| This dissertation investigates modal logics associated with certain subspaces of real numbers under topological d-semantics. In particular, we show that the d-logic of the real numbers is KD4G2. We also show that each of the logics K4, KD4, GL and GLn arise as the d-logic of some subspace of the rational numbers. We then consider enriching the (uni)modal language with the universal modality and obtain similar results concerning subspaces of rational numbers and each of the following minimal extensions, K4.U, KD4.U, GL.U and GL n.U. Such results include that KD4.U is the universal-d-logic of the rational numbers. We then prove that KD4G2.UC has the finite model property. Lastly, we show that KD4G2.UC is the universal-d-logic of the real numbers. |
