Search results for "g-coherence"

showing 10 items of 12 documents

Coherent conditional probabilities and proper scoring rules

2011

In this paper we study the relationship between the notion of coherence for conditional probability assessments on a family of conditional events and the notion of admissibility with respect to scoring rules. By extending a recent result given in literature for unconditional events, we prove, for any given strictly proper scoring rule s, the equivalence between the coherence of a conditional probability assessment and its admissibility with respect to s. In this paper we focus our analysis on the case of continuous bounded scoring rules. In this context a key role is also played by Bregman divergence and by a related theoretical aspect. Finally, we briefly illustrate a possible way of defin…

total coherenceSettore MAT/06 - Probabilita' E Statistica Matematicabregman divergencestrong dominanceconditional scoring rulesConditional probability assessments coherence penalty criterion proper scoring rules conditional scoring rules weak dominance strong dominance admissibility Bregman divergence g-coherence total coherence imprecise probability assessments.weak dominancestrong dominance; conditional probability assessments; imprecise probability assessments; gcoherence; proper scoring rules; bregman divergence; weak dominance; coherence; imprecise probability assessments.; admissibility; g-coherence; penalty criterion; conditional scoring rules; total coherencepenalty criteriongcoherenceproper scoring rulescoherenceconditional probability assessmentsg-coherenceimprecise probability assessmentsadmissibility
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Square of Opposition Under Coherence

2016

Various semantics for studying the square of opposition have been proposed recently. So far, only (Gilio et al., 2016) studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized qu…

Square of oppositionSettore MAT/06 - Probabilita' E Statistica Matematicat-coherenceGeneralized quantifierSquare of oppositionSettore M-FIL/02 - Logica E Filosofia Della Scienza02 engineering and technology01 natural sciencesSquare (algebra)OpticsProbability theory0202 electrical engineering electronic engineering information engineering0101 mathematicsMathematicsbusiness.industry010102 general mathematicsProbabilistic logicCoherence (statistics)Imprecise probabilityconditional eventimprecise probabilityAlgebrag-coherencegeneralized quantifier020201 artificial intelligence & image processingbusinessSentenceacceptance
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Some results on generalized coherence of conditional probability bounds

2003

Based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of g-coherence is equivalent to the 'avoiding uniform loss' property for lower and upper probabilities (a la Walley). Moreover, given a g-coherent imprecise assessment by our algorithms we can correct it obtaining the associated coherent assessment (in the sense of Walley and Williams). As is well known, the problems of checking g-coherence and propagating tight g-coherent intervals are NP and FP^NP complete, respectively, and thus NP-hard. Two notions which may be helpful to reduce co…

g-coherenceUncertain knowledge; coherence; g-coherence; imprecise probabilities; conditional probability bounds; lower and upper probabilities; non relevant gains; basic sets.Settore MAT/06 - Probabilita' E Statistica Matematicanon relevant gainsUncertain knowledgeconditional probability boundslower and upper probabilitiesbasic setsimprecise probabilitiesUncertain knowledge coherence g-coherence imprecise probabilities conditional probability bounds lower and upper probabilities non relevant gains basic setscoherence
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Logical Conditions for Coherent Qualitative and Numerical Probability Assessments

2003

Settore MAT/06 - Probabilita' E Statistica Matematicalower and upper probability boundsUncertain knowledge coherence g-coherence imprecise probabilities conditional probability bounds lower and upper probabilities coherent qualitative probability assessmentsqualitative probabilitieslogical conditionsGeneralized coherenceGeneralized coherence; lower and upper probability bounds; logical conditions; qualitative probabilities.
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Coherence Checking and Propagation of Lower Probability Bounds

2003

In this paper we use imprecise probabilities, based on a concept of generalized coherence (g-coherence), for the management of uncertain knowledge and vague information. We face the problem of reducing the computational difficulties in g-coherence checking and propagation of lower conditional probability bounds. We examine a procedure, based on linear systems with a reduced number of unknowns, for the checking of g-coherence. We propose an iterative algorithm to determine the reduced linear systems. Based on the same ideas, we give an algorithm for the propagation of lower probability bounds. We also give some theoretical results that allow, by suitably modifying our algorithms, the g-coher…

Probability boxMathematical optimizationSettore MAT/06 - Probabilita' E Statistica MatematicaPosterior probabilitynon relevant gainLaw of total probabilityConditional probabilitybasic setsbasic sets; basic sets.; g-coherence checking; lower conditional probability bounds; non relevant gains; propagationCoherence (statistics)Conditional probability distributiong-coherence checking; lower conditional probability bounds; non relevant gainsImprecise probabilityTheoretical Computer Sciencelower conditional probability boundRegular conditional probabilitynon relevant gainspropagationlower conditional probability boundsGeometry and Topologyg-coherence checkingSoftwareMathematics
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Probabilistic Logic under Coherence: Complexity and Algorithms

2005

In previous work [V. Biazzo, A. Gilio, T. Lukasiewicz and G. Sanfilippo, Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P, Journal of Applied Non-Classical Logics 12(2) (2002) 189---213.], we have explored the relationship between probabilistic reasoning under coherence and model-theoretic probabilistic reasoning. In particular, we have shown that the notions of g-coherence and of g-coherent entailment in probabilistic reasoning under coherence can be expressed by combining notions in model-theoretic probabilistic reasoning with concepts from default reasoning. In this paper, we continue this line of research. Based on the above sem…

conditional probability assessmentSettore MAT/06 - Probabilita' E Statistica MatematicaDivergence-from-randomness modelalgorithmsprobabilistic logicConditional probability assessments; probabilistic logic; g-coherence; g-coherent entailment; complexity and algorithms.Artificial IntelligenceProbabilistic logic networkprobabilistic logic under coherenceConditional probability assessmentsProbabilistic analysis of algorithmsNon-monotonic logicconditional constraintMathematicsg-coherent entailmentConditional probability assessments probabilistic logic g-coherence g-coherent entailment complexity and algorithms.Reasoning systemcomputational complexitymodel-theoretic probabilistic logicApplied Mathematicscomplexity and algorithmsProbabilistic logiclogical constraintProbabilistic argumentationg-coherenceconditional probability assessment logical constraint conditional constraint probabilistic logic under coherence model-theoretic probabilistic logic g-coherence g-coherent entailment computational complexity algorithmsProbabilistic CTLalgorithms; computational complexity; conditional constraint; conditional probability assessment; g-coherence; g-coherent entailment; logical constraint; model-theoretic probabilistic logic; probabilistic logic under coherenceAlgorithmAnnals of Mathematics and Artificial Intelligence
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Imprecise probability assessments and the Square of Opposition

There is a long history of investigations on the square of opposition spanning over two millenia. A square of opposition represents logical relations among basic sentence types in a diagrammatic way. The basic sentence types, traditionally denoted by A (universal affirmative: ''Every S is P''), E (universal negative: ''No S is P''), I (particular affirmative: ''Some S are P''), and O (particular negative: ''Some S are not P''), constitute the corners of the square, and the logical relations--contradiction, contrarity, subalternation, and sub-contrarity--form the diagonals and the sides of the square. We investigate the square of opposition from a probabilistic point of view. To manage impre…

conditional eventimprecise probabilityg-coherenceSquare of oppositionSettore MAT/06 - Probabilita' E Statistica Matematicat-coherencegeneralized quantifierSettore MAT/01 - Logica Matematicaacceptance
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Probabilistic Logic under Coherence‚ Model−Theoretic Probabilistic Logic‚ and Default Reasoning in System P

2016

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model-theoretic probabilistic reasoning and to default reasoning in System P. In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System P. That is, we provide a new probabilistic semantics for System P, which neither uses infinitesimal probabilities nor atomic bound (or bi…

Deductive reasoningSettore MAT/06 - Probabilita' E Statistica MatematicaConditional probability assessments conditional constraints probabilistic logic under coherence model-theoretic probabilistic logic g-coherence g-coherent entailment defaultreasoning from conditional knowledge bases System P conditional objects.conditional constraintsLogicDefault logicStatistics::Other StatisticsProbabilistic logic networkConditional probability assessmentsprobabilistic logic under coherenceNon-monotonic logicSystem PMathematicsg-coherent entailmentHardware_MEMORYSTRUCTURESmodel-theoretic probabilistic logicbusiness.industryProbabilistic logicSystem P; g-coherence; conditional objectsCoherence (statistics)default reasoning from conditional knowledge basesProbabilistic argumentationConditional probability assessments; conditional constraints; probabilistic logic under coherence; model-theoretic probabilistic logic; g-coherence; g-coherent entailment; default reasoning from conditional knowledge bases; System P; conditional objects.Philosophyg-coherenceProbabilistic CTLArtificial intelligencebusinessAlgorithmconditional objectsJournal of Applied Non−Classical Logics
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Generalized coherence and connection property of imprecise conditional previsions.

2008

In this paper we consider imprecise conditional prevision assessments on random quantities with finite set of possible values. We use a notion of generalized coherence which is based on the coherence principle of de Finetti. We consider the checking of g-coherence, by extending some previous results obtained for imprecise conditional probability assessments. Then, we study a connection property of interval-valued gcoherent prevision assessments, by extending a result given in a previous paper for precise assessments.

Settore MAT/06 - Probabilita' E Statistica MatematicaConditional random quantities; imprecise prevision assessments; generalized coherence; checking of g-coherence; connection property.Conditional random quantitiesimprecise prevision assessmentsconnection propertyConditional random quantities imprecise prevision assessments generalized coherence checking of g-coherence connection property.checking of g-coherencegeneralized coherence
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Algorithms for coherence checking and propagation of conditional probability bounds

2001

In this paper, we propose some algorithms for the checking of generalized coherence (g-coherence) and for the extension of imprecise conditional probability assessments. Our concept of g-coherence is a generalization of de Finetti’s coherence principle and is equivalent to the ”avoiding uniform loss” property for lower and upper probabilities (a la Walley). By our algorithms we can check the g-coherence of a given imprecise assessment and we can correct it in order to obtain the associated coherent assessment (in the sense of Walley and Williams). Exploiting some properties of the random gain we show how, in the linear systems involved in our algorithms, we can work with a reduced set of va…

reduced sets of variables and constraintsSettore MAT/06 - Probabilita' E Statistica MatematicaUncertain knowledgeUncertain knowledge probabilistic reasoning under coherence imprecise conditional probability assessments g-coherence checking g-coherent extension algorithms computational aspects reduced sets of variables reduced sets of linear constraints.g-coherent extensionimprecise conditional probability assessmentsg-coherence checkingUncertain knowledge; probabilistic reasoning under coherence; imprecise conditional probability assessments; g-coherence checking; g-coherent extension; algorithms.; computational aspects; reduced sets of variables and constraints.algorithmsprobabilistic reasoning under coherencecomputational aspects
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