From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings

Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in $\mathbb{R}^n$. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms

KLM-Style Defeasible Reasoning for Datalog

In many problem domains, particularly those related to mathematics and philosophy, classical logic has enjoyed great success as a model of valid reasoning and discourse. For real-world reasoning tasks, however, an agent typically only has partial knowledge of its domain, and at most a statistical understanding of relationships between properties. In this context, classical inference is considered overly restrictive, and many systems for non-monotonic reasoning have been proposed in the literature to deal with these tasks. A notable example is the Klm framework, which describes an agent's defeasible knowledge qualitatively in terms of conditionals of the form “if A, then typically B”. The goal of this research project is to investigate Klm-style semantics for defeasible reasoning over Datalog knowledge bases. Datalog is a declarative logic programming language, designed for querying large deductive databases. Syntactically, it can be viewed as a computationally feasible fragment of firstorder logic, so this continues a recent line of work in which the Klm framework is lifted to more expressive languages

Visualizing ALC Using Concept Diagrams

This paper addresses the problem of how to visualize axiomsfrom ALC using concept diagrams. We establish that 66.4% of OWL axioms defined for ontologies in the Manchester corpus are formulated over ALC, demonstrating the significance of considering how to visualize this relatively simple description logic. Our solution to the problem involves providing a general translation from ALC axioms into concept diagrams, which is sufficient to establish that all of ALC can be expressed. However, the translation itself is not designed to give optimally readable diagrams, which is particularly challenging to achieve in the general case. As such, we also improve the translations for a selected category of ALC axioms, to illustrate that more effective diagrams can be produced

If, then, therefore?:Neoplatonic Exegetical Logic Between the Categorical and the Hypothetical

In late antiquity, logic developed into what Ebbesen calls the LAS, the Late Ancient Standard. This paper discusses the Neoplatonic use of LAS, as informed by epistemological and metaphysical concerns. It demonstrates this through an analysis of the late ancient debate about hypothetical and categorical logic as manifest in the practice of syllogizing Platonic dialogues. After an introduction of the Middle Platonist view on Platonic syllogistic as present in Alcinous, this paper presents an overview of its application in the syllogizing practice of Proclus and others. That overview shows that the two types were considered two sides of the same coin, to be used for the appropriate occasions, and both relying on the methods of dialectic as revealing the structure of knowledge and reality. Pragmatics, dialectic, and didactic choices determine which type or combination is selected in syllogizing Plato. So even though there is no specific Neoplatonic logic, there is a specific Neoplatonic use of LAS

A vision for diagrammatic ontology engineering

Abstract. Ontology engineering is becoming more important, given the rapid rise of data in this information age. To better understand and rea-son about this data, ontologies provide us with insight into its structure. With this comes the involvement of a wide range of stakeholders, such as information analysts, software engineers, lawyers, and domain experts, alongside specialist ontology engineers. These specialists are likely to be adept at using existing approaches to ontology development, typically description logic or one of its various stylized forms. However, not all stakeholders can readily access such notations, which often have a very mathematical style. Many stakeholders, even including fluent ontology engineers, could benefit from visual approaches to ontology engineering, provided those approaches are accessible. This paper presents ongoing re-search into a diagrammatic approach to ontology engineering, outlining key research advances that are required

A Semi-Supervised Feature Engineering Method for Effective Outlier Detection in Mixed Attribute Data Sets

Outlier detection is one of the crucial tasks in data mining which can lead to the finding of valuable and meaningful information within the data. An outlier is a data point that is notably dissimilar from other data points in the data set. As such, the methods for outlier detection play an important role in identifying and removing the outliers, thereby increasing the performance and accuracy of the prediction systems. Outlier detection is used in many areas like financial fraud detection, disease prediction, and network intrusion detection. Traditional outlier detection methods are founded on the use of different distance measures to estimate the similarity between the points and are confined to data sets that are purely continuous or categorical. These methods, though effective, lack in elucidating the relationship between outliers and known clusters/classes in the data set. We refer to this relationship as the context for any reported outlier. Alternate outlier detection methods establish the context of a reported outlier using underlying contextual beliefs of the data. Contextual beliefs are the established relationships between the attributes of the data set. Various studies have been recently conducted where they explore the contextual beliefs to determine outlier behavior. However, these methods do not scale in the situations where the data points and their respective contexts are sparse. Thus, the outliers reported by these methods tend to lose meaning. Another limitation of these methods is that they assume all features are equally important and do not consider nor determine subspaces among the features for identifying the outliers. Furthermore, determining subspaces is computationally exacerbated, as the number of possible subspaces increases with increasing dimensionality. This makes searching through all the possible subspaces impractical. In this thesis, we propose a Hybrid Bayesian Network approach to capture the underlying contextual beliefs to detect meaningful outliers in mixed attribute data sets. Hybrid Bayesian Networks utilize their probability distributions to encode the information of the data and outliers are those points which violate this information. To deal with the sparse contexts, we use an angle-based similarity method which is then combined with the joint probability distributions of the Hybrid Bayesian Network in a robust manner. With regards to the subspace selection, we employ a feature engineering method that consists of two-stage feature selection using Maximal Information Coefficient and Markov blankets of Hybrid Bayesian Networks to select highly correlated feature subspaces. This proposed method was tested on a real world medical record data set. The results indicate that the algorithm was able to identify meaningful outliers successfully. Moreover, we compare the performance of our algorithm with the existing baseline outlier detection algorithms. We also present a detailed analysis of the reported outliers using our method and demonstrate its efficiency when handling data points with sparse contexts