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Generic Modal Cut Elimination Applied to Conditional Logics

Dirk Pattinson ; Lutz Schröder.

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal&nbsp;[&hellip;]

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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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Guarded and Unguarded Iteration for Generalized Processes

Sergey Goncharov ; Lutz Schröder ; Christoph Rauch ; Maciej Piróg.

Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain guarding operations. On the other hand, many models of&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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