Archive for Mathematical Logic 45 (8):1021-1032 (2006)

Authors
Philip Kremer
University of Toronto at Scarborough
Abstract
Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , 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
Keywords Mathematics   Algebra   Mathematics, general   Mathematical Logic and Foundations
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DOI 10.1007/s00153-006-0024-0
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References found in this work BETA

Past, Present, and Future.Arthur Norman Prior - 1967 - Oxford, England: Clarendon Press.
A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Past, present and future.Arthur Prior - 1967 - Revue Philosophique de la France Et de l'Etranger 157:476-476.
Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.

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Citations of this work BETA

The Modal Logic of Continuous Functions on the Rational Numbers.Philip Kremer - 2010 - Archive for Mathematical Logic 49 (4):519-527.
Dynamic Topological Logic Interpreted Over Minimal Systems.David Fernández-Duque - 2011 - Journal of Philosophical Logic 40 (6):767-804.

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