A sound and complete axiomatization for dynamic topological logic. (English) Zbl 1256.03025

Author’s abstract: Dynamic topological logic (\(\mathcal D \mathcal J \mathcal I\)) 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 \(\mathcal D \mathcal J \mathcal I\) 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 \(\mathcal D \mathcal J \mathcal I\) over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof.


03B45 Modal logic (including the logic of norms)
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