The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant
Gemma Robles, José M. Méndez · Logic Journal of IGPL · 2007
The logic BKc1 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 BKc1 with a negation connective. The aim of this paper is to define the logic BKc1F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc1 and BKc1F are definitionally equivalent.