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The assessment of explainability in Legal Judgement Prediction (LJP) systems is of paramount importance in building trustworthy and transparent systems, particularly considering the reliance of these systems on factors that may lack legal…

A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…

Large Language Models (LLMs) have demonstrated impressive capability in many natural language tasks. However, the auto-regressive generation process makes LLMs prone to produce errors, hallucinations and inconsistent statements when…

In this paper, the second of two companion pieces, we explore novel philosophical questions raised by recent progress in large language models (LLMs) that go beyond the classical debates covered in the first part. We focus particularly on…

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or…

We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…

Large Language Models (LLMs) are increasingly adopted as evaluators, offering a scalable alternative to human annotation. However, existing supervised fine-tuning (SFT) approaches often fall short in domains that demand complex reasoning.…

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

Large language models (LLMs), such as LLaMA, Alpaca, Vicuna, GPT-3.5 and GPT-4, have advanced the performance of AI systems on various natural language processing tasks to human-like levels. However, their generalisation and robustness when…

Reinforcement learning (RL) enhanced large language models (LLMs), particularly exemplified by DeepSeek-R1, have exhibited outstanding performance. Despite the effectiveness in improving LLM capabilities, its implementation remains highly…

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language…

This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…

Improving the multi-step reasoning ability of Large Language Models (LLMs) is a critical yet challenging task. The dominant paradigm, outcome-supervised reinforcement learning (RLVR), rewards only correct final answers, often propagating…

This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…

The emergent abilities of large language models (LLMs) have demonstrated great potential in solving medical questions. They can possess considerable medical knowledge, but may still hallucinate and are inflexible in the knowledge updates.…

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this…

This volume constitutes the pre-proceedings of the 31st International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2021), held on 7-8th September 2021 as a hybrid (blended) meeting, both in-person (at the Teachers'…

In this paper we outline a PhD research plan. This research contributes to the field of one-class incremental learning and classification in case of non-stationary environments. The goal of this PhD is to define a new classification…