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。

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

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