The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant

摘要

The logic B_Kc1 is the basic constructive logic in the ternary relational semantics (without a set of designated points) adequate to consistency understood as the absence of the negation of any theorem. Negation is introduced in B_Kc1 with a negation connective. The aim of this paper is to define the logic B_Kc1F. In this logic negation is introduced via a propositional falsity constant. We prove that B_Kc1 and B_Kc1F are definitionally equivalent.