorithm for the calculation of combined DempsterShafer belief which is almost linear in the size of the frame, thus making the calculation of belief feasible for a wider range of problems. We also indicate how these algorithms may be used in the calculation ..."
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We present a new type of Markov Chain algorithm for the calculation of combined DempsterShafer belief which is almost linear in the size of the frame, thus making the calculation of belief feasible for a wider range of problems. We also indicate how these algorithms may be used in the calculation of belief in product spaces associated with networks.
Logical Deduction using the Local Computation Framework
 Johannes Kepler Universität
, 1997
"... This paper describes how the framework can be used for the computation of logical deduction. ..."
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This paper describes how the framework can be used for the computation of logical deduction.
Available online at www.sciencedirect.com International Journal of Approximate Reasoning
, 2007
"... Extending uncertainty formalisms to linear constraints and other complex formalisms q ..."
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Extending uncertainty formalisms to linear constraints and other complex formalisms q
Uncertain Linear Constraints
"... Abstract. 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 ..."
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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 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 latticevalued possibilistic logic, and a DempsterShafer representation. 1
A Proposal for Computing With Imprecise Probabilities: A Framework for Multiple Representations of Uncertainty in Simulation Software
, 2007
"... We propose the design and construction of a programming language for the formal representation of uncertainty in modeling and simulation. Modeling under uncertainty has been of paramount importance in the past half century, as quantitative methods of analysis have been developed to take advantage of ..."
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We propose the design and construction of a programming language for the formal representation of uncertainty in modeling and simulation. Modeling under uncertainty has been of paramount importance in the past half century, as quantitative methods of analysis have been developed to take advantage of computational resources. Simulation is gaining prominence as the proper tool of scientific analysis under circumstances where it is infeasible or impractical to directly study the system in question. This programming language will be built as an extension to the Modelica programming language, which is an acausal objectoriented language for hybrid continuous and discreteevent simulations [22]. Our language extensions will serve as a platform for the research into representation and calibration of imprecise probabilities in quantitative risk analysis simulations. Imprecise probability is used a generic term for any mathematical model which measures chance or uncertainty without crisp numerical probabilities. The explicit representation of imprecise probability theories in a domainspecific programming language will facilitate the development of efficient algorithms for expressing, computing, and calibrating imprecise probability structures. Computation with imprecise probability structures will lead to quantitative risk analyses that are more informative than analyses using traditional probability theory. We have three primary research objectives: (i) the exploration of efficient representational structures and computational algorithms of DempsterShafer belief structures; (ii) the application of the imprecise
Applying the Local Computation Framework to Classical and NonClassical Logics
"... Algorithms to propagate uncertainty using Shenoy and Shafer's Local Computation framework give rise to efficient computation in a number of spheres of reasoning, such as Bayesian probability, DempsterShafer Belief, infinitesimal probability functions, and Zadeh's Possibility functions. ..."
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Algorithms to propagate uncertainty using Shenoy and Shafer's Local Computation framework give rise to efficient computation in a number of spheres of reasoning, such as Bayesian probability, DempsterShafer Belief, infinitesimal probability functions, and Zadeh's Possibility functions. Finite sets of possibilities (or constraints) can be propagated with this framework, and so deduction in a finite propositional calculus can be performed by considering sets of possible worlds. Recently Kohlas and Moral have shown how to use Local Computation to directly propagate sets of formulae in clausal form in a finite propositional calculus. In this report we explore the application of the Local Computation framework to other logics. We describe how a logic can be embedded in the framework, given that its semantics verifies certain properties. This is applied to firstorder predicate calculus, modal and conditional logics. We also discuss its application to predicate circumscription....
Extending Uncertainty Formalisms to Linear Constraints and Other Complex Formalisms
, 2007
"... 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 ..."
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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 latticevalued possibilistic logic, an assumptionbased reasoning formalism and a DempsterShafer 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.