Qualitative Spatial Logic over 2D Euclidean Spaces Is Not Finitely Axiomatisable

Du, Heshan; Alechina, Natasha

Abstract

Several qualitative spatial logics used in reasoning about geospatial data have a sound and complete axiomatisation over metric spaces. It has been open whether the same ax-iomatisation is also sound and complete for 2D Euclidean spaces. We answer this question negatively by showing that the axiomatisations presented in (Du et al. 2013; Du and Alechina 2016) are not complete for 2D Euclidean spaces and, moreover, the logics are not finitely axiomatisable.

Citation

Du, H., & Alechina, N. (2019). Qualitative Spatial Logic over 2D Euclidean Spaces Is Not Finitely Axiomatisable. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI-19). https://doi.org/10.1609/aaai.v33i01.33012776

• Conference Name: 33rd AAAI Conference on Artificial Intelligence (AAAI-19)
• Conference Location: Honolulu, Hawaii, USA
• Start Date: Jan 27, 2019
• End Date: Feb 1, 2019
• Acceptance Date: Oct 31, 2018
• Online Publication Date: Jul 17, 2019
• Publication Date: Jul 17, 2019
• Deposit Date: Dec 7, 2018
• Publicly Available Date: Sep 18, 2019
• Book Title: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI-19)
• DOI: https://doi.org/10.1609/aaai.v33i01.33012776
• Public URL: https://nottingham-repository.worktribe.com/output/1383431
• Publisher URL: https://aaai.org/Press/Proceedings/proceedings.php
• Related Public URLs: https://aaai.org/Conferences/AAAI-19/