Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces

Autor:	Mio, Matteo, Sarkis, Ralph, Vignudelli, Valeria
Rok vydání:	2023
Předmět:	Computer Science - Logic in Computer Science
Druh dokumentu:	Working Paper
Popis:	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. Comment: Implemented the revisions suggested by anonymous reviewers
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.14361 Zobrazit plný text záznamu View this record from Arxiv