Search results for "Iterated conditional"

showing 10 items of 15 documents

Probabilities of conditionals and previsions of iterated conditionals

2019

Abstract We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability to be the conditional probability. In our approach, however, we avoid triviality because the import-export principle is invalid. We then analyze an example of reasoning under partial knowledge where, given a conditional if A then C as information, the probability of A should intuitively increase. We explain this intuition by making some implicit background information explicit. We consider several (generalized) iterated conditionals, which allow…

Background informationSettore MAT/06 - Probabilita' E Statistica MatematicaInference02 engineering and technologyConditional probabilities and previsionTheoretical Computer ScienceConditional random quantitieAffirmation of the ConsequentArtificial Intelligence020204 information systemsFOS: Mathematics0202 electrical engineering electronic engineering information engineeringConjoined and iterated conditionalMathematicsIndependence and uncorrelation.Applied MathematicsProbability (math.PR)Conditional probabilityMathematics - LogicTrivialityIterated function020201 artificial intelligence & image processingLogic (math.LO)Mathematical economicsCoherenceSoftwareMathematics - ProbabilityIntuition
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Iterated Conditionals and Characterization of P-Entailment

2021

In this paper we deepen, in the setting of coherence, some results obtained in recent papers on the notion of p-entailment of Adams and its relationship with conjoined and iterated conditionals. We recall that conjoined and iterated conditionals are suitably defined in the framework of conditional random quantities. Given a family \(\mathcal {F}\) of n conditional events \(\{E_{1}|H_{1},\ldots , E_{n}|H_{n}\}\) we denote by \(\mathcal {C}(\mathcal {F})=(E_{1}|H_{1})\wedge \cdots \wedge (E_{n}|H_{n})\) the conjunction of the conditional events in \(\mathcal F\). We introduce the iterated conditional \(\mathcal {C}(\mathcal {F}_{2})|\mathcal {C}(\mathcal {F}_{1})\), where \(\mathcal {F}_{1}\)…

CombinatoricsPhysicsSettore MAT/06 - Probabilita' E Statistica MatematicaCoherence Conditional events Conditional random quantitiesConditional previsions Conjoined conditionals Iterated conditionalsProbabilistic entailment.Iterated functionProduct (mathematics)Characterization (mathematics)
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Generalized probabilistic modus ponens

2017

Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic modus ponens coincide with the re…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaProbabilistic logicConjoined conditionalPrevision0102 computer and information sciences02 engineering and technologyCoherence (philosophical gambling strategy)Settore MAT/01 - Logica MatematicaModus ponen01 natural sciencesConditional random quantitieTheoretical Computer ScienceModus ponendo tollens010201 computation theory & mathematicsIterated functionComputer Science0202 electrical engineering electronic engineering information engineeringIterated conditional020201 artificial intelligence & image processingRule of inferenceModus ponensCoherenceEvent (probability theory)Mathematics
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A multiagent system approach for image segmentation using genetic algorithms and extremal optimization heuristics

2006

We propose a new distributed image segmentation algorithm structured as a multiagent system composed of a set of segmentation agents and a coordinator agent. Starting from its own initial image, each segmentation agent performs the iterated conditional modes method, known as ICM, in applications based on Markov random fields, to obtain a sub-optimal segmented image. The coordinator agent diversifies the initial images using the genetic crossover and mutation operators along with the extremal optimization local search. This combination increases the efficiency of our algorithm and ensures its convergence to an optimal segmentation as it is shown through some experimental results.

Extremal optimizationMathematical optimizationSegmentation-based object categorizationbusiness.industryMulti-agent systemCrossoverComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONImage segmentationComputingMethodologies_ARTIFICIALINTELLIGENCEComputer Science::Multiagent SystemsArtificial IntelligenceComputer Science::Computer Vision and Pattern RecognitionSignal ProcessingSegmentationIterated conditional modesLocal search (optimization)Computer Vision and Pattern RecognitionbusinessAlgorithmSoftwareMathematicsPattern Recognition Letters
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Probabilistic inferences from conjoined to iterated conditionals

2017

Abstract There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P ( if A then B ) , is the conditional probability of B given A, P ( B | A ) . We identify a conditional which is such that P ( if A then B ) = P ( B | A ) with de Finetti's conditional event, B | A . An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as cond…

Indicative conditionalCounterfactual conditionalSettore MAT/06 - Probabilita' E Statistica MatematicaCompound conditionalInference02 engineering and technology050105 experimental psychologyTheoretical Computer ScienceArtificial Intelligence0202 electrical engineering electronic engineering information engineeringFOS: Mathematics0501 psychology and cognitive sciencesEvent (probability theory)Discrete mathematicsApplied Mathematics05 social sciencesProbability (math.PR)Probabilistic logicConditional probabilityCoherence (philosophical gambling strategy)Mathematics - Logic03b48 60A99Settore MAT/01 - Logica MatematicaLogical biconditionalCenteringp-EntailmentIterated conditional020201 artificial intelligence & image processingCounterfactualLogic (math.LO)CoherenceSoftwareMathematics - Probability
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MRF Model-Based Approach for Image Segmentation Using a Chaotic MultiAgent System

2006

In this paper, we propose a new Chaotic MultiAgent System (CMAS) for image segmentation. This CMAS is a distributed system composed of a set of segmentation agents connected to a coordinator agent. Each segmentation agent performs Iterated Conditional Modes (ICM) starting from its own initial image created initially from the observed one by using a chaotic mapping. However, the coordinator agent receives and diversifies these images using a crossover and a chaotic mutation. A chaotic system is successfully used in order to benefit from the special chaotic characteristic features such as ergodic property, stochastic aspect and dependence on initialization. The efficiency of our approach is s…

Markov random fieldbusiness.industryComputer scienceMulti-agent systemCrossoverChaoticInitializationImage segmentationComputingMethodologies_ARTIFICIALINTELLIGENCEComputer Science::Multiagent SystemsNonlinear Sciences::Chaotic DynamicsComputerSystemsOrganization_MISCELLANEOUSIterated conditional modesSegmentationArtificial intelligencebusinessAlgorithm
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A Multiresolution Approach Based on MRF and Bak–Sneppen Models for Image Segmentation

2006

The two major Markov Random Fields (MRF) based algorithms for image segmentation are the Simulated Annealing (SA) and Iterated Conditional Modes (ICM). In practice, compared to the SA, the ICM provides reasonable segmentation and shows robust behavior in most of the cases. However, the ICM strongly depends on the initialization phase. In this paper, we combine Bak-Sneppen model and Markov Random Fields to define a new image segmentation approach. We introduce a multiresolution technique in order to speed up the segmentation process and to improve the restoration process. Image pixels are viewed as lattice species of Bak-Sneppen model. The a-posteriori probability corresponds to a local fitn…

Random fieldMarkov chainbusiness.industrySegmentation-based object categorizationApplied MathematicsVariable-order Markov modelScale-space segmentationImage segmentationComputer Science::Computer Vision and Pattern RecognitionSegmentationComputer visionIterated conditional modesArtificial intelligencebusinessAlgorithmInformation SystemsMathematicsInformatica
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Chaotic multiagent system approach for MRF-based image segmentation

2005

In this paper, we propose a new chaotic approach for image segmentation based on multiagent system (MAS). We consider a set of segmentation agents organized around a coordinator agent. Each segmentation agent performs iterated conditional modes (ICM) starting from its own initial image created using a chaotic mapping. The coordinator agent diversifies the initial images using a crossover and a chaotic mutation operators. The efficiency of our chaotic MAS approach is shown through some experimental results.

Segmentation-based object categorizationbusiness.industryComputer scienceMulti-agent systemCrossoverComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONChaoticScale-space segmentationImage segmentationComputingMethodologies_ARTIFICIALINTELLIGENCENonlinear Sciences::Chaotic DynamicsComputer Science::Multiagent SystemsComputerSystemsOrganization_MISCELLANEOUSComputer Science::Computer Vision and Pattern RecognitionIterated conditional modesSegmentationComputer visionArtificial intelligencebusinessISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005.
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Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities

2022

We consider some notions of iterated conditionals by checking the validity of some desirable basic logical and probabilistic properties, which are valid for simple conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then, we analyze the two notions of iterated conditional introduced by Calabrese and de Finetti, respectively. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for …

Settore MAT/06 - Probabilita' E Statistica MatematicaCoherence Conditional events Conditional random quantities Conditional previsions Conjoined and disjoined conditionals Iterated conditionals Compound probability theorem Lower and upper bounds Import-export principle
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Connexive Logic, Probabilistic Default Reasoning, and Compound Conditionals

2023

We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, then A, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event A | not-A is p(A | not-A) = 0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms of suitable probabilistic constraints on con…

Settore MAT/06 - Probabilita' E Statistica MatematicaCoherence Compounds of conditionals Conditional events Conditional random quantities Connexive principles Default reasoning Iterated conditionals Probability logic.Settore MAT/01 - Logica Matematica
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