# A Van Benthem/Rosen theorem for coalgebraic predicate logic

@article{Schrder2015AVB, title={A Van Benthem/Rosen theorem for coalgebraic predicate logic}, author={Lutz Schr{\"o}der and Dirk Pattinson and Tadeusz Litak}, journal={J. Log. Comput.}, year={2015}, volume={27}, pages={749-773} }

Coalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics based on neighbourhoods and games. Coalgebraic predicate logic (CPL), a generalization of a neighbourhoodbased first-order logic introduced by Chang, has been identified as a natural first-order extension of coalgebraic modal logic, which in particular coincides with the standard first-order…

## 16 Citations

### A Quantified Coalgebraic van Benthem Theorem

- Computer ScienceFoSSaCS
- 2021

This paper unify and generalize the quantitative van Benthem theorem results to full coalgebraic generality, thus covering a wide range of system types including, besides fuzzy and probabilistic transition systems as in the existing examples, e.g. also metric transition systems; and removes the symmetry assumption on behavioural distances, Thus covering also quantitative notions of simulation.

### 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.

### A van Benthem Theorem for Quantitative Probabilistic Modal Logic

- Computer ScienceArXiv
- 2018

It is shown that quantitative Probabilistic modal logic lies dense in the bisimulation- invariant fragment, in the indicated sense of non-expansive formula evaluation, of quantitative probabilistic first-order logic; more precisely, bisimulations-invariant first- order formulas are approximable by modal formulas of bounded rank.

### Correspondence, Canonicity, and Model Theory for Monotonic Modal Logics

- MathematicsStud Logica
- 2021

We investigate the role of coalgebraic predicate logic , a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt–Thomason…

### A Characterization Theorem for a Modal Description Logic

- Philosophy, Computer ScienceIJCAI
- 2017

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard…

### Monotonic modal logics generalize normal modal logics by dropping the K axiom ( p → q ) → ( p → q ) and instead requiring

- Mathematics
- 2019

We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt-Thomason…

### A model-theoretic approach to descriptive general frames: the van Benthem characterization theorem

- MathematicsJ. Log. Comput.
- 2020

This paper proves an analogue of the van Benthem characterisation theorem for models based on descriptive general frames, an important class of general frames for which every modal logic is complete.

### 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.

### A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic

- Computer ScienceIJCAI
- 2019

A probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic, is proved, which indicates that behavioural distance can be approximated by concepts of bounded rank in Probabilistic fuzzy description logic.

### A van Benthem Theorem for Atomic and Molecular Logics

- Philosophy, Computer ScienceNCL
- 2022

A generalization of van Benthem modal characterization theorem for molecular logics is proved and it is shown how notions of bisimulation can be automatically deﬁned from the truth conditions of the connectives of any of these logics.

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