Modal logics of domains on the real plane

Studia Logica 42 (1):63-80 (1983)
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Abstract

This paper concerns modal logics appearing from the temporal ordering of domains in two-dimensional Minkowski spacetime. As R. Goldblatt has proved recently, the logic of the whole plane isS4.2. We consider closed or open convex polygons and closed or open domains bounded by simple differentiable curves; this leads to the logics:S4,S4.1,S4.2 orS4.1.2

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10.1007/bf01418760

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Valentin Shehtman
Moscow State University

Citations of this work

Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
Ontologies for Plane, Polygonal Mereotopology.Ian Pratt & Oliver Lemon - 1997 - Notre Dame Journal of Formal Logic 38 (2):225-245.
The modal logic of {beta(mathbb{N})}.Guram Bezhanishvili & John Harding - 2009 - Archive for Mathematical Logic 48 (3-4):231-242.

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References found in this work

Two-dimensional modal logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
An incomplete logic containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.
An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
Logics containing k4. part I.Kit Fine - 1974 - Journal of Symbolic Logic 39 (1):31-42.

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