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

Francesco Dagnino, Amin Farjudian, Eugenio Moggi

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review


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 - 20th International Colloquium, Proceedings
EditorsErika Ábrahám, Clemens Dubslaff, Silvia Lizeth Tarifa
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages19
ISBN (Print)9783031479625
Publication statusPublished - 2023
Externally publishedYes
Event20th International Colloquium on Theoretical Aspects of Computing, ICTAC 2023 - Lima, Peru
Duration: 4 Dec 20238 Dec 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14446 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Colloquium on Theoretical Aspects of Computing, ICTAC 2023


  • Enriched category
  • Monad
  • Quantale
  • Robustness
  • Topology

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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