Du, H, Alechina, N, Farjudian, A et al. (3 more authors) (2023) A Logic of East and West. Journal of Artificial Intelligence Research, 76. pp. 527-565. ISSN 1076-9757
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©2023 AI Access Foundation. All rights reserved. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | knowledge representation, qualitative reasoning, spatial reasoning, theorem proving |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number Alan Turing Institute No ref given |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Mar 2023 15:35 |
Last Modified: | 25 Jun 2023 23:16 |
Published Version: | http://dx.doi.org/10.1613/jair.1.14113 |
Status: | Published |
Publisher: | AI Access Foundation |
Identification Number: | 10.1613/jair.1.14113 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:197021 |