Related papers: Deep Network Guided Proof Search

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

Like any field of empirical science, AI may be approached axiomatically. We formulate requirements for a general-purpose, human-level AI system in terms of postulates. We review the methodology of deep learning, examining the explicit and…

Dropped Pronouns (DP) in which pronouns are frequently dropped in the source language but should be retained in the target language are challenge in machine translation. In response to this problem, we propose a semi-supervised approach to…

Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when…

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…

In this paper, we demonstrate how to do automated theorem proving in the presence of a large knowledge base of potential premises without learning from human proofs. We suggest an exploration mechanism that mixes in additional premises…

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…

With current state-of-the-art approaches aimed at enhancing the reasoning capabilities of Large Language Models(LLMs) through iterative preference learning inspired by AlphaZero, we propose to further enhance the step-wise reasoning…

Given their flexibility and encouraging performance, deep-learning models are becoming standard for motion prediction in autonomous driving. However, with great flexibility comes a lack of interpretability and possible violations of…

Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…

Tokenization is a key component of autoregressive (AR) generative models, converting raw data into more manageable units for modeling. Commonly, tokens describe local information, such as regions of pixels in images or word pieces in text,…

The use of large pretrained neural networks to create contextualized word embeddings has drastically improved performance on several natural language processing (NLP) tasks. These computationally expensive models have begun to be applied to…

Artificial Intelligence agents are required to learn from their surroundings and to reason about the knowledge that has been learned in order to make decisions. While state-of-the-art learning from data typically uses sub-symbolic…

The training of deep neural nets is expensive. We present a predictor- corrector method for the training of deep neural nets. It alternates a predictor pass with a corrector pass using stochastic gradient descent with backpropagation such…

Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

Resolution and superposition are common techniques which have seen widespread use with propositional and first-order logic in modern theorem provers. In these cases, resolution proof production is a key feature of such tools; however, the…

Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic. We describe a way to obtain higher-order theorem proving problems from Mizar articles that make use of…

Transformers, as the fundamental deep learning architecture, have demonstrated great capability in reasoning. This paper studies the generalizable first-order logical reasoning ability of transformers with their parameterized knowledge and…

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning…