In this article, we define general normal forms for any logic that has
propositional part and whose non-propositional connectives distribute over the
finite disjunctions. We do not require the non-propositional connectives to be
closed on the set of formulas, so our normal forms cover logics with partial
connectives too. We also show that most of the known normal forms in the
literature are in fact particular cases of our general forms. These general
normal forms are natural improvement of the distributive normal forms of J.
Hintikka and their modal analogues, e.g. [Anderson] and [Fine]
