Search results for "G-coherence"

showing 10 items of 12 documents

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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Probabilistic Logic under Coherence, Model-Theoretic Probabilistic Logic, and Default Reasoning

2001

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherence-based and model-theoretic probabilistic logic. Interestingly, 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. Crucially, we even show that probabilistic reasoning under coherence is a probabilistic generalization of default reasoning in system P. That is, we provide a new probabilistic semantics for system P, which is neither based on infinitesimal probabilities nor on atomic-bound (or also big-stepped) probabil…

Deductive reasoningSettore MAT/06 - Probabilita' E Statistica MatematicaKnowledge representation and reasoningComputer scienceDefault logicDivergence-from-randomness modelLogic modelcomputer.software_genreLogical consequenceProbabilistic logic networkConditional 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 objectsprobabilistic logic under coherenceNon-monotonic logicProbabilistic relevance modeldefault reasoningmodel-theoretic probabilistic logicbusiness.industryProbabilistic logicProbabilistic argumentationExpert systemg-coherencesystem pProbabilistic CTLArtificial intelligencebusinesscomputerdefault reasoning; g-coherence; model-theoretic probabilistic logic; probabilistic logic under coherence; system p
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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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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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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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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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From imprecise probability assessments to conditional probabilities with quasi additive classes of conditioning events

2012

In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of conditioning events which are consistent with the given initial assessment. Quasi additivity assures coherence for the obtained conditional probabilities. In order to reach our goal we define a finite sequence of conditional probabilities by exploiting some theoretical results on g-coherence. In particular, we use solutions of a finite sequence of linear systems.

conditional eventFOS: Computer and information sciencesSettore MAT/06 - Probabilita' E Statistica MatematicaArtificial Intelligence (cs.AI)Computer Science - Artificial Intelligencequasi additivityProbability (math.PR)FOS: MathematicsG-coherenceconditional probabilityinterval-valued probability assessmentMathematics - Probability
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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: 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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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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