Kutz, O. and Wolter, F. and Sturm, H. and Suzuki, N.-Y. and Zakharyaschev, Michael (2003) Logics of metric spaces. ACM Transactions on Computational Logic 4 (2), pp. 260-294. ISSN 1529-3785.
Abstract
We investigate the expressive power and computational properties of two different types of languages intended for speaking about distances. First, we consider a first-order language FM the two-variable fragment of which turns out to be undecidable in the class of distance spaces validating the triangular inequality as well as in the class of all metric spaces. Yet, this two-variable fragment is decidable in various weaker classes of distance spaces. Second, we introduce a variable-free modal language MS that, when interpreted in metric spaces, has the same expressive power as the two-variable fragment of FM. We determine natural and expressive fragments of MS which are decidable in various classes of distance spaces validating the triangular inequality, in particular, the class of all metric spaces.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 01 Nov 2021 13:32 |
| Last Modified: | 09 Aug 2023 12:52 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/46553 |
Statistics
Additional statistics are available via IRStats2.
Archive Staff Only (login required)
