Dynamic Topological Logic Interpreted over Minimal Systems

Journal of Philosophical Logic 40 (6):767-804 (2011)
Abstract
Dynamic Topological Logic ( ) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems , which are pairs consisting of a topological space X and a continuous function f : X → X . The function f is seen as a change in one unit of time; within one can model the long-term behavior of such systems as f is iterated. One class of dynamic topological systems where the long-term behavior of f is particularly interesting is that of minimal systems ; these are dynamic topological systems which admit no proper, closed, f -invariant subsystems. In such systems the orbit of every point is dense, which within translates into a non-trivial interaction between spatial and temporal modalities. This interaction, however, turns out to make the logic simpler, and while s in general tend to be undecidable, interpreted over minimal systems we obtain decidability, although not in primitive recursive time; this is the main result that we prove in this paper. We also show that interpreted over minimal systems is incomplete for interpretations on relational Kripke frames and hence does not have the finite model property; however it does have a finite non-deterministic quasimodel property. Finally, we give a set of formulas of which characterizes the class of minimal systems within the class of dynamic topological systems, although we do not offer a full axiomatization for the logic.
Keywords Dynamic topological logic  Spatial logic  Temporal logic  Multimodal logic  Topological dynamics
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,322
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
Philip Kremer & Grigori Mints (2005). Dynamic Topological Logic. Annals of Pure and Applied Logic 131 (1-3):133-158.

View all 6 references

Citations of this work BETA

No citations found.

Similar books and articles
Philip Kremer (2009). Dynamic Topological S5. Annals of Pure and Applied Logic 160 (1):96-116.
Analytics

Monthly downloads

Added to index

2011-11-11

Total downloads

11 ( #129,496 of 1,096,498 )

Recent downloads (6 months)

1 ( #238,630 of 1,096,498 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.