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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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An expressive completeness theorem for coalgebraic modal mu-calculi

Sebastian Enqvist ; Fatemeh Seifan ; Yde Venema.

Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas. More specifically, we investigate whether the coalgebraic&nbsp;[&hellip;]

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Some model theory for the modal $\mu$-calculus: syntactic characterisations of semantic properties

Gaëlle Fontaine ; Yde Venema.

This paper contributes to the theory of the modal $\mu$-calculus by proving some model-theoretic results. More in particular, we discuss a number of semantic properties pertaining to formulas of the modal $\mu$-calculus. For each of these properties we provide a corresponding syntactic fragment, in&nbsp;[&hellip;]

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Disjunctive bases: normal forms and model theory for modal logics

Sebastian Enqvist ; Yde Venema.

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for&nbsp;[&hellip;]

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Coalgebraic Geometric Logic: Basic Theory

Nick Bezhanishvili ; Jim de Groot ; Yde Venema.

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the category of topological spaces and continuous functions. We&nbsp;[&hellip;]

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