On topologically relevant fragments of the logic of linear flows of time. (English) Zbl 06484966

Heinemann, Bernhard

Paiva, Valeria (ed.) et al., Logic, language, information, and computation. 22nd international workshop, WoLLIC 2015, Bloomington, IN, USA, July 20–23, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-47708-3/pbk; 978-3-662-47709-0/ebook). Lecture Notes in Computer Science 9160, 27-37 (2015).

Summary: Moss and Parikh’s bi-modal logic of subset spaces not only facilitates reasoning about knowledge and topology, but also provides an interesting example of a bi-topological system. This results from the fact that two interrelated S4s are involved in it. In the search for other examples of such kind, the temporal logic of linear flows of time might cross one’s mind. And although the full system itself is not bi-S4, a specific fragment sharing most of the corresponding characteristics can be identified. We here examine, among other things, to what extent the two modalities determining the latter set of formulas are related with regard to the respective canonical topo-model.
For the entire collection see [Zbl 1319.03010].

MSC:

03B70

Logic in computer science

Keywords:

bi-modal logic; temporal logic; linear flows of time; topological semantics; canonical topo-model