Matteo Mio ; Ralph Sarkis ; Valeria Vignudelli - Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces

lmcs:12339 - Logical Methods in Computer Science, December 3, 2024, Volume 20, Issue 4 - https://doi.org/10.46298/lmcs-20(4:19)2024
Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric SpacesArticle

Authors: Matteo Mio ORCID; Ralph Sarkis ORCID; Valeria Vignudelli ORCID

We present a generalisation of the theory of quantitative algebras of Mardare, Panangaden and Plotkin where (i) the carriers of quantitative algebras are not restricted to be metric spaces and can be arbitrary fuzzy relations or generalised metric spaces, and (ii) the interpretations of the algebraic operations are not required to be nonexpansive. Our main results include: a novel sound and complete proof system, the proof that free quantitative algebras always exist, the proof of strict monadicity of the induced Free-Forgetful adjunction, the result that all monads (on fuzzy relations) that lift finitary monads (on sets) admit a quantitative equational presentation.

https://doi.org/10.46298/lmcs-20(4:19)2024
Source: arXiv.org:2304.14361
Volume: Volume 20, Issue 4
Published on: December 3, 2024
Accepted on: October 24, 2024
Submitted on: September 27, 2023
Keywords: Computer Science - Logic in Computer Science
Licence: Attribution 4.0 International (CC BY 4.0)
Funding:
    Source : OpenAIRE Graph
  • Quantitative Reasoning Methods for Probabilistic Logics; Funder: French National Research Agency (ANR); Code: ANR-20-CE48-0005

Classifications

Mathematics Subject Classification 20201
Sources:
  • [1] zbMATH Open.

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