The d-logic of the real line

Abstract

We show that the d-logic of the real line is KD4G2. In doing so, we shall provide necessary and sufficient conditions for the validity of the formulas Gn under both Kripke semantics and d-semantics. Furthermore, we characterize finite Kripke frames that are d-morphic images of the real line. We extend our exploration to the bimodal setting by the addition of the universal modality. In particular, we show that KD4Gn.UC has the finite model property (under Kripke semantics) for any n ≥ 2. We close by showing that KD4G2.UC is the logic of the real line under d-semantics adjoined with the universal modality.