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2020

A Logic of Directions

Du, Heshan, Alechina, Natasha, and Cohn, Anthony G.

Abstract

A Logic of Directions

We propose a logic of directions for points (LD) over 2D Euclidean space, which formalises primary direction relations east (E), west (W), and indeterminate east/west (Iew), north (N), south (S) and indeterminate north/south (Ins). We provide a sound and complete axiomatisation of it, and prove that its satisfiability problem is NP-complete.

Keywords

IndeterminateSatisfiabilityEuclidean spaceSpace (punctuation)Euclidean geometryMathematicsBoolean satisfiability problemComputer scienceAlgebra over a fieldAlgorithmArtificial intelligenceDiscrete mathematicsCalculus (dental)Pure mathematicsGeometry
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