A sound and complete axiomatization for Dynamic Topological Logic
David Fernández-Duque
Source: J. Symbolic Logic Volume 77, Issue 3
(2012), 947-969.
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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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1344862169
Zentralblatt MATH identifier: 06083960
Digital Object Identifier: doi:10.2178/jsl/1344862169
Mathematical Reviews number (MathSciNet): MR2987145
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