# Logic: a Brief Course

Springer Science & Business Media, Mar 29, 2012 - Mathematics - 130 pages
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.

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### Contents

 1 Introduction 3 2 Fundamental Logical Notions 7 3 The Resolution Method 12 4 Robinsons Completeness Theorem 19 5 Fast Classes for DPP 27 6 Godels Compactness Theorem 31 Syntax 35 Semantics 40
 Part II Predicate Logic 55 11 The Quantifiers There Exists and For All 56 12 Syntax of Predicate Logic 63 13 The Meaning of Clauses 70 14 Godels Completeness Theorem for the Logic of Clauses 79 15 Equality Axioms 89 16 The Predicate Logic L 95 17 Final Remarks 117

 9 Normal Forms 47 Expressivity and Efficiency 53