An original model for multi-target learning of logical rules for knowledge graph reasoning

Large-scale knowledge graphs provide structured representations of human knowledge. However, as it is impossible to collect all knowledge, knowledge graphs are usually incomplete. Reasoning based on existing facts paves a way to discover missing facts. In this paper, we study the problem of learning logical rules for reasoning on knowledge graphs for completing missing factual triplets. Learning logical rules equips a model with strong interpretability as well as the ability to generalize to similar tasks. We propose a model able to fully use training data which also considers multi-target scenarios. In addition, considering the deficiency in evaluating the performance of models and the quality of mined rules, we further propose two novel indicators to help with the problem. Experimental results empirically demonstrate that our model outperforms state-of-the-art methods on five benchmark datasets. The results also prove the effectiveness of the indicators

Discourse-Aware Graph Networks for Textual Logical Reasoning

Textual logical reasoning, especially question-answering (QA) tasks with logical reasoning, requires awareness of particular logical structures. The passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence). However, such structures are unexplored as current QA systems focus on entity-based relations. In this work, we propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs). The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features. This pipeline is applied to a general encoder, whose fundamental features are joined with the high-level logic features for answer prediction. Experiments on three textual logical reasoning datasets demonstrate the reasonability of the logical structures built in DAGNs and the effectiveness of the learned logic features. Moreover, zero-shot transfer results show the features' generality to unseen logical texts

Current and Future Challenges in Knowledge Representation and Reasoning

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade

Improving Certified Robustness via Statistical Learning with Logical Reasoning

Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation radius. Given that existing pure data-driven statistical approaches have reached a bottleneck, in this paper, we propose to integrate statistical ML models with knowledge (expressed as logical rules) as a reasoning component using Markov logic networks (MLN, so as to further improve the overall certified robustness. This opens new research questions about certifying the robustness of such a paradigm, especially the reasoning component (e.g., MLN). As the first step towards understanding these questions, we first prove that the computational complexity of certifying the robustness of MLN is #P-hard. Guided by this hardness result, we then derive the first certified robustness bound for MLN by carefully analyzing different model regimes. Finally, we conduct extensive experiments on five datasets including both high-dimensional images and natural language texts, and we show that the certified robustness with knowledge-based logical reasoning indeed significantly outperforms that of the state-of-the-art

Neural Diagrammatic Reasoning

Diagrams have been shown to be effective tools for humans to represent and reason about complex concepts. They have been widely used to represent concepts in science teaching, to communicate workflow in industries and to measure human fluid intelligence. Mechanised reasoning systems typically encode diagrams into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. This means the reasoning systems cannot be easily adapted to other diagrams without a new set of human-defined representation mapping and reasoning rules. Moreover such systems are not able to cope with diagram inputs as raw and possibly noisy images. The need for human input and the lack of robustness to noise significantly limit the applications of mechanised diagrammatic reasoning systems. A key research question then arises: can we develop human-like reasoning systems that learn to reason robustly without predefined reasoning rules? To answer this question, I propose Neural Diagrammatic Reasoning, a new family of diagrammatic reasoning systems which does not have the drawbacks of mechanised reasoning systems. The new systems are based on deep neural networks, a recently popular machine learning method that achieved human-level performance on a range of perception tasks such as object detection, speech recognition and natural language processing. The proposed systems are able to learn both diagram to symbol mapping and implicit reasoning rules only from data, with no prior human input about symbols and rules in the reasoning tasks. Specifically I developed EulerNet, a novel neural network model that solves Euler diagram syllogism tasks with 99.5% accuracy. Experiments show that EulerNet learns useful representations of the diagrams and tasks, and is robust to noise and deformation in the input data. I also developed MXGNet, a novel multiplex graph neural architecture that solves Raven Progressive Matrices (RPM) tasks. MXGNet achieves state-of-the-art accuracies on two popular RPM datasets. In addition, I developed Discrete-AIR, an unsupervised learning architecture that learns semi-symbolic representations of diagrams without any labels. Lastly I designed a novel inductive bias module that can be readily used in today’s deep neural networks to improve their generalisation capability on relational reasoning tasks.EPSRC Studentship and Cambridge Trust Scholarshi