mlsanityData to 7 Oct 2026

Weighted First-Order Model Counting in the Two-Variable Fragment With Counting Quantifiers

arXiv 2007.05619 ↗First posted 10 Jul 2020cs.AI cs.LOcited by 16

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Abstract (arXiv)

It is known due to the work of Van den Broeck et al [KR, 2014] that weighted first-order model counting (WFOMC) in the two-variable fragment of first-order logic can be solved in time polynomial in the number of domain elements. In this paper we extend this result to the two-variable fragment with counting quantifiers.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jul 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 5; 2024: 1; 2025: 5; 2026: 3.

16 papers.

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  1. 2022Lifted Inference with Linear Order Axiomcited by 13
  2. 2021Weighted Model Counting in FO2 with Cardinality Constraints and Counting Quantifiers: A Closed Form Formulacited by 8
  3. 2023Lifted Algorithms for Symmetric Weighted First-Order Model Samplingcited by 6
  4. 2023Lifted Inference beyond First-Order Logiccited by 5
  5. 2024Bridging Weighted First Order Model Counting and Graph Polynomialscited by 5
  6. 2023On Exact Sampling in the Two-Variable Fragment of First-Order Logiccited by 3
  7. 2025Faster Lifting for Ordered Domains with Predecessor Relationscited by 2
  8. 2023Weighted First Order Model Counting with Directed Acyclic Graph Axiomscited by 1
  9. 2023Synthesising Recursive Functions for First-Order Model Counting: Challenges, Progress, and Conjecturescited by 1
  10. 2025Towards Practical First-Order Model Countingcited by 1
  11. 2025Polynomial-Time Relational Probabilistic Inference in Open Universescited by 1
  12. 2025Model Enumeration of Two-Variable Logic with Quadratic Delay Complexitycited by 1
4 more
  1. 2025Tractable Weighted First-Order Model Counting with Bounded Treewidth Binary Evidencecited by 0
  2. 2026A Fast Model Counting Algorithm for Two-Variable Logic with Counting and Modulo Counting Quantifierscited by 0
  3. 2026Solving Combinatorial Counting Problems with Weighted First-Order Model Countingcited by 0
  4. 2026CombEval: A Framework for Evaluating Combinatorial Counting in Large Language Modelscited by 0