Related papers: REFACTOR: Learning to Extract Theorems from Proofs

Grammar induction is the task of learning a grammar from a set of examples. Recently, neural networks have been shown to be powerful learning machines that can identify patterns in streams of data. In this work we investigate their…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel…

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…

Verifying the correctness of a textual statement requires not only semantic reasoning about the meaning of words, but also symbolic reasoning about logical operations like count, superlative, aggregation, etc. In this work, we propose…

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…

A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…

Knowledge gaps and hallucinations are persistent challenges for Large Language Models (LLMs), which generate unreliable responses when lacking the necessary information to fulfill user instructions. Existing approaches, such as…

While reasoning models (e.g., DeepSeek R1) trained with reinforcement learning (RL), excel in textual reasoning, they struggle in scenarios requiring structured problem-solving, such as geometric reasoning, concise computation, or complex…

Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification,…

Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…

Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Most successful information extraction systems operate with access to a large collection of documents. In this work, we explore the task of acquiring and incorporating external evidence to improve extraction accuracy in domains where the…

The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…

While large language models (LLMs) are increasingly being used for program synthesis, they lack the global view needed to develop useful abstractions; they generally predict programs one at a time, often repeating the same functionality.…

Automatic generation of paraphrases from a given sentence is an important yet challenging task in natural language processing (NLP), and plays a key role in a number of applications such as question answering, search, and dialogue. In this…

Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…

Knowledge-based question answering relies on the availability of facts, the majority of which cannot be found in structured sources (e.g. Wikipedia info-boxes, Wikidata). One of the major components of extracting facts from unstructured…

Prediction without justification has limited applicability. As a remedy, we learn to extract pieces of input text as justifications -- rationales -- that are tailored to be short and coherent, yet sufficient for making the same prediction.…