Logic for Applications

Logic for Applications by Anil Nerode, Richard A. Shore.

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 applicatio...

Full description

Saved in:
Bibliographic Details
Main Authors: Nerode, Anil (Author), Shore, Richard A. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1997.
Edition:2nd ed. 1997.
Series:Texts in Computer Science,
Springer eBook Collection.
Subjects:
Architecture, Computer.
Mathematical logic.
Computers.
Computer logic.
Artificial intelligence.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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 and Foundation
  • 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.

Similar Items