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Completeness for the coalgebraic cover modality

Clemens Kupke ; Alexander Kurz ; Yde Venema.

We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical propositional logic with a so-called coalgebraic cover&nbsp;[&hellip;]

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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;]

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Positive fragments of coalgebraic logics

Adriana Balan ; Alexander Kurz ; Jiří Velebil.

Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions,&nbsp;[&hellip;]

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Strongly Complete Logics for Coalgebras

Alexander Kurz ; Jiri Rosicky.

Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under&nbsp;[&hellip;]

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Extending set functors to generalised metric spaces

Adriana Balan ; Alexander Kurz ; Jiří Velebil.

For a commutative quantale $\mathcal{V}$, the category $\mathcal{V}-cat$ can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor $T$ (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor&nbsp;[&hellip;]

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