Coalgebraic Predicate Logic

@inproceedings{Litak2012CoalgebraicPL,
  title={Coalgebraic Predicate Logic},
  author={Tadeusz Litak and Dirk Pattinson and Katsuhiko Sano and Lutz Schr{\"o}der},
  booktitle={ICALP},
  year={2012}
}
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 two natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, contrasting it with both coalgebraic modal logic and existing first… 

Model Theory and Proof Theory of Coalgebraic Predicate Logic

A generalization of first-order logic originating in a neglected work by C.C. Chang is proposed: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras and basic model-theoretic constructions and results obtain.

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