Topological completeness of extensions of S4

4 pages•Published: July 28, 2014

Guram Bezhanishvili, David Gabelaia and Joel Lucero-Bryan

Abstract

It was left as an open problem in (Bezhanishvili and Gabelaia, 2011) whether a connected normal extension of S4 without FMP is also the modal logic of some subalgebra of R+.
Our purpose here is to solve this problem affirmatively by showing that each connected normal extension of S4 (with or without FMP) is in fact the modal logic of some subalgebra of R+. We also prove that each normal extension of S4 (with or without FMP) is the modal logic of a subalgebra of Q+, as well as the modal logic of a subalgebra of C+.

Keyphrases: countable model property, modal logic, topological semantics

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 27-30.

Links:	https://easychair.org/publications/paper/Xb
	https://doi.org/10.29007/zh85

BibTeX entry

@inproceedings{TACL2013:Topological_completeness_extensions_S4,
  author    = {Guram Bezhanishvili and David Gabelaia and Joel Lucero-Bryan},
  title     = {Topological completeness of extensions of S4},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/Xb},
  doi       = {10.29007/zh85},
  pages     = {27-30},
  year      = {2014}}

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