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Model Theory and Proof Theory of Coalgebraic Predicate Logic

Tadeusz Litak ; Dirk Pattinson ; Katsuhiko Sano ; Lutz Schröder.

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such&nbsp;[&hellip;]

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Unguarded Recursion on Coinductive Resumptions

Sergey Goncharov ; Lutz Schröder ; Christoph Rauch ; Julian Jakob.

We study a model of side-effecting processes obtained by starting from a monad modelling base effects and adjoining free operations using a cofree coalgebra construction; one thus arrives at what one may think of as types of non-wellfounded side-effecting trees, generalizing the infinite resumption&nbsp;[&hellip;]

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Efficient and Modular Coalgebraic Partition Refinement

Thorsten Wißmann ; Ulrich Dorsch ; Stefan Milius ; Lutz Schröder.

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical relational systems but also, e.g. various forms of weighted systems&nbsp;[&hellip;]

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Coalgebraic Satisfiability Checking for Arithmetic $\mu$-Calculi

Daniel Hausmann ; Lutz Schröder.

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential-time upper bound&nbsp;[&hellip;]

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