4 citations · 6 across the 6 of their papers we have counts for
7 papers
Complete Diagrammatic Axiomatisations of Relative Entropy
Ralph Sarkis, Fabio Zanasi
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In thi…
Graded String Diagrams for Imprecise Probability and Causal Intervention
Ralph Sarkis, Fabio Zanasi
We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic…
Quantitative Monoidal Algebra: Axiomatising Distance with String Diagrams
Gabriele Lobbia, Wojciech Różowski, Ralph Sarkis +1
String diagrammatic calculi have become increasingly popular in fields such as quantum theory, circuit theory, probabilistic programming, and machine learning, where they enable re…
Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces
Matteo Mio, Ralph Sarkis, Valeria Vignudelli
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 metri…
Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning
Matteo Mio, Ralph Sarkis, Valeria Vignudelli
The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend th…
Semialgebras and Weak Distributive Laws
Daniela Petrişan, Ralph Sarkis
Motivated by recent work on weak distributive laws and their applications to coalgebraic semantics, we investigate the algebraic nature of semialgebras for a monad. These are algeb…
Combining nondeterminism, probability, and termination: equational and metric reasoning
Matteo Mio, Ralph Sarkis, Valeria Vignudelli
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our mai…