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Companions, Causality and Codensity

Damien Pous ; Jurriaan Rot.
In the context of abstract coinduction in complete lattices, the notion of compatible function makes it possible to introduce enhancements of the coinduction proof principle. The largest compatible function, called the companion, subsumes most enhancements and has been proved to enjoy many good&nbsp;[&hellip;]
Published on August 8, 2019
Volume 15, Issue 3

Presenting Distributive Laws

Marcello M. Bonsangue ; Helle Hvid Hansen ; Alexander Kurz ; Jurriaan Rot.
Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for&nbsp;[&hellip;]
Published on August 7, 2015
Volume 11, Issue 3

Coalgebraic trace semantics via forgetful logics

Bartek Klin ; Jurriaan Rot.
We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of generative probabilistic systems. We provide a sufficient condition&nbsp;[&hellip;]
Published on April 27, 2017
Volume 12, Issue 4

Expressive Logics for Coinductive Predicates

Clemens Kupke ; Jurriaan Rot.
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from&nbsp;[&hellip;]
Published on December 15, 2021
Volume 17, Issue 4

On Tools for Completeness of Kleene Algebra with Hypotheses

Damien Pous ; Jurriaan Rot ; Jana Wagemaker.
In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make specific assumptions about certain constants, as for instance&nbsp;[&hellip;]
Published on May 16, 2024
Volume 20, Issue 2
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