  We argue that the notion of epistemic \emph{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, $\mathbf{SEP}$, via the proposed constructive epistemic
logic and then put forward a solution for the paradox. We clarify that the
puzzle in the $\mathbf{SEP}$ is because of students'(wrong) assumption that the
day of the exam is necessarily predetermined.
