Temporalization of Modal Logic

Abstract

From a temporal logic, by eliminating formulas containing additional pair of modal operators, one obtains a 1-dimensional normal modal logic. The temporalizaion problem is the inverse problem of this. Morphological dilation and erosion operators correspond to modal operators: a dual pair to a usual modal pair and adjoint pair to a part of temporal quadruple. Morphological Analysis makes it clear the relation between ""duality"" and ""adjunction"" of morphological/modal operators. By using this, we solve the existence problem. Namely, for any normal modal logic, there exists a temporal logic such that by elimination, the original modal logic is obtained.