Rule-Guided Compositional Representation Learning on Knowledge Graphs with Hierarchical Types

The representation learning of the knowledge graph projects the entities and relationships in the triples into a low-dimensional continuous vector space. Early representation learning mostly focused on the information contained in the triplet itself but ignored other useful information. Since entities have different types of representations in different scenarios, the rich information in the types of entity levels is helpful for obtaining a more complete knowledge representation. In this paper, a new knowledge representation frame (TRKRL) combining rule path information and entity hierarchical type information is proposed to exploit interpretability of logical rules and the advantages of entity hierarchical types. Specifically, for entity hierarchical type information, we consider that entities have multiple representations of different types, as well as treat it as the projection matrix of entities, using the type encoder to model entity hierarchical types. For rule path information, we mine Horn rules from the knowledge graph to guide the synthesis of relations in paths. Experimental results show that TRKRL outperforms baselines on the knowledge graph completion task, which indicates that our model is capable of using entity hierarchical type information, relation paths information, and logic rules information for representation learning.

Characterizing Boundedness in Chase Variants

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

ADDING PROBABILITIES AND RULES TO OWL LITE SUBSETS BASED ON PROBABILISTIC DATALOG

This paper proposes two probabilistic extensions of variants of the OWL Lite description language, which are essential for advanced applications like information retrieval. The first step follows the axiomatic approach of combining description logics and Horn clauses: Subsets of OWL Lite are mapped in a sound and complete way onto Horn predicate logics (Datalog variants). Compared to earlier approaches, a larger fraction of OWL Lite can be transformed by switching to Datalog with equality in the head; however, some OWL Lite constructs cannot be transformed completely into Datalog. By using probabilistic Datalog, the new probabilistic OWL Lite subsets (both with support for Horn rules) are defined, and the semantics are given by the semantics of the corresponding probabilistic Datalog program. As inference engines for probabilistic Datalog are available, description logics and information retrieval systems can easily be combined.