Annals of Pure and Applied Logic 131 (1-3):133-158 (2005)

Authors
Philip Kremer
University of Toronto at Scarborough
Abstract
Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □ , and two temporal modalities, ○ and * , both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2004.06.004
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,107
Through your library

References found in this work BETA

Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Dynamic Topological Logic.Philip Kremer & Grigori Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
And Next.Georg Henrik von Wright & G. H. von Wright - 1970 - Journal of Symbolic Logic 35 (3):459-460.

View all 8 references / Add more references

Citations of this work BETA

Dynamic Topological Logic.Philip Kremer & Grigori Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
Completeness of S4 for the Lebesgue Measure Algebra.Tamar Lando - 2012 - Journal of Philosophical Logic 41 (2):287-316.

View all 24 citations / Add more citations

Similar books and articles

The Modal Logic of Continuous Functions on Cantor Space.Philip Kremer - 2006 - Archive for Mathematical Logic 45 (8):1021-1032.
Dynamic Topological Logic Interpreted Over Minimal Systems.David Fernández-Duque - 2011 - Journal of Philosophical Logic 40 (6):767-804.
The Modal Logic of Continuous Functions on the Rational Numbers.Philip Kremer - 2010 - Archive for Mathematical Logic 49 (4):519-527.
Dynamic Topological S5.Philip Kremer - 2009 - Annals of Pure and Applied Logic 160 (1):96-116.
Dynamic Topological Logic of Metric Spaces.David Fernández-Duque - 2012 - Journal of Symbolic Logic 77 (1):308-328.
Non-Deterministic Semantics for Dynamic Topological Logic.David Fernández - 2009 - Annals of Pure and Applied Logic 157 (2-3):110-121.
A Proof of Topological Completeness for S4 In.Grigori Mints & Ting Zhang - 2005 - Annals of Pure and Applied Logic 133 (1-3):231-245.

Analytics

Added to PP index
2014-01-16

Total views
29 ( #379,426 of 2,454,632 )

Recent downloads (6 months)
1 ( #449,377 of 2,454,632 )

How can I increase my downloads?

Downloads

My notes