Journal of Symbolic Logic

A sound and complete axiomatization for Dynamic Topological Logic

David Fernández-Duque

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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

Permanent link to this document
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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