  Standard epistemic logic studies propositional knowledge, yet many other
types of knowledge such as "knowing whether", "knowing what", "knowing how" are
frequently and widely used in everyday life as well as academic fields. In
"Conditionally Knowing What" by Wang and Fan, an axiomatization of the
epistemic logic with both regular "knowing that" operator and "conditionally
knowing what" operator is given. Then the decidability and complexity of this
logic command our study. In this paper, we direct our attention to the
arbitrary models instead of epistemic models, thus making things clearer, and
then give a axiomatization and a tableau for the modal logic with same
operators on arbitrary Kripke models. Given the tableau of this logic, the
complexity of the satisfiability problem of this logic is PSPACE-complete.
