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… 

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References

SHOWING 1-10 OF 53 REFERENCES

Coalgebraic Predicate Logic: Equipollence Results and Proof Theory

TLDR
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.

A finite model construction for coalgebraic modal logic

  • Lutz Schröder
  • Philosophy, Computer Science
    J. Log. Algebraic Methods Program.
  • 2007

Strong Completeness of Coalgebraic Modal Logics

TLDR
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

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

Rank-1 Modal Logics are Coalgebraic

TLDR
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

  • A. DawarM. Otto
  • Mathematics
    20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
  • 2005
TLDR
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

TLDR
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

TLDR
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).
...