## Journal of Symbolic Logic

### A sound and complete axiomatization for Dynamic Topological Logic

David Fernández-Duque

#### Abstract

Dynamic Topological Logic (𝒟𝒯ℒ) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of 𝒟𝒯ℒ over the class of all dynamical systems has proven to be quite elusive.

Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different context. We then provide a sound axiomatization for 𝒟𝒯ℒ over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof.

#### Article information

Source
J. Symbolic Logic, Volume 77, Issue 3 (2012), 947-969.

Dates
First available in Project Euclid: 13 August 2012

https://projecteuclid.org/euclid.jsl/1344862169

Digital Object Identifier
doi:10.2178/jsl/1344862169

Mathematical Reviews number (MathSciNet)
MR2987145

Zentralblatt MATH identifier
1256.03025

#### Citation

Fernández-Duque, David. A sound and complete axiomatization for Dynamic Topological Logic. J. Symbolic Logic 77 (2012), no. 3, 947--969. doi:10.2178/jsl/1344862169. https://projecteuclid.org/euclid.jsl/1344862169

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