Robustness in Metric Spaces over Continuous Quantales and the Hausdorff-Smyth Monad

Francesco Dagnino, Amin Farjudian, Eugenio Moggi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationTheoretical Aspects of Computing – ICTAC 2023
Subtitle of host publication20th International Colloquium, Lima, Peru, December 4–8, 2023, Proceedings
PublisherSpringer
Pages313–331
Volume14446
Edition1
ISBN (Electronic)9783031479632
ISBN (Print)9783031479625
DOIs
Publication statusPublished - 23 Nov 2023
Event20th International Colloquium on Theoretical Aspects of Computing
- Lima, Peru
Duration: 4 Dec 20238 Dec 2023

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume14446
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Colloquium on Theoretical Aspects of Computing
Abbreviated titleICTAC 2023
Country/TerritoryPeru
CityLima
Period4/12/238/12/23

Keywords

  • Quantale
  • Robustness
  • Monad
  • Topology
  • Enriched Category

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