In this paper, I consider a family of three-valued regular logics:
the well-known strong and weak S.C. Kleene’s logics and two intermedi-
ate logics, where one was discovered by M. Fitting and the other one by
E. Komendantskaya. All these systems were originally presented in the
semantical way and based on the theory of recursion. However, the proof
theory of them still is not fully developed. Thus, natural deduction sys-
tems are built only for strong Kleene’s logic both with one (A. Urquhart,
…
Read moreIn this paper, I consider a family of three-valued regular logics:
the well-known strong and weak S.C. Kleene’s logics and two intermedi-
ate logics, where one was discovered by M. Fitting and the other one by
E. Komendantskaya. All these systems were originally presented in the
semantical way and based on the theory of recursion. However, the proof
theory of them still is not fully developed. Thus, natural deduction sys-
tems are built only for strong Kleene’s logic both with one (A. Urquhart,
G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi,
A. Tamminga). The purpose of this paper is to provide natural deduction
systems for weak and intermediate regular logics both with one and two
designated values.
