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Mathematical Logic

Katalin Bimbo (Autor)

Buch | Hardcover

272 Seiten

2021
Productivity Press (Verlag)
978-1-4987-4413-3 (ISBN)

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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.

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.

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)

Erscheint lt. Verlag	1.1.2021
Reihe/Serie	Textbooks in Mathematics
Zusatzinfo	35 Illustrations, black and white
Verlagsort	Portland
Sprache	englisch
Maße	156 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4987-4413-3 / 1498744133
ISBN-13	978-1-4987-4413-3 / 9781498744133
Zustand	Neuware