Natural Deduction for Post’s Logics and their Duals

Abstract

In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued ( $$k\geqslant 3$$ ) logics as well as for all Dual Post’s k-valued logics.