Related papers: Towards Concise, Machine-discovered Proofs of G\"o…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Achieving human-like reasoning capabilities in Multimodal Large Language Models (MLLMs) has long been a goal. Current methods primarily focus on synthesizing positive rationales, typically relying on manual annotations or complex systems.…
Active automata learning (AAL) under a Minimally Adequate Teacher (MAT) has been successfully used to infer a regular language through membership and equivalence queries. This language might not be fully characterized: we are then…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
Data visualizations like charts are fundamental tools for quantitative analysis and decision-making across fields, requiring accurate interpretation and mathematical reasoning. The emergence of Multimodal Large Language Models (MLLMs)…
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…
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…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect…
This thesis delves into a fortiori arguments in deductive reasoning, underscoring their relevance in various domains such as law, philosophy, and artificial intelligence. The research is centred on employing GPT-3.5-turbo to automate the…
Fact-checking research has extensively explored verification but less so the generation of natural-language explanations, crucial for user trust. While Large Language Models (LLMs) excel in text generation, their capability for producing…
A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…
This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…
We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…
Current Large Language Models (LLMs) exhibit limited ability to understand table structures and to apply precise numerical reasoning, which is crucial for tasks such as table question answering (TQA) and table-based fact verification (TFV).…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Large language models have achieved remarkable progress on complex reasoning tasks. However, they often implicitly fabricate information when inputs are incomplete, producing confident but unreliable conclusions -- a failure mode we term…