Related papers: The Chase in Lean -- Crafting a Formal Library for…

Reasoning is an essential skill to enable Large Language Models (LLMs) to interact with the world. As tasks become more complex, they demand increasingly sophisticated and diverse reasoning capabilities for sequential decision-making,…

This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…

Understanding how data moves, transforms, and persists, known as data flow, is fundamental to reasoning in procedural tasks. Despite their fluency in natural and programming languages, large language models (LLMs), although increasingly…

While test-time reasoning enables language models (LMs) to tackle complex tasks, searching or planning in natural language can be slow, costly, and error-prone. But even when LMs struggle to emulate the precise reasoning steps needed to…

Large Language Models (LLMs) have displayed astonishing abilities in various tasks, especially in text generation, classification, question answering, etc. However, the reasoning ability of LLMs still faces many debates. The inherent…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…

We introduce LLM CHESS, an evaluation framework designed to probe the generalization of reasoning and instruction-following abilities in large language models (LLMs) through extended agentic interaction in the domain of chess. We rank over…

A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…

We present a semi-automated framework to construct and reason about programs in a deeply-embedded while-language. The while-language we consider is a simple computation model that can simulate (and be simulated by) Turing Machines with a…

By a pure logical framework we mean a framework which does not rely on any particular formal calculus. For example, Metamath is an instance of a pure logical framework. Another example is the Russell system…

Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…

Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language…

This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal…

Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…

Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…

A major target of linguistics and cognitive science has been to understand what class of learning systems can acquire the key structures of natural language. Until recently, the computational requirements of language have been used to argue…

The implicit theory that a simulation represents is precisely not in the individual choices but rather in the 'envelope' of possible trajectories - what is important is the shape of the whole envelope. Typically a huge amount of computation…