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17
Probabilistic argumentation systems: a new perspective on DempsterShafer theory
 International Journal of Intelligent Systems, Special Issue on the DempsterShafer Theory of Evidence
, 2003
"... The goal of this paper is to study the connection between DempsterShafer theory and probabilistic argumentation systems. By introducing a general method to translate probabilistic argumentation systems into corresponding DempsterShafer belief potentials, its contribution is twofold. On the one han ..."
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Cited by 31 (12 self)
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The goal of this paper is to study the connection between DempsterShafer theory and probabilistic argumentation systems. By introducing a general method to translate probabilistic argumentation systems into corresponding DempsterShafer belief potentials, its contribution is twofold. On the one hand, the paper proposes probabilistic argumentation systems as a convenient and powerful modeling language to be put on top of DempsterShafer theory. On the other hand, it shows how to use DempsterShafer theory as an efficient computational tool for numerical computations in probabilistic argumentation systems. 1
Probabilistic logic and probabilistic networks
, 2008
"... While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches ..."
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Cited by 17 (13 self)
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While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic fit into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences. Specifically, we show in Part I that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question: the standard probabilistic semantics (which takes probability functions as models), probabilistic argumentation (which considers the probability of a hypothesis being a logical consequence of the available evidence), evidential probability (which handles reference classes and frequency data), classical statistical inference
Probabilistic Argumentation Systems  A New Way to Combine Logic With Probability
 SOFTWARE REQUIREMENTS AND ARCHITECTURE: EUROPEAN MICROWAVE SIGNATURE LABORATORY  INFORMATION MANAGEMENT SYSTEM (EMSLIMS), VERSION 2.0
, 1995
"... Probability is usually closely related to Boolean structures, i.e. Boolean algebras or propositional logic. Here we show, how probability can be combined with NonBoolean structures, and in particular NonBoolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may o ..."
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Cited by 13 (0 self)
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Probability is usually closely related to Boolean structures, i.e. Boolean algebras or propositional logic. Here we show, how probability can be combined with NonBoolean structures, and in particular NonBoolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumptionbased reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumptionbased reasoning. The probability structure is then formally represented by random variables with
values in information algebras. Since these are in general NonBoolean structures some care must be exercised in order to introduce these random variables.
It is shown that this theory leads to an extension of DempsterShafer theory of
evidence and that information algebras provide in fact a natural frame for this
theory.
Implementing Belief Function Computations
 International Journal of Intelligent Systems
, 2003
"... This article discusses several implementation aspects for DempsterShafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization. © 2003 Wiley Peri ..."
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Cited by 13 (3 self)
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This article discusses several implementation aspects for DempsterShafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization. © 2003 Wiley Periodicals, Inc. 1.
Ordered valuation algebras: a generic framework for approximating inference
 International Journal of Approximate Reasoning
, 2004
"... The paper presents a generic approach of approximating inference. The method is based on the concept of valuation algebras with its wide range of possible applications in many different domains. We present convenient resourcebounded anytime algorithms, where the maximal time of computation is deter ..."
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Cited by 12 (1 self)
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The paper presents a generic approach of approximating inference. The method is based on the concept of valuation algebras with its wide range of possible applications in many different domains. We present convenient resourcebounded anytime algorithms, where the maximal time of computation is determined by the user. Key words: Approximation, anytime algorithms, resourcebounded computation, valuation algebras, local computation, binary join trees, bucket elimination, minibuckets. 1
ModelBased Reliability and Diagnostic: A Common Framework for Reliability and Diagnostics
 DX’02 THIRTEENTH INTERNATIONAL WORKSHOP ON PRINCIPLES OF DIAGNOSIS
, 2002
"... Technical systems are in general not guaranteed to work correctly. They are more or less reliable. One main problem for technical systems is the computation of the reliability of a system. A second main problem is the problem of diagnostic. In fact, these problems are in some sense dual to each othe ..."
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Cited by 6 (2 self)
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Technical systems are in general not guaranteed to work correctly. They are more or less reliable. One main problem for technical systems is the computation of the reliability of a system. A second main problem is the problem of diagnostic. In fact, these problems are in some sense dual to each other. In this
Semiring induced valuation algebras: Exact and approximate local computation algorithms
, 2008
"... ..."
On Valued Negation Normal Form Formulas ∗
"... Subsets of the Negation Normal Form formulas (NNFs) of propositional logic have received much attention in AI and proved as valuable representation languages for Boolean functions. In this paper, we present a new framework, called VNNF, for the representation of a much more general class of function ..."
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Cited by 5 (1 self)
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Subsets of the Negation Normal Form formulas (NNFs) of propositional logic have received much attention in AI and proved as valuable representation languages for Boolean functions. In this paper, we present a new framework, called VNNF, for the representation of a much more general class of functions than just Boolean ones. This framework supports a larger family of queries and transformations than in the NNF case, including optimization ones. As such, it encompasses a number of existing settings, e.g. NNFs, semiring CSPs, mixed CSPs, SLDDs, ADD, AADDs. We show how the properties imposed on NNFs to define more “tractable ” fragments (decomposability, determinism, decision, readonce) can be extended to VNNFs, giving rise to subsets for which a number of queries and transformations can be achieved in polynomial time. 1
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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Cited by 4 (2 self)
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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.
A Logic of Soft Constraints based on Partially Ordered Preferences
"... Abstract. Representing and reasoning with an agent’s preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiringbased CSPs, allows a partially ordered set of preference degrees, but th ..."
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Cited by 3 (3 self)
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Abstract. Representing and reasoning with an agent’s preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiringbased CSPs, allows a partially ordered set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably restricts the representational power. This paper constructs a logic of soft constraints where it is only assumed that the set of preference degrees is a partially ordered set, with a maximum element 1 and a minimum element 0. When the partially ordered set is a distributive lattice, this reduces to the idempotent semiringbased CSP approach, and the lattice operations can be used to define a sound and complete proof theory. A generalised possibilistic logic, based on partially ordered values of possibility, is also constructed, and shown to be formally very strongly related to the logic of soft constraints. It is shown how the machinery that exists for the distributive lattice case can be used to perform sound and complete deduction, using a compact embedding of the partially ordered set in a distributive lattice. 1