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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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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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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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