subjective logic

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1、SubjectiveLogicAudunJøsangDraft,5July20092PrefaceSubjectivelogicisatypeofprobabilisticlogicthatallowsprobabilityvaluestobeex-pressedwithdegreesofuncertainty.Probabilisticlogiccombinesthestrengthsoflogicandprobabilitycalculus,meaningthatithasbinarylogicscapacitytoexpressstruc

2、-turedargumentmodels,andithasthepowerofprobabilitiestoexpressdegreesoftruthofthosearguments.Subjectivelogicmakesitpossibletoexpressuncertaintyabouttheprobabilityvaluesthemselves,meaningthatitispossibletoreasonwithargumentmodelsinpresenceofuncertainorpartiallyincompleteeviden

3、ce.Thismanuscriptde-scribesthecentralelementsofsubjectivelogic.Morespecifically,itfirstdescribesasetofequivalentrepresentationsofuncertainprobabilitieswiththeirinterpretations.Itthendescribesthemostimportantsubjectivelogicoperators.Finally,itdescribeshowsubjectivelogiccanbeapp

4、liedintrustmodellingandforanalysingBayesiannetworks.Subjectivelogicisdirectlycompatiblewithbinarylogic,probabilitycalculusandclas-sicalprobabilisticlogic.Theadvantageofusingsubjectivelogicisthatrealworldsituationscanbemorerealisticallymodelled,andthatconclusionsmorecorrectly

5、re-flecttheignoranceanduncertaintiesthataccompanytheinputarguments.Contents1Introduction52BeliefRepresentationsinSubjectiveLogic72.1SubjectiveOpinionRepresentation...................82.1.1MultinomialOpinions.....................82.1.2BinomialOpinions.......................112

6、.2EvidenceRepresentation........................122.2.1TheDirichletDistribution...................132.2.2VisualisingDirichletDistributions...............142.2.3CoarseningExample:FromTernarytoBinary.........162.2.4EvidenceNotationofOpinions.................162.3ProbabilisticN

7、otationofOpinions...................182.4FuzzyCategoryRepresentation.....................193PropertiesofSubjectiveLogic214OperatorsofSubjectiveLogic234.1AdditionandSubtraction........................244.2BinomialMultiplicationandDivision.................254.2.1BinomialMultip

8、licationandComultiplication.........254.2.2BinomialDivisionandCodivision...