Shunsuke Yatabe

I am a logician, and I am interested in logical theories of the circular phenomenon. So I am studying set theories and truth theories within non-classical logics.
The study of logical theories of the circularity is important not only in logic but also in computer science. For, one of the key concepts, the recursion, has a circular nature since we should calculate the value of 2+1 in order to calculate the value of 2+2. However, it is well-known that the full form of the circularity implies a contradiction, e.g. Russell paradox, the comprehension principle which guarantees the existence of term {x : P(x)} for any formula P(x) implies a contradiction, or the liar paradox in truth theories with full T-scheme in classical logic. Therefore we have to restrict the form of the recursion to have a consistent theory if we keep classical logic.
It is well-known that both the comprehension principle and the full T-scheme do not imply a contradiction in many non-classical logics. These theories allow a very strong form of the circularity, namely a general form of the recursive definition in set theories in substructural logics, and co-inductive definitions in fuzzy truth theories. Such form of the circularity is not only interesting as itself, but also worth studying, for it is an ideal generalization of recursion in classical recursion theory.