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Large language models (LLMs) have demonstrated remarkable proficiency in generating detailed and coherent explanations of complex concepts. However, the extent to which these models truly comprehend the concepts they articulate remains…
Uncertainty quantification (UQ) is crucial for deploying machine learning models in high-stakes applications, where overconfident predictions can lead to serious consequences. An effective UQ method must balance computational efficiency…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there…
Ontologies are an important tool for structuring domain knowledge, but their development is a complex task that requires significant modelling and domain expertise. Ontology learning, aimed at automating this process, has seen advancements…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a…
Learning formulas in Linear Temporal Logic (LTLf) from finite traces is a fundamental research problem which has found applications in artificial intelligence, software engineering, programming languages, formal methods, control of…
Understanding whether fine-tuning elicits latent capabilities or teaches new ones is a fundamental question for language model evaluation and safety. We develop a formal information-theoretic framework for quantifying how much predictive…
Uncertainty quantification (UQ) is critical for assessing the reliability of machine learning interatomic potentials (MLIPs) in molecular dynamics (MD) simulations, identifying extrapolation regimes and enabling uncertainty-aware workflows…
Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word…
We investigate the use of Natural Language Inference (NLI) in automating requirements engineering tasks. In particular, we focus on three tasks: requirements classification, identification of requirements specification defects, and…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
We study secret elicitation: discovering knowledge that an AI possesses but does not explicitly verbalize. As a testbed, we train three families of large language models (LLMs) to possess specific knowledge that they apply downstream but…
Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order,…
Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…
Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…
Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula f, which…
The reasoning frontier of Large Language Models (LLMs) has advanced significantly through modern post-training paradigms (e.g., Reinforcement Learning from Verifiable Rewards (RLVR)). However, the efficacy of these methods remains…