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How Much Should This Symbol Weigh? A GNN-Advised Clause Selection

16 pagesPublished: June 3, 2023

Abstract

Clause selection plays a crucial role in modern saturation-based automatic theorem provers. A commonly used heuristic suggests prioritizing small clauses, i.e., clauses with few symbol occurrences. More generally, we can give preference to clauses with a low weighted symbol occurrence count, where each symbol’s occurrence count is multiplied by a respective symbol weight. Traditionally, a human domain expert would supply the symbol weights.
In this paper, we propose a system based on a graph neural network that learns to predict symbol weights with the aim of improving clause selection for arbitrary first-order logic problems. Our experiments demonstrate that by advising the automatic theorem prover Vampire on the first-order fragment of TPTP using a trained neural network, the prover’s problem solving capability improves by 6.6% compared to uniformly weighting symbols and by 2.1% compared to a goal-directed variant of the uniformly weighting strategy.

Keyphrases: automated theorem proving, clause selection, graph neural network, machine learning, saturation based theorem proving

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 96-111.

BibTeX entry
@inproceedings{LPAR2023:How_Much_Should_This,
  author    = {Filip Bártek and Martin Suda},
  title     = {How Much Should This Symbol Weigh? A GNN-Advised Clause Selection},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/2BSs},
  doi       = {10.29007/5f4r},
  pages     = {96-111},
  year      = {2023}}
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