Proof Theory and Algebra in Logic

Hiroakira Ono (Autor)

Buch | Softcover

160 Seiten

2019 | 1st ed. 2019
Springer Verlag, Singapore
978-981-13-7996-3 (ISBN)

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This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed inthe second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

Hiroakira Ono is an emeritus professor of Japan Advanced Institute for Science and Technology (JAIST). He moved to JAIST in 1993 after working at Hiroshima University for twenty years. Later he became a distinguished professor until his retirement from JAIST in 2012. His main interest is study of nonclassical logics, in particular substructural logics and intermediate logics, from both syntactic and semantical point of view. In addition to his co-authored book on substructural logics in 2007, he published six textbooks in Japanese, including those on logic and algebra, one of which gained a reputation as one of most popular textbooks on logic in Japan since its publication in 1994.

Introduction.- Part I Proof Theory.- Sequent systems.- Cut elimination for sequent systems.- Proof-theoretic analysis of logical properties.- Modal and substructural logics.- Deducibility and axiomatic extensions.- Part II Algebra in Logic.- Boolean algebras and classical logic.- Many-valued algebras.- Heyting algebras and intuitionistic logic.- Logics and varieties.- Residuated structures.- Modal algebras.- References.- Index.

Erscheinungsdatum	23.08.2019
Reihe/Serie	Short Textbooks in Logic
Zusatzinfo	4 Illustrations, black and white; VIII, 160 p. 4 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
	Geisteswissenschaften ► Philosophie ► Logik
	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	981-13-7996-3 / 9811379963
ISBN-13	978-981-13-7996-3 / 9789811379963
Zustand	Neuware