数理逻辑引论与归结原理

Preface

Chapter1Preliminaries

1.1Partiallyorderedsets

1.2Lattices

1.3Booleanalgebras

Chapter2PropositionalCalculus

2.1Propositionsandtheirsymbolization

2.2Semanticsofpropositionalcalculus

2.3Syntaxofpropositionalcalculus

Chapter3SemanticsofFirstOrderPredicateCalculus

3.1Firstorderlanguages

3.2Interpretationsandlogicallyvalidformulas

3.3Logicalequivalences

Chapter4SyntaxofFirstOrderPredicateCalculus

4.1TheformalsystemKL

4.2Provableequivalencerelations

4.3Prenexnormalforms

4.4CompletenessofthefirstordersystemKL

*4.5Quantifier-freeformulas

Chapter5SkolemsStandardFormsandHerbrandsTheorems

5.1Introduction

5.2Skolemstandardforms

5.3Clauses

*5.4Regularfunctionsystemsandregularuniverses

5.5HerbranduniversesandHerbrandstheorems

5.6TheDavis-Putnammethod

Chapter6ResolutionPrinciple

6.1Resolutioninpropositionalcalculus

6.2Substitutionsandunifications

6.3ResolutionPrincipleinpredicatecalculus

6.4CompletenesstheoremofResolutionPrinciple

6.5AsimplemethodforsearchingclausesetsS

Chapter7RefinementsofResolution

7.1Introduction

7.2Semanticresolution

7.3Lockresolution

7.4Linearresolution

Chapter8Many-ValuedLogicCalculi

8.1Introduction

8.2Regularimplicationoperators

8.3MV-algebras

8.4Lukasiewiczpropositionalcalculus

8.5R0-algebras

8.6ThepropositionaldeductivesystemL*

Chapter9QuantitativeLogic

9.1Quantitativelogictheoryintwo-valuedpropositionallogicsystemL

9.2QuantitativelogictheoryinLukasiewiczmany-valuedpropositionallogicsystemsLnandLuk

9.3Quantitativelogictheoryinmany-valuedR0-propositionallogicsystemsL*nandL*

9.4Structuralcharacterizationsofmaximallyconsistenttheories

9.5RemarksonGodelandProductlogicsystems

Bibliography

Indent

　　本书在第一版的基础上进行修订再版，全书共9章，内容可分为Boole代数理论，命题演算与谓词演算理论，归结原理理论，多值逻辑的最新理论等4部分。同时，在第一版的基础上对“计量逻辑学”，关于一阶系统K完备性的证明等诸多内容做了补充或改写。　　本书可供计算机专业、应用数学专业、人工智能专业的研究生与高年级本科生及教师阅读。