数理逻辑
出版社：世界图书出版公司北京公司
年代：2008
定价：45.0
书籍简介:
本书是一部难度适中的本科生数学教材。主要讲述了什么是数学证明，这些证明怎么能够被验证以及电脑在多大程度上能够执行数学证明。读者对象：本书适用于数学、计算机科学、人工智能和决策学等各个领域的本科生、研究生以及相关专业的研究人员。
书籍目录:
Preface
PARTA
IIntroduction
§1.AnExamplefromGroupTheory
§2.AnExamplefromtheTheoryofEquivalenceRelations
§3.APreliminaryAnalysis
§4.Preview
IISyntaxofFirst-OrderLanguages
§1.Alphabets
§2.TheAlphabetofaFirst-OrderLanguage
§3.TermsandFormulasinFirst-OrderLanguages
§4.InductionintheCalculusofTermsandintheCalculusofFormulas
§5.FreeVariablesandSentences
IIISemanticsofFirst-OrderLanguages
§1.StructuresandInterpretations
§2.StandardizationofConnectives
§3.TheSatisfactionRelation
§4.TheConsequenceRelation
§5.TwoLemmasontheSatisfactionRelation
§6.SomeSimpleFormalizations
§7.SomeRemarksonFormalizability
§8.Substitution
IVASequentCalculus
§1.SequentRules
§2.StructuralRulesandConnectiveRules
§3.DerivableConnectiveRules
§4.QuantifierandEqualityRules
§5.FurtherDerivableRulesandSequents
§6.SummaryandExample
§7.Consistency
VTheCompletenessTheorem
§1.HenkinsTheorem
§2.SatisfiabilityofConsistentSetsofFormulas(theCountableCase)
§3.SatisfiabilityofConsistentSetsofFormulas(theGeneralCase)
§4.TheCompletenessTheorem
VITheLowenheim-SkolemandtheCompactnessTheorem
§1.TheL6wenheim-SkolemTheorem
§2.TheCompactnessTheorem
§3.ElementaryClasses
§4.ElementarilyEquivalentStructures
VIITheScopeofFirst-OrderLogic
§1.TheNotionofFormalProof
§2.MathematicsWithintheFrameworkofFirst-OrderLogic
§3.TheZermelo-FraenkelAxiomsforSetTheory
§4.SetTheoryasaBasisforMathematics
VIIISyntacticInterpretationsandNormalForms
§1.Term-ReducedFormulasandRelationalSymbolSets
§2.
PARTB
IXExtensionsofFirst-OrderLogic
§1.Second-OrderLogic
§2.TheSystemL
§3.TheSystemL
XLimitationsoftheFormalMethod
§1.DecidabilityandEnumerability
§2.RegisterMachines
§3.TheHaltingProblemforRegisterMachines
§4.TheUndecidahilityofFirst-OrderLogic
§5.TrahtenbrotsTheoremandtheIncompletenessofSecond-OrderLogic
§6.TheoriesandDecidability
§7.Self-ReferentialStatementsandGOlelsIncompletenessTheorems
XIFreeModelsandLogicProgramming
§i.HerbrandsTheorem
§2.FreeModelsandUniversalHornFormulas
§3.HerbrandStructures
§4.PropositionalLogic
§5.PropositionalResolution
§6.First-OrderResolution(withoutUnification)
§7.LogicProgramming
XIIAnAlgebraicCharacterizationofElementaryEquiva-lence
§1.FiniteandPartialIsomorphisms
§2.FraissesTheorem
§3.ProofofFraissesTheorem
§4.EhrenfeuchtGames
XIIILindstromsTheorems
§1.LogicalSystems
§2.CompactRegularLogicalSystems
§3.LindstrSxnsFirstTheorem
§4.LindstrSmsSecondTheorem
References
SymbolIndex
SubjectIndex
内容摘要:
Ashortdigressionintomodeltheorywillhelpustoanalyzetheexpressivepowerofthefirst-orderlanguage,anditwillturnoutthattherearecertaindeficiencies.Forexample,thefirst-orderlanguagedoesnotallowtheformulationofanadequateaxiomsystemforarithmeticoranalysis.Ontheotherhand,thisdi~cultycanbeovercome---evenintheframeworkoffirst-orderlogic--bydevelopingmathematicsinset-theoreticterms.Weexplaintheprerequisitesfromsettheorynecessaryforthispurposeandthentreatthesubtlerelationbetweenlogicandsettheoryinathoroughmanner.Godelsincompletenesstheoremsarepresentedinconnectionwithseveralrelatedresults(suchasTrahtenbrotstheorem)whichallexemplifythelimitatiousofmachine-orientedproofmethods.Thenotionsofcomputabilitytheorythatarerelevanttothisdiscussionaregivenindetail.Theconceptofcomputabilityismadeprecisebymeansoftheregistermachineasacomputermodel.
书籍规格:
| 书籍详细信息 | |||
| 书名 | 数理逻辑站内查询相似图书 | ||
| 9787506292276 如需购买下载《数理逻辑》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN | |||
| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 45.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
书籍信息归属:
数理逻辑是世界图书出版公司北京公司于2008.05出版的中图分类号为 O141 的主题关于 数理逻辑－高等学校－教材－英文 的书籍。
添加好友请备注(图书代寻_9787506292276)