@article{jmsa2016415,
author={{Nogin, Maria and Xu, Bing},
title={The Relationship between the Topological Properties and Common Modal Logics},
journal={Journal of Mathematical Sciences and Applications},
volume={4},
number={1},
pages={29--33},
year={2016},
url={http://pubs.sciepub.com/jmsa/4/1/5},
issn={2333-8792},
abstract={A modal language is the language of the classical logic extended by additional operator(s), e.g. <img src=image/abs1.png></img>. Modal logics have a variety of interpretations and applications in different sciences, and depending on the context, different axioms involving <img src=image/abs2.png></img> may be assumed. In topological interpretations, the operator <img src=image/abs3.png></img> interpreted as interior. It is well known that the modal logic S4 is sound and complete over all topological spaces. In this paper we reverse the question. Given a set <i>X</i> and any interpretation of <img src=image/abs4.png></img> in X that satisfies a given subset of the axioms of S4, we determine which topological properties must be possessed by the image of the interpretation of <img src=image/abs5.png></img>.},
doi={10.12691/jmsa-4-1-5}
publisher={Science and Education Publishing}
}