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。
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书名 | 数理逻辑引论与归结原理(精) |
分类 | 科学技术-自然科学-数学 |
作者 | Guo-Jun Wang//Hong-Jun Zhou |
出版社 | 科学出版社 |
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简介 | 编辑推荐 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。 目录 Preface Chapter 1 Preliminaries 1.1 Partially ordered sets 1.2 Lattices 1.3 Boolean algebras Chapter 2 Propositional Calculus 2.1 Propositions and their symbolization 2.2 Semantics of propositional calculus 2.3 Syntax of propositional calculus Chapter 3 Semantics of First Order Predicate Calculus 3.1 First order languages 3.2 Interpretations and logically valid formulas 3.3 Logical equivalences Chapter 4 Syntax of First Order Predicate Calculus 4.1 The formal system KL 4.2 Provable equivalence relations 4.3 Prenex normal forms 4.4 Completeness of the first order system KL *4.5 Quantifier-free formulas Chapter 5 Skolem's Standard Forms and Herbrand's Theorems 5.1 Introduction 5.2 Skolem standard forms 5.3 Clauses *5.4 Regular function systems and regular universes 5.5 Herbrand universes and Herbrand's theorems 5.6 The Davis-Putnam method Chapter 6 Resolution Principle 6.1 Resolution in propositional calculus 6.2 Substitutions and unifications 6.3 Resolution Principle in predicate calculus 6.4 Completeness theorem of Resolution Principle 6.5 A simple method for searching clause sets S Chapter 7 Refinements of Resolution 7.1 Introduction 7.2 Semantic resolution 7.3 Lock resolution 7.4 Linear resolution Chapter 8 Many-Valued Logic Calculi 8.1 Introduction 8.2 Regular implication operators 8.3 MV-algebras 8.4 Lukasiewicz propositional calculus 8.5 R0-algebras 8.6 The propositional deductive system L* Chapter 9 Quantitative Logic 9.1 Quantitative logic theory in two-valued propositional logic system L 9.2 Quantitative logic theory in L ukasiewicz many-valued propositional logic systems Ln and Luk 9.3 Quantitative logic theory in many-valued R0-propositional logic systems L*n and L* 9.4 Structural characterizations of maximally consistent theories 9.5 Remarks on Godel and Product logic systems Bibliography Indent |
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