Download PDFOpen PDF in browserHow Much Should This Symbol Weigh? A GNN-Advised Clause Selection16 pages•Published: June 3, 2023AbstractClause 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.
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