The modal logic of continuous functions on the rational numbers

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. S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fern

• Type: Journal
• Year: 2010
• Where: AML
• Authors: Philip Kremer
• Keywords: AML 2010, Continuous Functions, S4-ish Topological Modality, Topological