Recent geometric-based approaches have been shown to efficiently model complex logical queries (including the intersection operation) over Knowledge Graphs based on the natural representation of Venn diagram. Existing geometric-based models (using points, boxes embeddings), however, cannot handle the logical negation operation. Further, those using cones embeddings are limited to representing queries by two-dimensional shapes, which reduced their effectiveness in capturing entities query relations for correct answers. To overcome this challenge, we propose unbounded cylinder embeddings (namely CylE), which is a novel geometric-based model based on three-dimensional shapes. Our approach can handle a complete set of basic first-order logic operations (conjunctions, disjunctions and negations). CylE considers queries as Cartesian products of unbounded sector-cylinders and consider a set of nearest boxes corresponds to the set of answer entities. Precisely, the conjunctions can be represented via the intersections of unbounded sector-cylinders. Transforming queries to Disjunctive Normal Form can handle queries with disjunctions. The negations can be represented by considering the closure of complement for an arbitrary unbounded sector-cylinder. Empirical results show that the performance of multi-hop reasoning task using CylE significantly increases over state-of-the-art geometric-based query embedding models for queries without negation. For queries with negation operations, though the performance is on a par with the best performing geometric-based model, CylE significantly outperforms a recent distribution-based model.

Geometric representation of query embeddings (using points, particles, rectangles and cones) can effectively achieve the task of answering complex logical queries expressed in first-order logic (FOL) form over knowledge graphs, allowing intuitive encodings. However, current geometric-based methods depend on the neural approach to model FOL operators (conjunction, disjunction and negation), which are not easily explainable with considerable computation cost. We overcome this challenge by introducing a symbolic modeling approach for the FOL operators, emphasizing the direct calculation of the intersection between geometric shapes, particularly sector-cones in the embedding space, to model the conjunction operator. This approach reduces the computation cost as a non-neural approach is involved in the core logic operators. Moreover, we propose to accelerate the learning in the relation projection operator using the neural approach to emphasize the essential role of this operator in all query structures. Although empirical evidence for explainability is challenging, our approach demonstrates a significant improvement in answering complex logical queries (both non-negative and negative FOL forms) over previous geometric-based models.

NLP systems are often challenged by difficulties arising from noisy, non-standard, and domain specific corpora. The task of lexical normalisation aims to standardise such corpora, but currently lacks suitable tools to acquire high-quality annotated data to support deep learning based approaches. In this paper, we present LexiClean, the first open-source web-based annotation tool for multi-task lexical normalisation. LexiClean’s main contribution is support for simultaneous in situ token-level modification and annotation that can be rapidly applied corpus wide. We demonstrate the usefulness of our tool through a case study on two sets of noisy corpora derived from the specialised-domain of industrial mining. We show that LexiClean allows for the rapid and efficient development of high-quality parallel corpora. A demo of our system is available at: https://youtu.be/P7_ooKrQPDU.