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September 2012 A sound and complete axiomatization for Dynamic Topological Logic
David Fernández-Duque
J. Symbolic Logic 77(3): 947-969 (September 2012). DOI: 10.2178/jsl/1344862169

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.

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David Fernández-Duque. "A sound and complete axiomatization for Dynamic Topological Logic." J. Symbolic Logic 77 (3) 947 - 969, September 2012. https://doi.org/10.2178/jsl/1344862169

Information

Published: September 2012
First available in Project Euclid: 13 August 2012

zbMATH: 1256.03025
MathSciNet: MR2987145
Digital Object Identifier: 10.2178/jsl/1344862169

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 3 • September 2012
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