A Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)
Abstract
We argue that the notion of epistemic possible worlds in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic) Epistemic Logic. Regarding non-predetermined possibilities, we propose a constructive epistemic logic and prove soundness and completeness theorems for it. We extend the proposed logic by adding a public announcement operator. To declare the significance of our work, we formulate the well-known Surprise Exam Paradox, SEP, via the proposed constructive epistemic logic and then put forward a solution for the paradox. We clarify that the puzzle in the SEP is because of students'(wrong) assumption that the day of the exam is necessarily predetermined.