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 axiomatisation 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.
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CITATION STYLE
Du, H., & Alechina, N. (2019). Qualitative spatial logic over 2d euclidean spaces is not finitely axiomatisable. In 33rd AAAI Conference on Artificial Intelligence, AAAI 2019, 31st Innovative Applications of Artificial Intelligence Conference, IAAI 2019 and the 9th AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019 (pp. 2776–2783). AAAI Press. https://doi.org/10.1609/aaai.v33i01.33012776
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