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ID:57120351
大小:4.89 MB
页数:65页
时间:2020-08-01
《Cellular Automata Generalized to an Inferential System:元胞自动机广义推理系统课件.ppt》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、CellularAutomataGeneralizedToAnInferentialSystemDavidJ.BlowerCogonSystemsPensacolaFL27thInternationalWorkshoponBayesianInferenceandMaximumEntropyMethodsinScienceandEngineering,SaratogaSprings,NewYork,11July2019MotivationWhyisitimpossibletopredictthebehaviourofacel
2、lularautomaton?TheMotivatingQuestionButisn’tthequintessentialfeatureofprobabilitytheoryandinferentialsystemstheabilitytopredictfutureevents?ProposedSolutionJaynesusedprobabilitytheorytogeneralizeclassicallogicfunctions.TreatCAfromaninferentialandinformationalpoint
3、ofview.WhyExamineCellularAutomata?BecauseCellularAutomataareastand-inforanysufficientlydetailedcomplicatedontologicalexplanationforhowtheworldworks.IssuesinOrderAddressedBooleanAlgebraLogicFunctionsCellularAutomataWhyStartwithBooleanAlgebra?Thefollowingfewslideson
4、BooleanAlgebraaresolelytosetthestageforanalogousoperationswithclassicallogicfunctions(andcellularautomata).SomeBasicBooleanQuestionsHowareBooleanfunctionsdefined?HowaresyntacticallycorrectBooleanformulasproduced?WhatisagoodcanonicalexpressionforBooleanfunctions?Wh
5、yIsItHelpful?UsefulforbothlogicfunctionsandcellularautomataAxiomsofBooleanAlgebrausedinBayes’sTheoremCanonicalexpressionssubstitutedforcomplicatedlogicandCArulesFormalRules,BooleanAlgebra,andProbabilityTheoryPerfectchoicefordiscussingformalmanipulationrulesofproba
6、bilitytheorywheretheactualnumericalassignmentsarenottheissue.BooleanAlgebraonafinitecarriersetisa“closed”system,thatis,thereisalwaysananswer.Moreover,neithernumbersnorarithmeticoperationsarerequiredtofindthatanswer.BooleanAlgebraThecarriersetBinaryoperatorsSpecial
7、ElementsFunctiondefinition:Amappingfromthesetoforderedpairsofthecarriertoanelementinthecarrierset.CharacterizedbythequintupleBooleanAlgebraAnexampleofacarriersetwithfourelementsAll16orderedpairsfromthecarriersetAmappingfromanelementofBxBintoanelementofBExampleofBo
8、oleanFunctionFunctionTableBooleanFormulaSubstitutespecificargumentsBoole’sExpansionTheoremAnyBooleanfunctioncanbeexpandedinthefollowingmanner.Applyingth
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