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Query Languages for Machine-Learning Models

arXiv 2601.09381 ↗First posted 14 Jan 2026cs.LO cs.AI cs.DBcited by 0

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Abstract (arXiv)

In this paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Gr"adel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.

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References · 9

  1. 2023What Formal Languages Can Transformers Express? A Surveycited by 120
  2. 2021The Logic of Graph Neural Networkscited by 84
  3. 2023The Descriptive Complexity of Graph Neural Networkscited by 26
  4. 2017First-Order Logic with Counting: At Least, Weak Hanf Normal Forms Always Exist and Can Be Computed!cited by 9
  5. 2020Learning Concepts Described by Weight Aggregation Logiccited by 4
  6. 2019Aggregate Queries on Sparse Databasescited by 3
  7. 2024Query languages for neural networkscited by 2
  8. 2026Recursive querying of neural networks via weighted structurescited by 2
  9. 2024Provenance Analysis and Semiring Semantics for First-Order Logiccited by 1

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