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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.

Logic, Symbolic and mathematical. --- Logic. --- Reasoning. --- Thought and thinking. --- Philosophy --- Mathematics --- Philosophy & Religion --- Physical Sciences & Mathematics --- Mathematical Theory --- Logic --- Mathematics. --- Math --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematical logic. --- Semantics. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Science --- Formal semantics --- Semasiology --- Semiology (Semantics) --- Comparative linguistics --- Information theory --- Language and languages --- Lexicology --- Meaning (Psychology) --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science. --- Informatics

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Mathematical logic --- Lexicology. Semantics --- semantiek --- wiskunde

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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.

Mathematical logic --- Lexicology. Semantics --- semantiek --- wiskunde

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This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

Automatic theorem proving --- Logic, Symbolic and mathematical --- Congresses. --- Computer Science --- Engineering & Applied Sciences --- Congresses --- Mathematics. --- Programming languages (Electronic computers). --- Algorithms. --- Mathematical logic. --- Artificial intelligence. --- Mathematical Logic and Foundations. --- Programming Languages, Compilers, Interpreters. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- Algorithm Analysis and Problem Complexity. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algorism --- Algebra --- Arithmetic --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Math --- Science --- Foundations --- Logic [Symbolic and mathematical ] --- Logic, Symbolic and mathematical. --- Computer science. --- Computer software. --- Artificial Intelligence. --- Software, Computer --- Computer systems --- Informatics --- Automatic theorem proving - Congresses. --- Logic, Symbolic and mathematical - Congresses