Epistemic logic of shallow depths has been developed by Kaneko–Suzuki using classical logic. In this paper, we adopt intuitionistic logic as the base logic to limit each player’s reasoning to constructive one. The resulting logical system is denoted by IG<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$_{EF}$$</EquationSource> </InlineEquation>, and we introduce...</equationsource></inlineequation>