Related papers: Towards Concise, Machine-discovered Proofs of G\"o…
G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
G{\"o}del's completeness theorem for classical first-order logic is one of the most basic theorems of logic. Central to any foundational course in logic, it connects the notion of valid formula to the notion of provable formula.We survey a…
DatalogMTL extends the classical Datalog language with metric temporal logic (MTL), enabling expressive reasoning over temporal data. While existing reasoning approaches, such as materialisation based and automata based methods, offer…
Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…
The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks stepwise. However, training CoT capabilities requires detailed reasoning data, which is…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…
While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…
Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes…
As an essential operation of legal retrieval, legal case matching plays a central role in intelligent legal systems. This task has a high demand on the explainability of matching results because of its critical impacts on downstream…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
This paper introduces a new metamodel-based knowledge representation that significantly improves autonomous learning and adaptation. While interest in hybrid machine learning / symbolic AI systems leveraging, for example, reasoning and…
Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FSTRA). As such, it can be used as an automated theorem prover (ATP) for this theory. {log} is able to automatically…
This paper describes some experiments involving the automated theorem-proving program OTTER in the system TRC of illative combinatory logic. We show how OTTER can be steered to find a contradiction in an inconsistent variant of TRC, and…