AI 中文总结
该研究提出时空多面体可达性逻辑，扩展动态拓扑逻辑并公理化相关h-动态可达空间，证明其针对预期可逆动力系统类的可靠性与完备性。
AI 中文摘要
我们引入时空多面体可达性逻辑，将动态拓扑逻辑扩展为多面体语义与基于路径的空间可达性算子。公式在多面体上解释，可允许赋值覆盖多面体子集；空间模态解释为内部，二元算子γ(φ,ψ)表示通过φ区域到达ψ点，时间模态由PL同胚及其逆解释。我们定义h-动态可达空间，并对拓扑、有限、Alexandroff、多面体空间等已知可达性逻辑的对应h-动态扩展进行公理化。主要结果是针对预期可逆动力系统类的可靠性与完备性。
英文摘要
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.
