A Logic of Directions

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

doi:10.24963/ijcai.2020/235

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2023

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“…Here, for every level of indeterminacy τ ∈ N >1 , we show that the satisfiability problem of LEW is NP-complete. These results were presented by Du, Alechina, and Cohn (2020) for a 2D extension of LEW , i.e., a logic of directions. In this paper, we provide additional finite axiomatisability results.…”

Section: Introductionmentioning

confidence: 98%

A Logic of East and West

Alechina²,

Farjudian³

et al. 2023

jair

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We propose a logic of east and west (LEW ) for points in 1D Euclidean space. It formalises primitive direction relations: east (E), west (W) and indeterminate east/west (Iew). It has a parameter τ ∈ N>1, which is referred to as the level of indeterminacy in directions. For every τ ∈ N>1, we provide a sound and complete axiomatisation of LEW , and prove that its satisfiability problem is NP-complete. In addition, we show that the finite axiomatisability of LEW depends on τ : if τ = 2 or τ = 3, then there exists a finite sound and complete axiomatisation; if τ > 3, then the logic is not finitely axiomatisable. LEW can be easily extended to higher-dimensional Euclidean spaces. Extending LEW to 2D Euclidean space makes it suitable for reasoning about not perfectly aligned representations of the same spatial objects in different datasets, for example, in crowd-sourced digital maps.

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Section: Introductionmentioning

confidence: 98%