MARC Record from harvard_bibliographic_metadata

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020 $a9789401599344
020 $a9789401599344
020 $a9789048160792
024 7 $a10.1007/978-94-015-9934-4$2doi
035 $a(Springer)9789401599344
040 $aSpringer
050 4 $aQA8.9-10.3
072 7 $aPBC$2bicssc
072 7 $aPBCD$2bicssc
072 7 $aMAT018000$2bisacsh
082 04 $a511.3$223
100 1 $aAndrews, Peter B.,$eauthor.
245 13 $aAn Introduction to Mathematical Logic and Type Theory: To Truth Through Proof /$cby Peter B. Andrews.
250 $aSecond Edition.
264 1 $aDordrecht :$bSpringer Netherlands :$bImprint: Springer,$c2002.
300 $aXVIII, 390 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aApplied Logic Series,$x1386-2790 ;$v27
505 0 $aPreface 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.
520 $aIn 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.
650 20 $aComputational linguistics.
650 24 $aArtificial Intelligence (incl. Robotics)
650 20 $aLogic.
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aLogic.
650 0 $aElectronic data processing.
650 0 $aArtificial intelligence.
650 0 $aLogic, Symbolic and mathematical.
650 0 $aComputational linguistics.
650 24 $aMathematical Logic and Foundations.
650 24 $aComputing Methodologies.
776 08 $iPrinted edition:$z9789048160792
830 0 $aApplied Logic Series ;$v27.
988 $a20131119
906 $0VEN