Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw(φ → ψ) → (Kwφ → Kwψ). Knowing whether logic cannot define many common frame properties, and its expressive po...