数理逻辑引论与归结原理 内容简介

　　Introduction to Mathematical Logic Resolution Principle， Second Edition in nine chapters， discusses Boolean algebra theory， propositional calculus and predicated calculus theory， resolution principle theory and the latest theory ofmultivalue logic. The book also includes supplement or altemations on the proofofthe completion of K in first-ordcr system，conceming "Quantitative Logic".

数理逻辑引论与归结原理 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
Index

自然科学 数学 高等数学

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