Faculty of Computer Science

Research Group Theoretical Computer Science

Oberseminar: Heterogene formale Methoden

Abstract:

Knowledge graph embeddings give a low-dimensional representation of entities and relations while preserving their semantic meaning. These embeddings reflect commonalities between concepts in the representation space through geometric terms. As a result, reasoning can be carried out by geometric operations. Although embedding conceptual knowledge into geometric objects offers an opportunity to link machine learning to logic and reasoning, most embeddings have limited ontological expressiveness because they can not represent partial information, negation of concepts, and non-functional relations. Constructing fully expressive embeddings is a challenging task because ontology languages such as description logic have several features for representing non-trivial conceptual knowledge, and these properties are difficult to ground in machine learning methods. Recent advances in knowledge representation and reasoning have shown promising outcomes for representing ontologies using convex regions in vector space such that embeddings are logically consistent with respect to the conceptualization provided by the underlying ontology. This presentation will discuss strategies for linking machine learning and logical reasoning by embedding ontologies into vector space. We demonstrate how conjunction, disjunction, and negation operators can be expressed through geometric terms. In particular, we are focused on cone-based semantics in euclidean space.