mlsanityData to 13 Oct 2026

Graded modal logic and counting bisimulation

arXiv 1910.00039 ↗First posted 30 Sep 2019math.LO cs.LOcited by 13

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Abstract (arXiv)

This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation. We focus on showing expressive completeness of graded multi-modal logic for those first-order properties of pointed Kripke structures that are preserved under counting bisimulation equivalence among all or among just all finite pointed Kripke structures.

Key facts. Cited by 13 papers in the map (data through 13 Oct 2026). First posted on arXiv 30 Sep 2019.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 2; 2024: 2; 2025: 5; 2026: 2.

13 papers.

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  1. 2021The Logic of Graph Neural Networkscited by 84
  2. 2022Expressiveness and Approximation Properties of Graph Neural Networkscited by 63
  3. 2023A Theory of Link Prediction via Relational Weisfeiler-Leman on Knowledge Graphscited by 32
  4. 2024Link Prediction with Relational Hypergraphscited by 9
  5. 2023Understanding Expressivity of GNN in Rule Learningcited by 7
  6. 2025The Correspondence Between Bounded Graph Neural Networks and Fragments of First-Order Logiccited by 6
  7. 2025Logical Characterizations of GNNs with Mean Aggregationcited by 6
  8. 2025Halting Recurrent GNNs and the Graded μ-Calculuscited by 2
  9. 2024Are Targeted Messages More Effective?cited by 1
  10. 2025Graph Learning via Logic-Based Weisfeiler-Leman Variants and Tabularizationcited by 0
  11. 2025Enhancing Logical Expressiveness in Graph Neural Networks via Path-Neighbor Aggregationcited by 0
  12. 2026Unifying approach to uniform expressivity of graph neural networkscited by 0
1 more
  1. 2026Structural Preservation and the Logical Expressiveness of Graph Neural Networkscited by 0