# A Van Benthem/Rosen theorem for coalgebraic predicate logic

@article{Schrder2017AVB, 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={2017}, 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…

### 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.

### The van Benthem Characterisation Theorem for Descriptive Models

- Mathematics
- 2019

This thesis investigate the modal and first-order model theory of the class of models over descriptive general frames. Descriptive general frames are Stone spaces with a suitable relation over which…

### A van Benthem Theorem for Fuzzy Modal Logic

- Computer ScienceLICS
- 2018

It is shown that the fuzzy first-order formulas that are non-expansive w.r.t. the natural notion of bisimulation distance are exactly those that can be approximated by fuzzy modal formulas.

## References

SHOWING 1-10 OF 53 REFERENCES

### 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.

### Expressivity of coalgebraic modal logic: The limits and beyond

- PhilosophyTheor. Comput. Sci.
- 2008

### A finite model construction for coalgebraic modal logic

- Philosophy, Computer ScienceJ. Log. Algebraic Methods Program.
- 2007

### Strong Completeness of Coalgebraic Modal Logics

- PhilosophySTACS
- 2009

This work presents a generic canonical model construction in the semantic framework of coalgebraic modal logic, which pinpoints coherence conditions between syntax and semantics of modal logics that guarantee strong completeness.

### Coalgebraic Predicate Logic

- MathematicsICALP
- 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…

### Coalgebraic modal logic: soundness, completeness and decidability of local consequence

- PhilosophyTheor. Comput. Sci.
- 2003

### Rank-1 Modal Logics are Coalgebraic

- Computer ScienceJ. Log. Comput.
- 2010

Every rank 1 modal logic has a sound and strongly complete coalgebraic semantics, i.e. every coalgebras for an endofunctor can always be axiomatised in rank 1.

### Modal characterisation theorems over special classes of frames

- Mathematics20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
- 2005

The present investigation primarily concerns ramifications for specific classes of structures defined through conditions on the underlying frames, with a focus on frame classes that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics.

### 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.

### Simulations and Bisimulations for Coalgebraic Modal Logics

- MathematicsCALCO
- 2013

A modular notion of equivalence is arrived at that, when used with a separating set of monotone predicate liftings, coincides with T-behavioural equivalence regardless of whether T preserves weak pullbacks (unlike the notion of T-bisimilarity).