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A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…

We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in…

We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important…

Neural extractive summarization models usually employ a hierarchical encoder for document encoding and they are trained using sentence-level labels, which are created heuristically using rule-based methods. Training the hierarchical encoder…

Prompting and fine-tuning have emerged as two competing paradigms for augmenting language models with new capabilities, such as the use of tools. Prompting approaches are quick to set up but rely on providing explicit demonstrations of each…

The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…

Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with intensional predicates typically degrades performance. In…

Integer Linear Programming (ILP) has been proposed as a formalism for encoding precise structural and semantic constraints for Natural Language Inference (NLI). However, traditional ILP frameworks are non-differentiable, posing critical…

This paper presents a hybrid methodology that enhances the training process of deep learning (DL) models by embedding domain expert knowledge using ontologies and answer set programming (ASP). By integrating these symbolic AI methods, we…

Many forms of inductive logic programming (ILP) use \emph{metarules}, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a…

This paper presents INPROVF, an automatic framework that combines large language models (LLMs) and formal methods to speed up the repair process of high-level robot controllers. Previous approaches based solely on formal methods are…

Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…

We address the problem of learning human-interpretable descriptions of a complex system from a finite set of positive and negative examples of its behavior. In contrast to most of the recent work in this area, which focuses on descriptions…

Recognizing information disorder is difficult because judgments about manipulation depend on cultural and linguistic context. Yet current Large Language Models (LLMs) often behave as monocultural, English-centric "black boxes," producing…

In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…

Large Language Models (LLMs), particularly smaller variants, still struggle with complex reasoning tasks. While inference-time prompting can guide reasoning, existing methods often rely on sequential queries. Ensemble approaches offer a…

Hybrid learning methods use theoretical knowledge of a domain and a set of classified examples to develop a method for classification. Methods that use domain knowledge have been shown to perform better than inductive learners. However,…

In this Masters thesis we present an implementation of a fragment of "book HoTT" as an object logic for the interactive proof assistant Isabelle. We also give a mathematical description of the underlying theory of the Isabelle/Pure logical…

Large Language Models (LLMs) deliver state-of-the-art performance across many tasks but impose high computational and memory costs, limiting their deployment in resource-constrained or real-time settings. To address this, we propose…

This paper describes a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…