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arXiv · 2608.25691

Dynamic Polyhedral Logic

Nick Bezhanishvili·Laura Bussi·Vincenzo Ciancia·David Fernández-Duque·David Gabelaia
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Abstract

We introduce spatio-temporal polyhedral reachability logics, extending dynamic topological logic with polyhedral semantics and a path-based spatial reachability operator. Formulas are interpreted over polyhedra, with admissible valuations ranging over polyhedral subsets; the spatial modality is interpreted as interior, the binary operator $γ(φ,ψ)$ expresses reachability of a $ψ$-point through a $φ$-region, and the temporal modalities are interpreted by a PL-homeomorphism and its inverse. We define h-dynamic reachability spaces and axiomatize the corresponding h-dynamic extensions of the known reachability logics of topological, finite, Alexandroff, and polyhedral spaces. The main result is soundness and completeness for the intended classes of invertible dynamical systems.

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Nick Bezhanishvili, Laura Bussi, Vincenzo Ciancia, David Fernández-Duque, David Gabelaia. 2026-08-26. Dynamic Polyhedral Logic. https://arxiv.org/abs/2608.25691

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