Tarek R. Besold

Ouns El Harzli, Bernardo Cuenca Grau, Artur d'Avila Garcez et al.

Fibring of modal logics is a well-established formalism for combining countable families of modal logics into a single fibred language with common semantics, characterized by fibred models. Inspired by this formalism, fibring of neural networks was introduced as a neurosymbolic framework for combining learning and reasoning in neural networks. Fibring of neural networks uses the (pre-)activations of a trained network to evaluate a fibring function computing the weights of another network whose outputs are injected back into the original network. However, the exact correspondence between fibring of neural networks and fibring of modal logics was never formally established. In this paper, we close this gap by formalizing the idea of fibred models \emph{compatible} with fibred neural networks. Using this correspondence, we then derive non-uniform logical expressiveness results for Graph Neural Networks (GNNs), Graph Attention Networks (GATs) and Transformer encoders. Longer-term, the goal of this paper is to open the way for the use of fibring as a formalism for interpreting the logical theories learnt by neural networks with the tools of computational logic.

Alessandro Lonardi, Samy Badreddine, Tarek R. Besold et al.

Post-hoc explainability for Knowledge Graph Completion (KGC) lacks formalization and consistent evaluations, hindering reproducibility and cross-study comparisons. This paper argues for a unified approach to post-hoc explainability in KGC. First, we propose a general framework to characterize post-hoc explanations via multi-objective optimization, balancing their effectiveness and conciseness. This unifies existing post-hoc explainability algorithms in KGC and the explanations they produce. Next, we suggest and empirically support improved evaluation protocols using popular metrics like Mean Reciprocal Rank and Hits@$k$. Finally, we stress the importance of interpretability as the ability of explanations to address queries meaningful to end-users. By unifying methods and refining evaluation standards, this work aims to make research in KGC explainability more reproducible and impactful.

Christoph Wehner, Chrysa Iliopoulou, Ute Schmid et al.

In this paper, we introduce a post-hoc and local explainable AI method tailored for Knowledge Graph Embedding (KGE) models. These models are essential to Knowledge Graph Completion yet criticized for their opaque, black-box nature. Despite their significant success in capturing the semantics of knowledge graphs through high-dimensional latent representations, their inherent complexity poses substantial challenges to explainability. While existing methods like Kelpie use resource-intensive perturbation to explain KGE models, our approach directly decodes the latent representations encoded by KGE models, leveraging the smoothness of the embeddings, which follows the principle that similar embeddings reflect similar behaviours within the Knowledge Graph, meaning that nodes are similarly embedded because their graph neighbourhood looks similar. This principle is commonly referred to as smoothness. By identifying symbolic structures, in the form of triples, within the subgraph neighborhoods of similarly embedded entities, our method identifies the statistical regularities on which the models rely and translates these insights into human-understandable symbolic rules and facts. This bridges the gap between the abstract representations of KGE models and their predictive outputs, offering clear, interpretable insights. Key contributions include a novel post-hoc and local explainable AI method for KGE models that provides immediate, faithful explanations without retraining, facilitating real-time application on large-scale knowledge graphs. The method's flexibility enables the generation of rule-based, instance-based, and analogy-based explanations, meeting diverse user needs. Extensive evaluations show the effectiveness of our approach in delivering faithful and well-localized explanations, enhancing the transparency and trustworthiness of KGE models.

Lorijn Zaadnoordijk, Tarek R. Besold, Rhodri Cusack

After a surge in popularity of supervised Deep Learning, the desire to reduce the dependence on curated, labelled data sets and to leverage the vast quantities of unlabelled data available recently triggered renewed interest in unsupervised learning algorithms. Despite a significantly improved performance due to approaches such as the identification of disentangled latent representations, contrastive learning, and clustering optimisations, the performance of unsupervised machine learning still falls short of its hypothesised potential. Machine learning has previously taken inspiration from neuroscience and cognitive science with great success. However, this has mostly been based on adult learners with access to labels and a vast amount of prior knowledge. In order to push unsupervised machine learning forward, we argue that developmental science of infant cognition might hold the key to unlocking the next generation of unsupervised learning approaches. Conceptually, human infant learning is the closest biological parallel to artificial unsupervised learning, as infants too must learn useful representations from unlabelled data. In contrast to machine learning, these new representations are learned rapidly and from relatively few examples. Moreover, infants learn robust representations that can be used flexibly and efficiently in a number of different tasks and contexts. We identify five crucial factors enabling infants' quality and speed of learning, assess the extent to which these have already been exploited in machine learning, and propose how further adoption of these factors can give rise to previously unseen performance levels in unsupervised learning.

Roberto Confalonieri, Tillman Weyde, Tarek R. Besold et al.

Explainability in Artificial Intelligence has been revived as a topic of active research by the need of conveying safety and trust to users in the `how' and `why' of automated decision-making. Whilst a plethora of approaches have been developed for post-hoc explainability, only a few focus on how to use domain knowledge, and how this influences the understandability of global explanations from the users' perspective. In this paper, we show how ontologies help the understandability of global post-hoc explanations, presented in the form of symbolic models. In particular, we build on Trepan, an algorithm that explains artificial neural networks by means of decision trees, and we extend it to include ontologies modeling domain knowledge in the process of generating explanations. We present the results of a user study that measures the understandability of decision trees using a syntactic complexity measure, and through time and accuracy of responses as well as reported user confidence and understandability. The user study considers domains where explanations are critical, namely, in finance and medicine. The results show that decision trees generated with our algorithm, taking into account domain knowledge, are more understandable than those generated by standard Trepan without the use of ontologies.

Tarek R. Besold, Sara L. Uckelman

The increasing incorporation of Artificial Intelligence in the form of automated systems into decision-making procedures highlights not only the importance of decision theory for automated systems but also the need for these decision procedures to be explainable to the people involved in them. Traditional realist accounts of explanation, wherein explanation is a relation that holds (or does not hold) eternally between an explanans and an explanandum, are not adequate to account for the notion of explanation required for artificial decision procedures. We offer an alternative account of explanation as used in the context of automated decision-making that makes explanation an epistemic phenomenon, and one that is dependent on context. This account of explanation better accounts for the way that we talk about, and use, explanations and derived concepts, such as `explanatory power', and also allows us to differentiate between reasons or causes on the one hand, which do not need to have an epistemic aspect, and explanations on the other, which do have such an aspect. Against this theoretical backdrop we then review existing approaches to explanation in Artificial Intelligence and Machine Learning, and suggest desiderata which truly explainable decision systems should fulfill.

Tarek R. Besold, Artur d'Avila Garcez, Sebastian Bader et al.

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.

Derek Doran, Sarah Schulz, Tarek R. Besold

We characterize three notions of explainable AI that cut across research fields: opaque systems that offer no insight into its algo- rithmic mechanisms; interpretable systems where users can mathemat- ically analyze its algorithmic mechanisms; and comprehensible systems that emit symbols enabling user-driven explanations of how a conclusion is reached. The paper is motivated by a corpus analysis of NIPS, ACL, COGSCI, and ICCV/ECCV paper titles showing differences in how work on explainable AI is positioned in various fields. We close by introducing a fourth notion: truly explainable systems, where automated reasoning is central to output crafted explanations without requiring human post processing as final step of the generative process.

Tarek R. Besold, Artur d'Avila Garcez, Keith Stenning et al.

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means); and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: Logic Programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of Input/Output logic for dealing with uncertainty in dynamic normative contexts.

Arne Recknagel, Tarek R. Besold

Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. One of the voting procedures most often discussed in the literature and, due to its intuitiveness, also conceptually quite appealing is Charles Dodgson's scoring rule, basically using the respective closeness to being a Condorcet winner for evaluating competing alternatives. In this paper, we offer insights on the practical limits of algorithms computing the exact Dodgson scores from a number of votes. While the problem itself is theoretically intractable, this work proposes and analyses five different solutions which try distinct approaches to practically solve the issue in an effective manner. Additionally, three of the discussed procedures can be run in parallel which has the potential of drastically reducing the problem size.