Logic: A Brief Course

✍ Scribed by Daniele Mundici (auth.)

• Publisher: Springer-Verlag Mailand
• Year: 2012
• Tongue: English
• Leaves: 132
• Series: Unitext
• Edition: 1
• Category: Library

✦ Synopsis

This short book, geared towards undergraduate students of computer science and mathematics, is specifically designed for a first course in mathematical logic. A proof of Gödel's completeness theorem and its main consequences is given using Robinson's completeness theorem and Gödel's compactness theorem for propositional logic. The reader will familiarize himself with many basic ideas and artifacts of mathematical logic: a non-ambiguous syntax, logical equivalence and consequence relation, the Davis-Putnam procedure, Tarski semantics, Herbrand models, the axioms of identity, Skolem normal forms, nonstandard models and, interestingly enough, proofs and refutations viewed as graphic objects. The mathematical prerequisites are minimal: the book is accessible to anybody having some familiarity with proofs by induction. Many exercises on the relationship between natural language and formal proofs make the book also interesting to a wide range of students of philosophy and linguistics.

✦ Table of Contents

Front Matter....Pages I-XI
Front Matter....Pages 1-1
Introduction....Pages 3-6
Fundamental Logical Notions....Pages 7-11
The Resolution Method....Pages 13-17
Robinson’s Completeness Theorem....Pages 19-26
Fast Classes for DPP....Pages 27-30
Gödel’s Compactness Theorem....Pages 31-34
Propositional Logic: Syntax....Pages 35-39
Propositional Logic: Semantics....Pages 41-46
Normal Forms....Pages 47-51
Recap: Expressivity and Efficiency....Pages 53-54
Front Matter....Pages 55-55
The Quantifiers “There Exists” and “For All”....Pages 57-61
Syntax of Predicate Logic....Pages 63-69
The Meaning of Clauses....Pages 71-78
Gödel’s Completeness Theorem for the Logic of Clauses....Pages 79-88
Equality Axioms....Pages 89-93
The Predicate Logic L ....Pages 95-116
Final Remarks....Pages 117-120
Back Matter....Pages 121-130

✦ Subjects

Mathematical Logic and Foundations; Mathematical Logic and Formal Languages; Semantics