rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: An
    title: Introduction to Mathematical Logic and Type Theory: To Truth Through Proof
  name:
    name part: Andrews, Peter B.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    date issued: 2002
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xviii, 390 pages)
  abstract: In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
  table of contents: Preface to the Second Edition -- Preface -- Introduction -- 1. Propositional Calculus -- 2. First-Order Logic -- 3. Provability and Refutability -- 4. Further Topics in First-Order Logic -- 5. Type Theory -- 6. Formalized Number Theory -- 7. Incompleteness and Undecidability -- Supplementary Exercises -- Summary of Theorems -- Bibliography -- List of Figures -- Index.
  note: by Peter B. Andrews.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Logic
  subject:
    topic: Electronic data processing
  subject:
    topic: Artificial intelligence
  subject:
    topic: Logic, Symbolic and mathematical
  subject:
    topic: Computational linguistics
  subject:
    topic: Artificial intelligence
  subject:
    topic: Computational linguistics
  subject:
    topic: Electronic data processing
  subject:
    topic: Logic
  subject:
    topic: Logic, Symbolic and mathematical
  subject:
    topic: Mathematics
  classification: QA8.9-10.3
  classification: 511.3
  related item:
    title info:
      title: Applied logic series ; 27
  identifier: 9789401599344 (electronic bk.)
  identifier: 9401599343 (electronic bk.)
  identifier: 9789048160792
  identifier: 9048160790
  identifier: 9401599343
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130321
    record change date: 20260422175520.0
    record identifier: in00003579102
    language of cataloging:
      language term: eng