Logic: a brief course
(eBook)
Author:
Series:
Published:
Milan ; New York : Springer, ©2012.
Format:
eBook
ISBN:
9788847023611, 8847023610, 8847023602, 9788847023604
Content Description:
1 online resource (xi, 124 pages)
Status:
Available Online
Description
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 G©œdel's completeness theorem and its main consequences is given using Robinson's completeness theorem and G©œdel'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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Citations
APA Citation (style guide)
Mundici, D. (2012). Logic: a brief course. Milan ; New York, Springer.
Chicago / Turabian - Author Date Citation (style guide)Mundici, Daniele, 1946-. 2012. Logic: A Brief Course. Milan ; New York, Springer.
Chicago / Turabian - Humanities Citation (style guide)Mundici, Daniele, 1946-, Logic: A Brief Course. Milan ; New York, Springer, 2012.
MLA Citation (style guide)Mundici, Daniele. Logic: A Brief Course. Milan ; New York, Springer, 2012.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Language:
English
UPC:
10.1007/978-88-470-2361-1
Notes
Description
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 G©œdel's completeness theorem and its main consequences is given using Robinson's completeness theorem and G©œdel'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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Grouped Work ID:
81132d1c-c080-734c-cf24-3f6ea13b700b
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| Last File Modification Time | Apr 05, 2024 08:57:53 AM |
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| 505 | 0 | 0 | |g pt. I.|t Propositional Logic --|t Introduction --|t Fundamental Logical Notions --|t The Resolution Method --|t Robinson's Completeness Theorem --|t Fast Classes for DPP --|t Gödel's Compactness Theorem --|t Propositional Logic: Syntax --|t Propositional Logic: Semantics --|t Normal Forms --|t Recap: Expressivity and Efficiency --|g pt. II.|t Predicate Logic --|t The Quantifiers "There Exists" and "For All" --|t Syntax of Predicate Logic --|t The Meaning of Clauses --|t Gödel's Completeness Theorem for the Logic of Clauses --|t Equality Axioms --|t The Predicate Logic L --|t Final Remarks. |
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