We introduce algebraic machine reasoning, a new reasoning framework that is well-suited
for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process …

Traditional automated theorem proving systems for first-order logic depend on speed-
optimized search and many handcrafted heuristics designed to work over a wide range of …

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning
in mathematical language to rigorous derivations in formal systems. In recent years, the …

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the
role of lemmas in automated theorem proving. The paper describes experiments with a …

An automated theorem proving (ATP) system's capacity for reasoning is significantly
influenced by the inference rules it uses. The recently introduced standard contradiction …

Using reinforcement learning for automated theorem proving has recently received much
attention. Current approaches use representations of logical statements that often rely on the …

This work describes a new version of a previously published Python package—gym-
saturation: a collection of OpenAI Gym environments for guiding saturation-style provers …

Neurosymbolic AI combines the interpretability, parsimony, and explicit reasoning of
classical symbolic approaches with the statistical learning of data-driven neural approaches …

gym-saturationis an OpenAI Gym environment for reinforcement learning (RL) agents
capable of proving theorems. Currently, only theorems written in a formal language of the …

Abstract Automated Theorem Proving (ATP) systems search for a proof in a rapidly growing
space of possibilities. Heuristics have a profound impact on search, and ATP systems make …