Logic for Applications
2nd Edition
Published on 28. September 2012
Book
Paperback/Softback
XIII, 456 pages
978-1-4612-6855-0 (ISBN)
Description
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Reviews / Votes
From reviews of the first edition: "... must surely rank as one of the most fruitful textbooks introduced into computer science ... We strongly suggest it as a textbook ..." SIGACT News
From the reviews of the second edition:
".the book achieves its goal of being a unified introduction into classical logic, logic programming and certain non-classical logics. .the book succeeded in presenting a uniform framework for describing different logics. The author's thorough approach to describing logic programming, via introduction of resolution-based refutations and subsequent study of different kinds of resolutions allows the reader to gradually switch from the study of logic to the study of logical programming paradigm and provides a lot of intuition about the behavior of logic programs.
As such the book can be recommended both as a textbook for senior/graduate course in logic/logic programming, and as a reading or reference for graduate students in the areas related to discrete mathematics."
(Alexander Dekhtyar, William Gasarch's Book Review Column, SIGACT News)
More details
Series
Edition
Second Edition 1997
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Professional/practitioner
Illustrations
XIII, 456 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 26 mm
Weight
715 gr
ISBN-13
978-1-4612-6855-0 (9781461268550)
DOI
10.1007/978-1-4612-0649-1
Schweitzer Classification
Other editions
Additional editions
Anil Nerode | Richard A. Shore
Logic for Applications
Book
01/1997
2nd Edition
Springer
€149.79
Shipment within 5-7 days
Previous edition
Richard Nerode | Anil Nerode | Richard A. Shore
Logic for Applications
Book
09/1993
Springer
€36.75
Article exhausted; check for reprint
Persons
Anil Nerode, Distinguished Professor of Mathematics at Cornell University, has, over a period of 66 years, made significant contributions to mathematical logic, automata theory, computability theory, and hybrid systems engineering, publishing around 100 papers and 5 books. He first learned elliptic function theory as a graduate student from André Weil in the early 1950s and has taught it over the years, resulting in the present book.
¿Noam Greenberg is Professor of Mathematics at Victoria University of Wellington, New Zealand. His main research interests are computability theory, algorithmic randomness, reverse mathematics, higher recursion theory, computable model theory, and set theory. He was a Royal Society of New Zealand Rutherford Discovery Fellow and is a Fellow of the Royal Society of New Zealand.
Content
I Propositional Logic.- 1 Orders and Trees.- 2 Propositions, Connectives and Truth Tables.- 3 Truth Assignments and Valuations.- 4 Tableau Proofs in Propositional Calculus.- 5 Soundness and Completeness of Tableau Proofs.- 6 Deductions from Premises and Compactness.- 7 An Axiomatic Approach*.- 8 Resolution.- 9 Refining Resolution.- 10 Linear Resolution, Horn Clauses and PROLOG.- II Predicate Logic.- 1 Predicates and Quantifiers.- 2 The Language: Terms and Formulas.- 3 Formation Trees, Structures and Lists.- 4 Semantics: Meaning and Truth.- 5 Interpretations of PROLOG Programs.- 6 Proofs: Complete Systematic Tableaux.- 7 Soundness and Completeness of Tableau Proofs.- 8 An Axiomatic Approach*.- 9 Prenex Normal Form and Skolemization.- 10 Herbrand's Theorem.- 11 Unification.- 12 The Unification Algorithm.- 13 Resolution.- 14 Refining Resolution: Linear Resolution.- III PROLOG.- 1 SLD-Resolution.- 2 Implementations: Searching and Backtracking.- 3 Controlling the Implementation: Cut.- 4 Termination Conditions for PROLOG Programs.- 5 Equality.- 6 Negation as Failure.- 7 Negation and Nonmonotonic Logic.- 8 Computability and Undecidability.- IV Modal Logic.- 1 Possibility and Necessity; Knowledge or Belief.- 2 Frames and Forcing.- 3 Modal Tableaux.- 4 Soundness and Completeness.- 5 Modal Axioms and Special Accessibility Relations.- 6 An Axiomatic Approach*.- V Intuitionistic Logic.- 1 Intuitionism and Constructivism.- 2 Frames and Forcing.- 3 Intuitionistic Tableaux.- 4 Soundness and Completeness.- 5 Decidability and Undecidability.- 6 A Comparative Guide.- VI Elements of Set Theory.- 1 Some Basic Axioms of Set Theory.- 2 Boole's Algebra of Sets.- 3 Relations, Functions and the Power Set Axiom.- 4 The Natural Numbers, Arithmetic and Infinity.- 5 Replacement, Choice andFoundation.- 6 Zermelo-Fraenkel Set Theory in Predicate Logic.- 7 Cardinality: Finite and Countable.- 8 Ordinal Numbers.- 9 Ordinal Arithmetic and Transfinite Induction.- 10 Transfinite Recursion, Choice and the Ranked Universe.- 11 Cardinals and Cardinal Arithmetic.- Appendix A: An Historical Overview.- 1 Calculus.- 2 Logic.- 3 Leibniz's Dream.- 4 Nineteenth Century Logic.- 5 Nineteenth Century Foundations of Mathematics.- 6 Twentieth Century Foundations of Mathematics.- 7 Early Twentieth Century Logic.- 8 Deduction and Computation.- 9 Recent Automation of Logic and PROLOG.- 10 The Future.- Appendix B: A Genealogical Database.- Index of Symbols.- Index of Terms.