Modal logic with the difference modality of topological $T_0$-spaces

Rajab Aghamov

Modal logic with the difference modality of topological $T_0$-spaces

Logic 2019-12-03 v2

Authors: Rajab Aghamov

Abstract

The aim of the paper is to study the topological modal logic of $T_0$ spaces, with the difference modality (for $T_n$ , where $n\geq1$ the corresponding logics were known). We consider propositional modal logic with two modal operators $\square$ and $[\ne]$ . $\square$ is interpreted as an interior operator and $[\ne]$ corresponds to the inequality relation. We introduce the logic $S4DT_0$ and show that $S4DT_0$ is the logic of all $T_0$ spaces and has the finite model property.

Keywords

modal logic topological spaces t0 spaces difference modality s4dt0 finite model property

Cite

@article{arxiv.1810.02150,
  title  = {Modal logic with the difference modality of topological $T_0$-spaces},
  author = {Rajab Aghamov},
  journal= {arXiv preprint arXiv:1810.02150},
  year   = {2019}
}