Add to ORKGWe 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: Appendix remove
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distanc...
The monad of convex sets of probability distributions is a well-known tool for modelling the combina...
We develop a theory for the commutative combination of quantitative effects, their tensor, given as ...
International audienceWe explore the possibility of extending Mardare et al.’s quantitative algebras...
International audienceWe explore the possibility of extending Mardare et al.’s quantitative algebras...
Quantitative algebras are algebras enriched in the category Met of metric spaces or UMet of ultramet...
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We de...
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures whi...
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We de...
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We de...
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures whi...
Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpandi...
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures whi...
International audienceThis paper studies quantitative refinements of Abramsky's applica-tive similar...
International audienceThis paper studies quantitative refinements of Abramsky's applica-tive similar...
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distanc...
The monad of convex sets of probability distributions is a well-known tool for modelling the combina...
We develop a theory for the commutative combination of quantitative effects, their tensor, given as ...
International audienceWe explore the possibility of extending Mardare et al.’s quantitative algebras...
International audienceWe explore the possibility of extending Mardare et al.’s quantitative algebras...
Quantitative algebras are algebras enriched in the category Met of metric spaces or UMet of ultramet...
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We de...
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures whi...
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We de...
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We de...
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures whi...
Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpandi...
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures whi...
International audienceThis paper studies quantitative refinements of Abramsky's applica-tive similar...
International audienceThis paper studies quantitative refinements of Abramsky's applica-tive similar...
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distanc...
The monad of convex sets of probability distributions is a well-known tool for modelling the combina...
We develop a theory for the commutative combination of quantitative effects, their tensor, given as ...