數(shù)理邏輯引論與歸結(jié)原理

前言

　　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.By‘a(chǎn)cquaint themselves to a certain extent withwe primarily mean that they should understand the introduc-tion 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.

內(nèi)容概要

本書(shū)在第一版的基礎(chǔ)上進(jìn)行修訂再版，全書(shū)共9章，內(nèi)容可分為Boole代數(shù)理論，命題演算與謂詞演算理論，歸結(jié)原理理論，多值邏輯的最新理論等4部分。同時(shí)，在第一版的基礎(chǔ)上對(duì)“計(jì)量邏輯學(xué)”，關(guān)于一階系統(tǒng)K完備性的證明等諸多內(nèi)容做了補(bǔ)充或改寫(xiě)。     本書(shū)可供計(jì)算機(jī)專(zhuān)業(yè)、應(yīng)用數(shù)學(xué)專(zhuān)業(yè)、人工智能專(zhuān)業(yè)的研究生與高年級(jí)本科生及教師閱讀。

書(shū)籍目錄

PrefaceChapter 1  Preliminaries  1.1  Partially ordered sets  1.2  Lattices  1.3  Boolean algebrasChapter 2  Propositional Calculus  2.1  Propositions and their symbolization  2.2  Semantics of propositional calculus  2.3  Syntax of propositional calculusChapter 3  Semantics of First Order Predicate Calculus  3.1  First order languages  3.2  Interpretations and logically valid formulas  3.3  Logical equivalencesChapter 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 formulasChapter 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 methodChapter 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 SChapter 7  Refinements of Resolution  7.1  Introduction  7.2  Semantic resolution  7.3  Lock resolution  7.4  Linear resolutionChapter 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 systemsBibliographyIndent

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