Abstract
Recently, tenors have been widely used to encode triples in an RDF graph, which is sometimes called a knowledge graph, for the purpose of knowledge completion and embedding. An interesting question is, can we use tensors to represent OWL ontologies, and handle logical reasoning with ontologies by tensor operations. In this paper, we take the first effort to theoretically build the connection between tensor-based representation and a Horn fragment of OWL, Horn-\(\mathcal {SHOIQ}\), i.e., to study how to encode Horn-\(\mathcal {SHOIQ}\) ontologies to tensors, and further consider using tensor operations to handle ontology materialization, which is an important logical reasoning service for ontology-based applications. We show that the soundness and completeness of ontology materialization can be guaranteed by using tensor operations.
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Notes
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Here, we use ‘\(\ge \)1’ to include the situations where redundant occurs. Specifically, if \(\tau (\alpha )\) occurs as an addend in \(\varPhi ^i(\mathfrak {O})\) more than once, it can be checked that \(\varPhi ^i(\mathfrak {O})\bullet \tau (\alpha )\ge 1\).
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Zhou, Z. (2017). Tensor-Based Representation and Reasoning of Horn-\(\mathcal {SHOIQ}\) Ontologies. In: Li, J., Zhou, M., Qi, G., Lao, N., Ruan, T., Du, J. (eds) Knowledge Graph and Semantic Computing. Language, Knowledge, and Intelligence. CCKS 2017. Communications in Computer and Information Science, vol 784. Springer, Singapore. https://doi.org/10.1007/978-981-10-7359-5_4
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