# Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective

@inproceedings{Venema2014ExpressivenessMB, title={Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective}, author={Yde Venema}, booktitle={Johan van Benthem on Logic and Information Dynamics}, year={2014} }

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 include fixpoint operators, showing that the modal \({\mu }\)-calculus \({\mu }\)ML is the bisimulation-invariant fragment of monadic second-order logic MSO. Their proof uses parity automata that operate on Kripke models, and feature a transition map defined in terms of certain fragments of monadic…

## 11 Citations

### Weak MSO: automata and expressiveness modulo bisimilarity

- Computer ScienceCSL-LICS
- 2014

We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal μ-calculus where the application of the least fixpoint operator…

### 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.

### The Power of the Weak

- Computer ScienceACM Trans. Comput. Log.
- 2020

This work proves two results of the same kind, one for the alternation-free or noetherian fragment μNML of μML on the modal side and one for WMSO, weak monadic second-order logic, on the second- order side, and introduces classes of parity automata characterising the expressiveness of W MSO and NMSO and of μCML and μN ML.

### 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…

### 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.

### Characterization theorems for PDL and FO(TC)

- Computer ScienceArXiv
- 2015

It is shown that PDL is expressively equivalent to the bisimulation-invariant fragment of both $\mathrm{FO(TC^1)}$ and WCL (weak chain logic) and the main contributions can be divided in three parts: fixpoint extensions of first-order logic, automata and expressiveness on trees, and Automata and drive automata.

### 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…

### 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…

### Model theory of monadic predicate logic with the infinity quantifier

- Computer ScienceArch. Math. Log.
- 2022

It is obtained that the four semantic properties of M E ∞, a variation of monadic first-order logic that features the generalised quantifier exists, are decidable for L -sentences.

### Model theory of monadic predicate logic with the infinity quantifier

- Materials ScienceArchive for Mathematical Logic
- 2021

This paper establishes model-theoretic properties of ME∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

## References

SHOWING 1-10 OF 29 REFERENCES

### Logical questions concerning the μ-calculus: Interpolation, Lyndon and Łoś-Tarski

- MathematicsJournal of Symbolic Logic
- 2000

A classical logician's view of the μ-calculus is taken: a new logic should not be allowed into the community of logics without at least considering the standard questions that any logic is bothered with.

### 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…

### Automata for Coalgebras: An Approach Using Predicate Liftings

- MathematicsICALP
- 2010

A general upper bound for the complexity of the nonemptiness problem is obtained, under some mild conditions on Λ and T, and related to the automata-theoretic approach to the tableaux-based one of Cirstea et alii, how to obtain their results, based on the existence of a complete tableau calculus, in the framework.

### Automata and fixed point logic: A coalgebraic perspective

- Mathematics, Computer ScienceInf. Comput.
- 2006

### EXPTIME Tableaux for the Coalgebraic µ-Calculus

- Computer Science, MathematicsCSL
- 2009

The coalgebraic µ-calculus is introduced, an extension of the general (coalgebraic) framework with fixpoint operators that yields completeness of the associated tableau calculus and EXPTIME decidability and parametric results in the underlying class of models.

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

- PhilosophyTheor. Comput. Sci.
- 2003

### On the Expressive Completeness of the Propositional mu-Calculus with Respect to Monadic Second Order Logic

- PhilosophyCONCUR
- 1996

It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional Μ-calculus, which implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the Μ -calculus.

### Universal coalgebra: a theory of systems

- MathematicsTheor. Comput. Sci.
- 2000

### Model theoretic methods for fragments of FO and special classes of (finite) structures

- Computer ScienceFinite and Algorithmic Model Theory
- 2011

The leading model theoretic theme is expressive completeness – or the characterisation of fragments of first-order logic as expressively complete over some class of (finite) structures for first- order properties with some prescribed semantic preservation behaviour.