Proof Theory and Algebra in Logic

• Main Author: Ono, Hiroakira (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Short Textbooks in Logic,
• Subjects: Logic.; Mathematical logic.; Algebra.; Ordered algebraic structures.; Mathematical Logic and Formal Languages.; Mathematical Logic and Foundations.; Order, Lattices, Ordered Algebraic Structures.

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 resul...

Table of Contents:

• 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.