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12
Probabilistic Deduction with Conditional Constraints over Basic Events
 J. Artif. Intell. Res
, 1999
"... We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NPhard. We then concentrate on the special case of probabilistic deduction in conditional constrai ..."
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Cited by 44 (30 self)
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We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NPhard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees. 1. Introduction Dealing wit...
Inference in Credal Networks with BranchAndBound Algorithms
 IN INT. SYMP. ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS
, 2003
"... A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NPhard even for categorical variables and polytree mo ..."
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Cited by 11 (1 self)
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A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NPhard even for categorical variables and polytree models. We describe
Efficient Global Probabilistic Deduction from Taxonomic and Probabilistic KnowledgeBases over Conjunctive Events
 In Proceedings CIKM97
, 1997
"... We present a new, efficient linear programming approach to probabilistic deduction from probabilistic knowledgebases over conjunctive events. We show that this approach enables us to solve the classical problem of probabilistic deduction along a chain of basic events in polynomial time in the lengt ..."
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Cited by 11 (6 self)
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We present a new, efficient linear programming approach to probabilistic deduction from probabilistic knowledgebases over conjunctive events. We show that this approach enables us to solve the classical problem of probabilistic deduction along a chain of basic events in polynomial time in the length of the chain. We then elaborate how taxonomic knowledge can be exploited in our new approach for an increased efficiency. We also present important new results for the classical linear programming approach to probabilistic deduction under taxonomic knowledge. 1 Introduction There are many approaches to nonBayesian probabilistic deduction in the literature. They can be classified in global techniques based on linear programming and in local methods founded on the iterative application of inference rules. NonBayesian probabilistic deduction by solving linear programs is discussed e.g. in [23], [13], [24], [17], [14], [2], [15], and [22]. It can be performed within rich probabilistic lang...
Belief updating and learning in semiqualitative probabilistic networks
 Conference on Uncertainty in Artificial Intelligence. AUAI
, 2005
"... This paper explores semiqualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NP PPComplete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can ..."
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Cited by 9 (5 self)
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This paper explores semiqualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NP PPComplete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesianminded method that employs the Imprecise Dirichlet Model to generate setvalued estimates. 1
Resolution and the Integrality of Satisfiability Problems
 Mathematical Programming
, 1995
"... A satisfiability problem can be regarded as a nondisjoint union of set covering problems. We show that if the resolution method of theorem proving is applied to the satisfiability problem, its constraint set defines an integral polytope if and only if the constraint sets of the set covering problems ..."
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Cited by 8 (0 self)
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A satisfiability problem can be regarded as a nondisjoint union of set covering problems. We show that if the resolution method of theorem proving is applied to the satisfiability problem, its constraint set defines an integral polytope if and only if the constraint sets of the set covering problems do. In this sense, resolution reduces the integrality question for the satisfiability problem to that for the set covering problem. 1 Introduction The satisfiability problem of propositional logic asks whether a set of logical clauses can be true simultaneously. The clauses can be represented as linear inequalities that have a 01 solution if and only if the clauses are satisfiable. In many cases one is not only interested in the 01 solubility of this constraint set but in solving a 01 optimization problem subject to it. Such a problem is implicit, for instance, in the maximum satisfiability problem [13, 15], which assigns weights to the constraints and seeks the maximum weight feasible ...
Magic Inference Rules for Probabilistic Deduction under Taxonomic Knowledge
 In Proc. of the 14th Conference on Uncertainty in Artificial Intelligence
, 1998
"... We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledgebases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are locally complete for conjunctive events and under additional ..."
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Cited by 8 (4 self)
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We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledgebases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are locally complete for conjunctive events and under additional taxonomic knowledge. We discover that our inference rules are extremely complex and that it is at first glance not clear at all where the deduced tightest bounds come from. Moreover, analyzing the global completeness of our inference rules, we find examples of globally very incomplete probabilistic deductions. More generally, we even show that all systems of inference rules for taxonomic and probabilistic knowledgebases over conjunctive events are globally incomplete. We conclude that probabilistic deduction by the iterative application of inference rules on interval restrictions for conditional probabilities, even though considered very promising in the literature so far, seems very limite...
Propositional and relational Bayesian networks associated with imprecise and qualitative probabilistic assessments
 IN PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2004
"... This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and firstorder constructs together with precise, imprecise, indeterminate and qualitative probabilistic as ..."
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Cited by 8 (4 self)
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This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and firstorder constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically.
Separation Properties of Sets of Probability Measures
 In Conference on Uncertainty in Artificial Intelligence
, 2000
"... This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to dseparati ..."
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Cited by 5 (1 self)
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This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to dseparation but still fails to guarantee a belief separation property. To overcome this unsatisfactory situation, a strong Markov condition is proposed, based on epistemic independence. The main result is that the strong Markov condition leads to strong independence and does enforce separation properties; this result implies that (1) separation properties of Bayesian networks do extend to epistemic independence and sets of probability measures, and (2) strong independence has a clear justi cation based on epistemic independence and the strong Markov condition. 1
Decomposition and Synthesis of Decision Tables with respect to Generalized Decision Functions
 In: S.K. Pal, A. Skowron
, 1999
"... : An approach to the attribute set decomposition of decision tables is proposed. It enables to combine nondeterministic decision rules based on the generalized decision functions for different subsets of conditions. Optimal decomposition onto conditions subsets is proposed to be searched from Bayes ..."
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Cited by 1 (0 self)
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: An approach to the attribute set decomposition of decision tables is proposed. It enables to combine nondeterministic decision rules based on the generalized decision functions for different subsets of conditions. Optimal decomposition onto conditions subsets is proposed to be searched from Bayesianlike networks. Computational complexity of searching for such networks is discussed. 1 Introduction In recent years rough set approach, originated by [8], turned out to be very effective as applicable to data mining and decision support systems. However, reallife problems require reconsidering rough set tools in view of large data bases, where the number of objects as well as the average number of conditional attributes in rough set based decision rules becomes too high to classify new cases. For these and also other purposes a great effort has been spent on initial decomposition of information systems and decision tables with large number of objects and attributes (see e.g. [6], [7], ...
Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals
"... Abstract. This paper proposes a probabilistic description logic that combines (i) constructs of the wellknown ALC logic, (ii) probabilistic assertions, and (iii) limited use of nominals. We start with our recently proposed logic crALC, where any ontology can be translated into a relational Bayesian ..."
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Cited by 1 (1 self)
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Abstract. This paper proposes a probabilistic description logic that combines (i) constructs of the wellknown ALC logic, (ii) probabilistic assertions, and (iii) limited use of nominals. We start with our recently proposed logic crALC, where any ontology can be translated into a relational Bayesian network with partially specified probabilities. We then add nominals to restrictions, while keeping crALC’s interpretationbased semantics. We discuss the clash between a domainbased semantics for nominals and an interpretationbased semantics for queries, keeping the latter semantics throughout. We show how inference can be conducted in crALC and present examples with real ontologies that display the level of scalability of our proposals. Key words: ALC logic, nominals, Bayesian/credal networks. 1