Halo semantics define four modal operators from nonstandard analysis; the new ω-accumulation operator satisfies Axiom 4 universally and supports K4 completeness on infinite spaces and GL on infinite ω-scattered spaces.
The Review of Symbolic Logic 3, pp
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Sound and complete axiomatizations are provided for path-reachability logic with Cantor derivative in T1 topologies and metric spaces, with decidability via neighborhood semantics that yields the finite model property.
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Halo Semantics for Modal Logic
Halo semantics define four modal operators from nonstandard analysis; the new ω-accumulation operator satisfies Axiom 4 universally and supports K4 completeness on infinite spaces and GL on infinite ω-scattered spaces.