Non-Ignorance and Knowledge

Epistemic logic was proposed by Hintikka to model human knowledge and beliefs. Since then, a lot of work has been done to improve epistemic logic for applications to several problems. One of the interesting problems is to relate the concept of ignorance to that of knowledge. In this paper, we introduce a logic for non-ignorance LNI by extending the classical propositional logic with the operator Ni. We describe its axiomatization and Kripke semantics. We show some technical results including a completeness and discuss some applications and extensions.