In this paper, we will propose a new concept of products of modal logics, which will resemble the products familiar from measure theory and topology. Our products of modal logics can be defined either by means of normal products of general frames or by means of normal products of modal algebras. It enables us to develop a duality theory between these two. This brings about a desired effect that the definition of the normal product of modal logics L_1 and L_2 is not affected by the choice of classes of general frames (or, modal algebras) which determine L_1 and L_2. We also show some transfer results, including transfer of the finite model property.
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