Abstract
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distance function and by allowing it to take values in structures (e.g., quantales) that are more general than the set of non-negative real numbers. Quantale-valued metric spaces have gained prominence due to their use in quantitative reasoning on programs/systems, and for defining various notions of behavioral metrics.
We investigate imprecision and robustness in the framework of quantale-valued metric spaces, when the quantale is continuous. In particular, we study the relation between the robust topology, which captures robustness of analyses, and the Hausdorff-Smyth hemi-metric. To this end, we define a preorder-enriched monad PS, called the Hausdorff-Smyth monad, and when Q is a continuous quantale and X is a Q-metric space, we relate the topology induced by the metric on PS(X) with the robust topology on the powerset P(X) defined in terms of the metric on X.
Original language | English |
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Title of host publication | Theoretical Aspects of Computing – ICTAC 2023 |
Subtitle of host publication | 20th International Colloquium, Lima, Peru, December 4–8, 2023, Proceedings |
Publisher | Springer |
Pages | 313–331 |
Volume | 14446 |
Edition | 1 |
ISBN (Electronic) | 9783031479632 |
ISBN (Print) | 9783031479625 |
DOIs | |
Publication status | Published - 23 Nov 2023 |
Event | 20th International Colloquium on Theoretical Aspects of Computing - Lima, Peru Duration: 4 Dec 2023 → 8 Dec 2023 |
Publication series
Name | Lecture Notes in Computer Science |
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Publisher | Springer |
Volume | 14446 |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 20th International Colloquium on Theoretical Aspects of Computing |
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Abbreviated title | ICTAC 2023 |
Country/Territory | Peru |
City | Lima |
Period | 4/12/23 → 8/12/23 |
Keywords
- Quantale
- Robustness
- Monad
- Topology
- Enriched Category