Epistemic Logic Founded on Nonignorance


Author to whom all correspondence should be addressed; e-mail: akama@jcom.home.ne.jp.


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 an epistemic logic LNI founded on nonignorance 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.