79 citations · 365 across the 37 of their papers we have counts for
29 papers · 1 filter
A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures
Mateo Torres-Ruiz, Robin Piedeleu, Alexandra Silva +1
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which co…
A Complete Axiomatisation of Equivalence for Discrete Probabilistic Programming
Robin Piedeleu, Mateo Torres-Ruiz, Alexandra Silva +1
We introduce a sound and complete equational theory capturing equivalence of discrete probabilistic programs, that is, programs extended with primitives for Bernoulli distributions…
Graphical Quadratic Algebra
Dario Stein, Fabio Zanasi, Robin Piedeleu +1
Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relations…
A Categorical Approach to DIBI Models
Tao Gu, Jialu Bao, Justin Hsu +2
The logic of Dependence and Independence Bunched Implications (DIBI) is a logic to reason about conditional independence (CI); for instance, DIBI formulas can characterise CI in pr…
String Diagrams for -calculi and Functional Computation
Dan Ghica, Fabio Zanasi
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the…
An Introduction to String Diagrams for Computer Scientists
Robin Piedeleu, Fabio Zanasi
This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitio…
A Finite Axiomatisation of Finite-State Automata Using String Diagrams
Robin Piedeleu, Fabio Zanasi
We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of stri…
A Complete Diagrammatic Calculus for Boolean Satisfiability
Tao Gu, Robin Piedeleu, Fabio Zanasi
We propose a calculus of string diagrams to reason about satisfiability of Boolean formulas, and prove it to be sound and complete. We then showcase our calculus in a few case stud…
String Diagrams for Layered Explanations
Leo Lobski, Fabio Zanasi
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been a…
Rewriting for Symmetric Monoidal Categories with Commutative (Co)Monoid Structure
Aleksandar Milosavljevic, Robin Piedeleu, Fabio Zanasi
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found applicat…
String Diagram Rewrite Theory III: Confluence with and without Frobenius
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger +2
In this paper we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorically as double-pushout rewriting…
String Diagram Rewrite Theory II: Rewriting with Symmetric Monoidal Structure
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger +2
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or disc…
Reverse Derivative Ascent: A Categorical Approach to Learning Boolean Circuits
Paul Wilson, Fabio Zanasi
We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differenti…
Coalgebraic Semantics for Probabilistic Logic Programming
Tao Gu, Fabio Zanasi
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming…
String Diagram Rewrite Theory I: Rewriting with Frobenius Structure
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger +2
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the m…
Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness
Tobias Kappé, Paul Brunet, Alexandra Silva +2
Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally mis…
Contextual Equivalence for Signal Flow Graphs
Filippo Bonchi, Robin Piedeleu, Pawel Sobocinski +1
We extend the signal flow calculus---a compositional account of the classical signal flow graph model of computation---to encompass affine behaviour, and furnish it with a novel op…
Bialgebraic Semantics for String Diagrams
Filippo Bonchi, Robin Piedeleu, Pawel Sobocinski +1
Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as…
Kleene Algebra with Observations
Tobias Kappé, Paul Brunet, Jurriaan Rot +3
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not s…
Causal Inference by String Diagram Surgery
Bart Jacobs, Aleks Kissinger, Fabio Zanasi
Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s.…
The Power of the Weak
Facundo Carreiro, Alessandro Facchini, Yde Venema +1
A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal -calculus () is equivalent modulo bisimil…
Model Theory of Monadic Predicate Logic with the Infinity Quantifier
Facundo Carreiro, Alessandro Facchini, Yde Venema +1
This paper establishes model-theoretic properties of , a variation of monadic first-order logic that features the generalised quantifier (`t…
Rewriting in Free Hypergraph Categories
Fabio Zanasi
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called…
Universal Constructions for (Co)Relations: categories, monoidal categories, and props
Brendan Fong, Fabio Zanasi
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits an…