Some Considerations of Bi-Intuitionistic Logics

                               

Abstract

Bi-intuitionistic logic (BiInt) is intuitionistic logic extended with co-implication (<), a logical connective dual to ordinary implication. In classical logic, since B < A means B ∧ ¬A, nothing particularly interesting occurs by introducing co-implication. The main aim of my talk is to examine how the intuitionistic world is affected by the introduction of co-implication, by checking basic logical properties of extensions of BiInt in comparison with those of extensions of intuitionistic logic. First, we will discuss the subject from syntactical perspectives, including sequent formulations, (local) deduction theorems, and negative translations. Next, we will focus our attention on the symmetry features peculiar to extensions of BiInt.

About the Speaker

Hiroakira Ono is Professor Emeritus at the Japan Advanced Institute of Science and Technology (JAIST). After obtaining his Ph.D. from Kyoto University, he worked at several universities and research institutes in Japan, making contributions to non-classical logics through proof-theoretic and algebraic methods. He has also authored books including Residuated Lattices: An Algebraic Glimpse at Substructural Logics and Proof Theory and Algebra in Logic.