Work

Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces

Year: 2024

Type: article

Abstract: 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.

Source: Logical Methods in Computer Science

DOI: 10.46298/lmcs-20(4:19)2024

Authors: Matteo Mio, Ralph Sarkis, Valeria Vignudelli

Institutions: École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de l'Informatique du Parallélisme

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: Quantitative Reasoning Methods for Probabilistic Logics