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Interpreting Topological Logics over Euclidean Spaces

AAAI Press, Menlo Park, California
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  • Mathematics


Topological logics are a family of languages for representing and reasoning about topological data. In this paper, we consider propositional topological logics able to express the property of connectedness. The satisfiability problem for such logics is shown to depend not only on the spaces they are interpreted in, but also on the subsets of those spaces over which their variables are allowed to range. We identify the crucial notion of tameness, and chart the surprising patterns of sensitivity to the presence of non-tame regions exhibited by a range of topological logics in low-dimensional Euclidean spaces.

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