Context-Free Path Querying by Matrix Multiplication

Graph data models are widely used in many areas, for example, bioinformatics, graph databases. In these areas, it is often required to process queries for large graphs. Some of the most common graph queries are navigational queries. The result of query evaluation is a set of implicit relations between nodes of the graph, i.e. paths in the graph. A natural way to specify these relations is by specifying paths using formal grammars over the alphabet of edge labels. An answer to a context-free path query in this approach is usually a set of triples (A, m, n) such that there is a path from the node m to the node n, whose labeling is derived from a non-terminal A of the given context-free grammar. This type of queries is evaluated using the relational query semantics. Another example of path query semantics is the single-path query semantics which requires presenting a single path from the node m to the node n, whose labeling is derived from a non-terminal A for all triples (A, m, n) evaluated using the relational query semantics. There is a number of algorithms for query evaluation which use these semantics but all of them perform poorly on large graphs. One of the most common technique for efficient big data processing is the use of a graphics processing unit (GPU) to perform computations, but these algorithms do not allow to use this technique efficiently. In this paper, we show how the context-free path query evaluation using these query semantics can be reduced to the calculation of the matrix transitive closure. Also, we propose an algorithm for context-free path query evaluation which uses relational query semantics and is based on matrix operations that make it possible to speed up computations by using a GPU.Comment: 9 pages, 11 figures, 2 table

Explainable Reasoning over Knowledge Graphs for Recommendation

Incorporating knowledge graph into recommender systems has attracted increasing attention in recent years. By exploring the interlinks within a knowledge graph, the connectivity between users and items can be discovered as paths, which provide rich and complementary information to user-item interactions. Such connectivity not only reveals the semantics of entities and relations, but also helps to comprehend a user's interest. However, existing efforts have not fully explored this connectivity to infer user preferences, especially in terms of modeling the sequential dependencies within and holistic semantics of a path. In this paper, we contribute a new model named Knowledge-aware Path Recurrent Network (KPRN) to exploit knowledge graph for recommendation. KPRN can generate path representations by composing the semantics of both entities and relations. By leveraging the sequential dependencies within a path, we allow effective reasoning on paths to infer the underlying rationale of a user-item interaction. Furthermore, we design a new weighted pooling operation to discriminate the strengths of different paths in connecting a user with an item, endowing our model with a certain level of explainability. We conduct extensive experiments on two datasets about movie and music, demonstrating significant improvements over state-of-the-art solutions Collaborative Knowledge Base Embedding and Neural Factorization Machine.Comment: 8 pages, 5 figures, AAAI-201

Context-aware Path Ranking for Knowledge Base Completion

Knowledge base (KB) completion aims to infer missing facts from existing ones in a KB. Among various approaches, path ranking (PR) algorithms have received increasing attention in recent years. PR algorithms enumerate paths between entity pairs in a KB and use those paths as features to train a model for missing fact prediction. Due to their good performances and high model interpretability, several methods have been proposed. However, most existing methods suffer from scalability (high RAM consumption) and feature explosion (trains on an exponentially large number of features) problems. This paper proposes a Context-aware Path Ranking (C-PR) algorithm to solve these problems by introducing a selective path exploration strategy. C-PR learns global semantics of entities in the KB using word embedding and leverages the knowledge of entity semantics to enumerate contextually relevant paths using bidirectional random walk. Experimental results on three large KBs show that the path features (fewer in number) discovered by C-PR not only improve predictive performance but also are more interpretable than existing baselines

A Plausibility Semantics for Abstract Argumentation Frameworks

We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default reasoning. In this context, we consider the path from structured to logical to shallow semantic instantiations. The resulting well-justified JZ-extension semantics diverges from more traditional approaches.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014). This is an improved and extended version of the author's ECSQARU 2013 pape

A Perfect Match for Reasoning, Explanation, and Reason Maintenance

Path query languages have been previously shown to com- plement RDF rule languages in a natural way and have been used as a means to implement the RDFS derivation rules. RPL is a novel path query language specifically designed to be incorporated with RDF rules and comes in three avors: Node-, edge- and path- avored expressions allow to express conditional regular expressions over the nodes, edges, or nodes and edges appearing on paths within RDF graphs. Providing reg- ular string expressions and negation, RPL is more expressive than other RDF path languages that have been proposed. We give a compositional semantics for RPL and show that it can be evaluated efficiently, while several possible extensions of it cannot