相关论文: TacticToe: Learning to Prove with Tactics

Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…

Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…

Despite advances in mathematical reasoning capabilities, Large Language Models (LLMs) still struggle with calculation verification when using established prompting techniques. We present MDToC (Metacognitive Dynamic Tree of Concepts), a…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

Trial-and-error is a fundamental strategy for humans to solve complex problems and a necessary capability for Artificial Intelligence (AI) systems operating in real-world environments. Although several trial-and-error AI techniques have…

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…

Tabular prediction can benefit from in-table rows as few-shot evidence, yet existing tabular models typically perform instance-wise inference and LLM-based prompting is often brittle. Models do not consistently leverage relevant rows, and…

Tic Tac Toe is amongst the most well-known games. It has already been shown that it is a biased game, giving more chances to win for the first player leaving only a draw or a loss as possibilities for the opponent, assuming both the players…

Monte Carlo Tree Search can be used for automated theorem proving. Holophrasm is a neural theorem prover using MCTS combined with neural networks for the policy and the evaluation. In this paper we propose to improve the performance of the…

We present TACO, a toolsuite for the development and automatic verification of fault-tolerant and threshold-based distributed algorithms. Our toolsuite implements three approaches for model checking threshold automata in different decidable…

A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…

Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful…

We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…

Machine teaching is an algorithmic framework for teaching a target hypothesis via a sequence of examples or demonstrations. We investigate machine teaching for temporal logic formulas -- a novel and expressive hypothesis class amenable to…

In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…

Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…

We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

Humans learn to play video games significantly faster than the state-of-the-art reinforcement learning (RL) algorithms. People seem to build simple models that are easy to learn to support planning and strategic exploration. Inspired by…