Mathematical Logic
1st Edition
Published on 1. January 2021
Book
Hardback
272 pages
978-1-4987-4413-3 (ISBN)
Description
This graduate level text on first-order logic highlights the importance of this area as well as the abundance of results and some applications. The best-known of textbooks originated in an earlier era, and despite frequent updating by their authors, they reflect a general view and a particular approach that is less adequate today. The addition of "metatheory" clarifies that this is not a textbook in which the emphasis is on the basics such as formalizing English sentences and learning the use of one or another calculus. This textbook takes a fresh look at the current state of first-order logic, and integrates newer results with a reevaluated stock of earlier ones.
More details
Series
Language
English
Place of publication
Portland
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Illustrations
35 s/w Abbildungen
35 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
ISBN-13
978-1-4987-4413-3 (9781498744133)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Person
Katalin Bimbo is Associate Professor at University of Alberta. She has published three other well-received books on logic including Proof Theory: Sequent Calculi and Related Formalisms (CRC Press, 2014). She received a Faculty of Arts Reasearch Excllence Awared in 2012.
Content
Chapter 1. Language and interpretation of first-order logic
Chapter 2. Proof systems: sequent calculus, tableaux, axiomatic calculus
Chapter 3. Propositional logic (as a restriction of rst-order logic), truth tables, disjunctive and conjunctive normal forms, prenex normal forms
Chapter 4. Resolution calculus and its applications; equivalence of proof calculi
Chapter 5. Core metatheorems I: Soundness and completeness proofs (including separate proofs for propositional logic and di erent constructions for the quanti cational case)
Chapter 6. Core metatheorems II: Compactness, upward and downward L*owenheim{Skolem theorems, Lindstr *om's theorem
Chapter 7. Core metatheorems III: Craig's interpolation theorem, Robinson's consistency theorem, Beth's de nability theorem
Chapter 8. Core metatheorems IV: Undecidability, the impact of the metatheorems
Chapter 9. Expressibility and de nability (variations on the set of logical connectives and the set of logical operators; choosing and modifying the non-logical vocabulary)
Chapter 10. Algebraizations (Boolean algebra for propositional logic, cylindric algebra and polyadic algebra for rst-order logic)
Chapter 11. Mathematical theories within first-order logic (varieties: semi-groups, groups, etc.; ordered structures; arithmetic; set theory)
Chapter 12. Decidability (propositional logic, classes of quanti cational formulas speci ed by quanti er prex, by shape of formulas)
Chapter 13. Complexity (satis ability problem, validity problem)
Chapter 14. Categorial view (category of proofs, quanti ers as adjoint functors)
Chapter 2. Proof systems: sequent calculus, tableaux, axiomatic calculus
Chapter 3. Propositional logic (as a restriction of rst-order logic), truth tables, disjunctive and conjunctive normal forms, prenex normal forms
Chapter 4. Resolution calculus and its applications; equivalence of proof calculi
Chapter 5. Core metatheorems I: Soundness and completeness proofs (including separate proofs for propositional logic and di erent constructions for the quanti cational case)
Chapter 6. Core metatheorems II: Compactness, upward and downward L*owenheim{Skolem theorems, Lindstr *om's theorem
Chapter 7. Core metatheorems III: Craig's interpolation theorem, Robinson's consistency theorem, Beth's de nability theorem
Chapter 8. Core metatheorems IV: Undecidability, the impact of the metatheorems
Chapter 9. Expressibility and de nability (variations on the set of logical connectives and the set of logical operators; choosing and modifying the non-logical vocabulary)
Chapter 10. Algebraizations (Boolean algebra for propositional logic, cylindric algebra and polyadic algebra for rst-order logic)
Chapter 11. Mathematical theories within first-order logic (varieties: semi-groups, groups, etc.; ordered structures; arithmetic; set theory)
Chapter 12. Decidability (propositional logic, classes of quanti cational formulas speci ed by quanti er prex, by shape of formulas)
Chapter 13. Complexity (satis ability problem, validity problem)
Chapter 14. Categorial view (category of proofs, quanti ers as adjoint functors)