Related papers: Skolemisation for Intuitionistic Linear Logic

It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…

Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms…

Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training.…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

Reasoning in mathematical domains remains a significant challenge for relatively small language models (LMs). Many current methods focus on specializing LMs in mathematical reasoning and rely heavily on knowledge distillation from powerful…

Autoformalisation, the task of expressing informal mathematical statements in formal language, is often viewed as a direct translation process. This, however, disregards a critical preceding step: conjecturing. Many mathematical problems…

Despite the significant improvements achieved by large language models (LLMs) in English reasoning tasks, these models continue to struggle with multilingual reasoning. Recent studies leverage a full-parameter and two-stage training…

We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…

The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning…

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…

Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial…

Sequence classification is the task of predicting a class label given a sequence of observations. In many applications such as healthcare monitoring or intrusion detection, early classification is crucial to prompt intervention. In this…

Tokenization is a hardcoded compression step which remains in the training pipeline of Large Language Models (LLMs), despite a general trend towards architectures becoming increasingly end-to-end. Prior work has shown promising results at…

This work aims to improve the generalization of logic-based legal reasoning systems by integrating recent advances in NLP with legal-domain adaptive few-shot learning techniques using LLMs. Existing logic-based legal reasoning pipelines…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

Chain-of-Thought (CoT) reasoning is a critical capability for large language models (LLMs), enabling them to tackle com- plex multi-step tasks. While base LLMs, pre-trained on general text corpora, often struggle with reasoning due to a…

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…

Recent advancements in Large Language Models (LLMs) have led to their widespread adoption in daily applications. Despite their impressive capabilities, they remain vulnerable to adversarial attacks, as even minor meaning-preserving changes…

Curriculum learning (CL), motivated by the intuition that learning in increasing order of difficulty should ease generalization, is commonly adopted both in pre-training and post-training of large language models (LLMs). The intuition of CL…