Hiroakira Ono Distinguished Professor
Research Center for Integrated Science

■Degrees

M.S. from University of Tokyo (1968), Ph.D.from Kyoto University (1973)

■Professional Career

Associate Professor of Tsuda College (1973), Associate Professor (1976) and Professor (1985) of Hiroshima University, Professor of JAIST (1993), Vice-president of JAIST (2006-2008), Distinguished Professor of JAIST (2008- )

■Specialties

Algebraic logic, Substructural logics and residuated lattices, Applications of logic to computer science

■Research Keywords

Algebraic logic, Substructural logics, Modal logics, Residuated structures

■Research Interests

Algebraic approach to Substructural logics
Substructural logics are logics lacking some of structural rules, if they are formalized in sequent systems. They include many important nonclassical logics like linear logic, relevant logics, Lukasiewicz's many-valued logics and Lambek's calculus. The study of substructural logics will provide us a uniform viewpoint in studying various nonclassical logics. I am now developing an algebraic study of substructural logics. This seems quite promising, and in fact, algebraists are also interested in algebraic structures related to these logics. Thus I started a research project, called "Algebra & Substructural Logics" and have organized international workshops on this topics twice at JAIST, and the third one was held in Poland in 2006. With some collaboratos, I have published a book with the title "Residuated Lattices: an algebraic glimpse at substructural logics" in the spring of 2007.
Modal logic
Due to the developement of semantical methods in recent years, we have now very strong and deep results on nonclassical propositional logics, in particular on intermediate and modal propositional logics. On the other hand, because of the incompleteness of predicate logics with respect to the standard semantics, we know only a little about them. Recently we have made a certain progress on this subject by applying algebraic methods. We are developing also a general theory of both multi-modal and intuitionistic modal propositional logics. Another topics in which we are interested is the study of logical aspects of reasonings and judgements appearing in everyday life, based on logics of knowledge and belief.
Mechanical theorem proving
We are working also at theorem provers for nonclassical logics, in particular for modal logics and substructural logics. Our main concern is to find efficient algorithms for finding both proof-trees and counter-models.

■Publications

■Extramural Activities