The modal logic of continuous functions on cantor space

Abstract Let L be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality and a temporal modality , understood as `next'. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e. ordered pairs X, f , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result.

• Type: Journal
• Year: 2006
• Where: AML
• Authors: Philip Kremer
• Keywords: AML 2006, S4-ish Topological Modality, Topological, Topological Space