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Mathematics > Logic

arXiv:2204.08374 (math)
[Submitted on 18 Apr 2022]

Title:Untangled: A Complete Dynamic Topological Logic

Authors:David Fernández-Duque, Yoàv Montacute
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Abstract:Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fernández-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a complete axiomatisation in an extended language. In this paper, we consider dynamic topological logic over scattered spaces, which are topological spaces where every nonempty subspace has an isolated point. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original trimodal language. In particular, we show that the version of $\mathbf{DTL}$ based on the class of scattered spaces is finitely axiomatisable over the original language, and that the natural axiomatisation is sound and complete.
Subjects: Logic (math.LO); Logic in Computer Science (cs.LO)
Cite as: arXiv:2204.08374 [math.LO]
  (or arXiv:2204.08374v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2204.08374

Submission history

From: Yoàv Montacute [view email]
[v1] Mon, 18 Apr 2022 15:37:07 UTC (37 KB)
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