Semi-qualitative reasoning about distances: a preliminary report

Sturm, H. and Suzuki, N.-Y. and Wolter, F. and Zakharyaschev, Michael (2000) Semi-qualitative reasoning about distances: a preliminary report. In: Ojeda-Aciego, M. and de Guzman, I.P. and Brewka, G. and Pereira, L.M. (eds.) JELIA 2000: Logics in Artificial Intelligence, European Workshop. Lecture Notes in Computer Science 1919. Springer, pp. 37-56. ISBN 9783540411314.

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Official URL: https://doi.org/10.1007/3-540-40006-0_4

Abstract

We introduce a family of languages intended for representing knowledge and reasoning about metric (and more general distance) spaces. While the simplest language can speak only about distances between individual objects and Boolean relations between sets, the more expressive ones are capable of capturing notions such as ‘somewhere in (or somewhere out of) the sphere of a certain radius’, ‘everywhere in a certain ring’, etc. The computational complexity of the satisfiability problem for formulas in our languages ranges from NP-completeness to undecidability and depends on the class of distance spaces in which they are interpreted. Besides the class of all metric spaces, we consider, for example, the spaces ℝ × ℝ and ℕ × ℕ with their natural metrics.

Metadata

Item Type:	Book Section
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	08 Nov 2021 16:33
Last Modified:	09 Aug 2023 12:52
URI:	https://eprints.bbk.ac.uk/id/eprint/46639

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