Intuitionistic epistemic logic with two modal operators

In this article, we add a diamond to the box-based propositional language of intuitionistic doxastic logic $$\mathbf{IEL}^{-}$$ and intuitionistic epistemic logic $$\mathbf{IEL}$$ introduced by Artemov and Protopopescu. The main results of this article are the proofs of completeness with respect to their appropriate relational semantics of the resulting intuitionistic doxastic logic $$\mathbf{L}_{\mathbf{dox}}$$ and intuitionistic epistemic logic $$\mathbf{L}_{\mathbf{epi}}$$ .