Abstract
Modal reduction principles (MRPs) are modal formulas of the following form: Mp → Np, where M, N are (possibly empty) sequences of modal operators (i.e. □ or ◊). The notation M, N will be used to abbreviate such an MRP. We study a certain semantic correspondence between modal formulas and relational properties and obtain two main results. (1) On transitive semantic structures every MRP corresponds to a first-order relational property. (2) For the general case a syntactic criterion exists for distinguishing modal formulas with corresponding first-order properties from the others.
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