# 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…

## 19 Citations

### Model Theory and Proof Theory of Coalgebraic Predicate Logic

- MathematicsLog. Methods Comput. Sci.
- 2018

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.

### Model Theory and Proof Theory of CPL

- MathematicsArXiv
- 2017

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.

### Coalgebraic Predicate Logic: Equipollence Results and Proof Theory

- Computer Science, PhilosophyTbiLLC
- 2011

This work identifies syntactically the fragments of CPL corresponding to extended modal formalisms and shows that the full CPL is equipollent with coalgebraic hybrid logic with the downarrow binder and the universal modality.

### An expressive completeness theorem for coalgebraic modal mu-calculi

- MathematicsLog. Methods Comput. Sci.
- 2017

It is shown that in order to provide such a characterization result it suffices to find an adequate uniform construction for the coalgebraic type functor, and a characterization theorem for the monotone modal mu-calculus is derived, with respect to a natural monadic second-order language for monot one neighborhood models.

### Coalgebraic Predicate Logic as a common generalisation of first-order logic and coalgebraic modal logic , combining first-order quantification with coalgebraic syntax based on predicate liftings

- Mathematics
- 2017

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…

### A Van Benthem/Rosen theorem for coalgebraic predicate logic

- PhilosophyJ. Log. Comput.
- 2017

This work generalizes to the CPL setting the classical van Benthem/Rosen theorem stating that both over arbitrary and over finite models, modal logic is precisely the bisimulation-invariant fragment of first-order logic.

### Monadic Second-Order Logic and Bisimulation Invariance for Coalgebras

- Mathematics2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

One of the main results provides a characterization of the monotone modal mu-calculus extended with the global modalities, as the fragment of monadic second order logic for themonotone neighborhood functor that is invariant for global bisimulations.

### UvA-DARE ( Digital Academic Repository ) An expressive completeness theorem for coalgebraic modal μ-calculi

- Mathematics
- 2017

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…

### UvA-DARE ( Digital Academic Repository ) Monadic Second-Order Logic and Bisimulation Invariance for

- Mathematics
- 2015

Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic MSOT interpreted over coalgebras for an arbitrary set functor T. Similar to well-known…

### Expressiveness modulo bisimilarity: a coalgebraic perspective

- Computer Science
- 2013

One of van Benthem’s seminal results is the Bisimulation Theorem characterizing modal logic as the bisimulation-invariant fragment of first-order logic. Janin and Walukiewicz extended this theorem to…

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