A Logic of East and West for Intervals

This paper proposes a logic of east and west for intervals (LEWI), which extends the logic of east and west for points. For intervals in 1D Euclidean space, the logic LEWI formalises the qualitative direction relations "east", "west", "definitely east", "definitely west", "partially east", "partially west", etc. To cope with imprecision in geometry representations, the logic LEWI is parameterized by a margin of error σ ∈ ℝ_{> 0} and a level of indeterminacy in directions τ ∈ ℕ_{> 1}. For every τ, we provide an axiomatisation of the logic LEWI, and prove that it is sound and complete with respect to 1D Euclidean space.