The philosophy of logic distinguishes between the ontological research attitude and the epistemic research attitude. On the other hand, there is the distinction between two types of negation: the classical / external / indefinite (~) and the non-classical / internal / definite (¬). The paper presents a propositional calculus with two types of negation (~,¬), which includes both the classical and the intuitionistic propositional calculus. We associate classical negation (~) with the ontological research attitude and definite negation (¬) with the epistemic one. The last and the richest construction introduced here is thus accompanied by the ontological-epistemic research attitude.
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