New Modification of the Subformula Property for a Modal Logic

Abstract

A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability for the logic follows from this.