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# Automated reasoning about metric and topology

Hustadt, U. and Tishkovsky, D. and Wolter, F. and Zakharyaschev, Michael (2006) Automated reasoning about metric and topology. In: Fisher, M. and van der Hoek, W. and Konev, B. and Lisitsa, A. (eds.) JELIA 2006: Logics in Artificial Intelligence. Lecture Notes in Computer Science 4160. Springer, pp. 490-493. ISBN 9783540396253.

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## Abstract

In this paper we compare two approaches to automated reasoning about metric and topology in the framework of the logic MT introduced in [10]. MT -formulas are built from set variablesp 1,p 2,... (for arbitrary subsets of a metric space) using the Booleans ∧, ∨, →, and ¬, the distance operators∃ < a and ∃  ≤ a , for a∈Q>0 , and the topological interior and closure operators I and C. Intended models for this logic are of the form I=(Δ,d,pI1,pI2,…) where (Δ,d) is a metric space and pIi⊆Δ . The extension φI⊆Δ of an MT -formula ϕ in I is defined inductively in the usual way, with I and C being interpreted as the interior and closure operators induced by the metric, and (∃<aφ)I={x∈Δ∣∃y∈φI d(x,y)<a} . In other words, (Iφ)I is the interior of φI , (∃<aφ)I is the open a-neighbourhood of φI , and (∃≤aφ)I is the closed one. A formula ϕ is satisfiable if there is a model I such that φI≠∅ ; ϕ is valid if ¬ϕ is not satisfiable.

Item Type: Book Section Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences Sarah Hall 25 Oct 2021 17:42 09 Aug 2023 12:52 https://eprints.bbk.ac.uk/id/eprint/46483

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