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".
目錄：
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
內容試閱：
Modern mathematics has acquired a significant growth level with the rapid progress of science and technology.Conversely we can also say that the development of modern mathematics serves to lay the foundations for the progress of science and technology.Mathematics till date has not only been a towering big tree having the luxuriant growth of leaves and branches but has also deeply rooted itself in the areas of morden science and technology.According to the Mathematics Subject Classification 2000 provided by the American Mathematical Society，the subjects have been numbered from 00，01，up to 97 except absence of a minority and each class has been further classified into tens of sorts of research directions.It iS thus clear that the contents of mathematics are vast as the open sea and mathematicians having a good command of each branch like in the times of Euler no longer exist.
As stated above，modern mathematics has numerous branches，the research contents and methods of distinct branches are very different.Hence it is not re- alistic to expect mathematical researchers to be proficient in all branches.But it is，in our view，necessary for them to acquaint themselves to a certain extent with the contents and methods of mathematical logic.Byacquaint themselves to a certain extent with'' we primarily mean that they should understand the introduction to mathematical logic，i.e.the theory of logical calculi，including propositional and first order predicate calculi，because it is not only the common foundation of axiomatic set theory，model theory，proof theory and recursion theory in mathe- matical logic，but also the part in which non-logical experts are most interested.Particularly for scholars who are engaged in teaching and scientific research in spe- cialized subjects of computer，applied mathematics，artificial intelligence and SO on and for university students and graduate students who are studying in these specialities，a familiarity with logical calculi is necessary.
The theory of logical calculi is an effective tool.A familiarity with the methods and techniques in logical calculi will lay a foundation for further studying subjects such as resolution principle，logic programming and theorem automated proving，and the methods and techniques of resolution principle play a crucial role in logic programming and automated reasoning.If we could have a textbook which introduces commonly the theory of logical calculi and，based on this，presents clearly and precisely the theory of resolution principle，it would be of great value for teachers，students and researchers engaged in the specialities of computer，applied mathematics and artificial intelligence.This textbook is intended as an attempt in this direction.
The reference is regarded as a classic one.It introduces several proof procedures which are based on Herbrand''s theorem after examining in a great detail the theory of resolution principle，and provides basic contents such as problem solving and program design in theorem automated proving.The reference is a good book and was cited by the related literature at home and abroad.It is a pity that the reference lays special emphasis on the resolution principle，while the introduction to the theory of logical calculi is limited to only the part that is directly used later in the book.Important contents such as the equivalence of a prenex normal form to the original formula and the completeness of propositional and predicate calculi are not involved.Hence the contents of are inadequate for the readers who expect to study logical calculi.The reference makes a complement to ，but the contents of logical calculi are still inadequate.The references on mathematical logic listed in this book are all masterpieces，in which the introduction to logical calculi is a high standard and is orthodox.For example，the proof for the completeness of propositional logic adopts the method of consistent extensions，and the proof for the completeness of the first order predicate logic adopts the traditional extension method by adding countably infinite individual constants or by adding countably infinite variable symbols.These methods are of course rigorous and the arguments are unassailable.However，these methods seem too professional.In addition，the related literature lacks in general the content of resolution principle.Hence it becomes necessary to publish a textbook as mentioned above，which introduces first the theory of logical calculi in a common way and，based on this，presents clearly and precisely the theory of resolution
principle.
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