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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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Epistemic Updates on Algebras

Alexander A Kurz ; Alessandra A Palmigiano.

We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-Moss- Solecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a&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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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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Relation lifting, with an application to the many-valued cover modality

Marta Bilkova ; Alexander Kurz ; Daniela Petrisan ; Jiri Velebil.

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the "powerset monad" on&nbsp;[&hellip;]

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Nominal Coalgebraic Data Types with Applications to Lambda Calculus

Alexander Kurz ; Daniela Luan Petrişan ; Paula Severi ; Fer-Jan de Vries.

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.

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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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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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Completeness of Nominal PROPs

Samuel Balco ; Alexander Kurz.

We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric&nbsp;[&hellip;]

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Many-valued coalgebraic logic over semi-primal varieties

Alexander Kurz ; Wolfgang Poiger ; Bruno Teheux.

We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift&nbsp;[&hellip;]

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