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.

“I cannot think of a better textbook as the backbone of an introductory course in proof theory, given how clear and self-contained the material is. … ‘Proof Theory and Algebra in Logic’ is an inspiring book that sows the seeds for further studies, and it is the perfect bridge towards more advanced research topics.” (Gianluca Caterina, MAA Reviews, June 21, 2021)