{"type":"ScholarlyArticle","title":"EL Embeddings: Geometric Construction of Models for the Description Logic EL++","authors":[{"name":"Maxat Kulmanov","slug":"maxat-kulmanov","given":"Maxat","family":"Kulmanov","affiliation":"Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE) , Computational Bioscience Research"},{"name":"Wang Liu-Wei","slug":"wang-liu-wei","given":"Wang","family":"Liu-Wei","affiliation":"Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE) , Computational Bioscience Research"},{"name":"Yuan Yan","slug":"yuan-yan","given":"Yuan","family":"Yan","affiliation":"Department of Mathematics & Statistics , Dalhousie University , Halifax , Nova Scotia , Canada; Center (CBRC) , King Abdullah University of Science and Technology , Thuwal 23955 , Saudi Arabia"},{"name":"Robert Hoehndorf","slug":"robert-hoehndorf","given":"Robert","family":"Hoehndorf","affiliation":"Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE) , Computational Bioscience Research"}],"abstract":"An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can be used for machine learning, similarity search, or similar tasks. We address the problem of finding vector space embeddings for theories in the Description Logic ??⁺⁺ that are also models of the TBox. To find such embeddings, we define an optimization problem that characterizes the model-theoretic semantics of the operators in ??⁺⁺ within ℝⁿ, thereby solving the problem of finding an interpretation function for an ??⁺⁺ theory given a particular domain Δ. Our approach is mainly relevant to large ??⁺⁺ theories and knowledge bases such as the ontologies and knowledge graphs used in the life sciences. We demonstrate that our method can be used for improved prediction of protein--protein interactions when compared to semantic similarity measures or knowledge graph embeddings.","doi":"10.24963/ijcai.2019/845","url":"https://ijcai.org/proceedings/2019/845","pdf":"https://ijcai.org/proceedings/2019/0845.pdf","markdown":"https://ijcai.org/proceedings/2019/845.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/845","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Understanding Intelligence and Human-level AI in the New Machine Learning era","track":"Understanding Intelligence and Human-level AI in the New Machine Learning era","number":845,"pages":{"first":6103,"last":6109},"keywords":["Special Track on Understanding Intelligence and Human-level AI in the New Machine Learning era: Machine Learning and Classical AI (Special Track on Human AI and Machine Learning)","Special Track on Understanding Intelligence and Human-level AI in the New Machine Learning era: Integrating Learning and (any form of) Reasoning (Special Track on Human AI and Machine Learning)"],"videos":[],"references":[{"position":1,"raw":"[Albrecht and Schlicker, 2007] Mario Albrecht and Andreas Schlicker. FunSimMat: a comprehensive func- tional similarity database. Nucleic Acids Research, 36(suppl1):D434-D439, 10 2007.","title":"FunSimMat: a comprehensive functional similarity database","authors":"Albrecht, Schlicker, Mario Albrecht, Andreas Schlicker","year":"2007","venue":"Nucleic Acids Research","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alshahrani et al., 2017] Mona Alshahrani, et al. Neuro- symbolic representation learning on biological knowledge graphs. Bioinformatics, 33(17):2723-2730, 2017.","title":"Neurosymbolic representation learning on biological knowledge graphs","authors":"Mona Alshahrani","year":"2017","venue":"Bioinformatics","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Ashburner et al., 2000] Michael Ashburner, et al. Gene on- tology: tool for the unification of biology. Nature Genet- ics, 25(1):25-29, May 2000.","title":"Gene ontology: tool for the unification of biology","authors":"Michael Ashburner","year":"2000","venue":"Nature Genetics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Baader et al., 2005] Franz Baader, et al. Pushing the el en- velope. LTCS-Report LTCS-05-01, Chair for Automata Theory, Institute for Theoretical Computer Science, Dres- den University of Technology, Germany, 2005.","title":"Pushing the el envelope","authors":"Baader","year":"2005","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Baader, 2003] Franz Baader. The Description Logic Hand- book : Theory, Implementation and Applications. Cam- bridge University Press, January 2003.","title":"The Description Logic Handbook : Theory, Implementation and Applications","authors":"Franz Baader, Baader","year":"2003","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Barwise and Etchemendy, 2002] Jon Barwise and John Etchemendy. Language, Proof and Logic. Center for the Study of Language and Inf, April 2002.","title":"Language, Proof and Logic","authors":"Etchemendy Barwise","year":"2002","venue":"Center for the Study of Language and Inf","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bordes et al., 2013] Antoine Bordes, et al. Translating embeddings for modeling multi-relational data. In Ad- vances in Neural Information Processing Systems 26, pages 2787-2795. 2013.","title":"Translating embeddings for modeling multi-relational data","authors":"Bordes","year":"2013","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Golbreich and Horrocks, 2007] Christine Golbreich and Ian Horrocks. The OBO to OWL mapping, GO to OWL 1.1! In Christine Golbreich, et al., editors, Proceedings of OWL: Experiences and Directions 2007 (OWLED-2007). CEUR-WS.org, 2007.","title":"The OBO to OWL mapping, GO to OWL 1.1!","authors":"Horrocks Golbreich, Christine Golbreich, Ian Horrocks","year":"2007","venue":"Proceedings of OWL: Experiences and Directions 2007 (OWLED-2007)","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Grau et al., 2008] Bernardo Grau, et al. OWL 2: The next step for OWL. Web Semantics: Science, Services and Agents on the World Wide Web, 6(4):309-322, November 2008.","title":"OWL 2: The next step for OWL","authors":"Bernardo Grau","year":"2008","venue":"Web Semantics: Science, Services and Agents on the World Wide Web","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Harispe et al., 2015] Sebastien Harispe, et al. Semantic similarity from natural language and ontology analysis. Synthesis Lectures on Human Language Technologies, 8(1):1-254, 2015.","title":"Semantic similarity from natural language and ontology analysis","authors":"Harispe","year":"2015","venue":"Synthesis Lectures on Human Language Technologies","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hoehndorf et al., 2011] Robert Hoehndorf, et al. A com- mon layer of interoperability for biomedical ontologies based on OWL EL. Bioinformatics, 27(7):1001-1008, April 2011.","title":"A common layer of interoperability for biomedical ontologies based on OWL EL","authors":"Robert Hoehndorf","year":"2011","venue":"Bioinformatics","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Jabeen et al., 2019] Hajira Jabeen, et al. BioKEEN: A li- brary for learning and evaluating biological knowledge graph embeddings. Bioinformatics, 02 2019.","title":"BioKEEN: A library for learning and evaluating biological knowledge graph embeddings","authors":"Hajira Jabeen","year":"2019","venue":"Bioinformatics","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Kingma and Ba, 2014] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. CoRR, abs/1412.6980, 2014.","title":"Adam: A method for stochastic optimization","authors":"P Diederik, Jimmy Kingma, Ba","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kulmanov and Hoehndorf, 2017] Maxat Kulmanov and Robert Hoehndorf. Evaluating the effect of annotation size on measures of semantic similarity. Journal of Biomedical Semantics, 8(1):7, 2017.","title":"Maxat Kulmanov and Robert Hoehndorf. Evaluating the effect of annotation size on measures of semantic similarity","authors":"Hoehndorf Kulmanov","year":"2017","venue":"Journal of Biomedical Semantics","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Mendez, 2012] Julian Mendez. jcel: A modular rule-based reasoner. In Proceedings of the 1st International Workshop on OWL Reasoner Evaluation (ORE-2012), Manchester, UK, July 1st, 2012, 2012.","title":"jcel: A modular rule-based reasoner","authors":"Julian Mendez","year":"2012","venue":"Proceedings of the 1st International Workshop on OWL Reasoner Evaluation (ORE-2012)","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Mikolov et al., 2013] Tomas Mikolov, et al. Distributed rep- resentations of words and phrases and their compositional- ity. In Proceedings of the 26th International Conference on Neural Information Processing Systems -Volume 2, pages 3111-3119, 2013.","title":"Distributed representations of words and phrases and their compositionality","authors":"Mikolov","year":"2013","venue":"Proceedings of the 26th International Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Motik et al., 2009] Boris Motik, et al. Owl 2 web ontology language: Profiles. Recommendation, World Wide Web Consortium (W3C), 2009.","title":"Owl 2 web ontology language: Profiles. Recommendation","authors":"Motik","year":"2009","venue":"World Wide Web Consortium (W3C)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Nickel et al., 2016] Maximilian Nickel, et al. A review of relational machine learning for knowledge graphs. Pro- ceedings of the IEEE, 104(1):11-33, Jan 2016.","title":"A review of relational machine learning for knowledge graphs","authors":"Maximilian Nickel","year":"2016","venue":"Proceedings of the IEEE","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Pesquita et al., 2009] Catia Pesquita, et al. Semantic sim- ilarity in biomedical ontologies. PLoS Comput Biol, 5(7):e1000443, 07 2009.","title":"Semantic similarity in biomedical ontologies","authors":"Catia Pesquita","year":null,"venue":"PLoS Comput Biol","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Resnik, 1995] Philip Resnik. Using information content to evaluate semantic similarity in a taxonomy. In Proceed- ings of the 14th International Joint Conference on Artifi- cial Intelligence -Volume 1, pages 448-453, 1995.","title":"Using information content to evaluate semantic similarity in a taxonomy","authors":"Philip Resnik, Resnik","year":"1995","venue":"Proceedings of the 14th International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/1995/59"},{"position":21,"raw":"[Roth et al., 2016] Alexander Roth, et al. The STRING database in 2017: quality-controlled protein-protein asso- ciation networks, made broadly accessible. Nucleic Acids Research, 45(D1):D362-D368, 10 2016.","title":"The STRING database in 2017: quality-controlled protein-protein association networks, made broadly accessible","authors":"Alexander Roth","year":"2016","venue":"Nucleic Acids Research","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Schulz et al., 2009] Stefan Schulz, et al. Snomed reaching its adolescence: Ontologists' and logicians' health check. International Journal of Medical Informatics, 78:S86 - S94, 2009. MedInfo 2007.","title":"Snomed reaching its adolescence: Ontologists' and logicians' health check","authors":"Schulz","year":"2007","venue":"International Journal of Medical Informatics","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Smaili et al., 2018] Fatima Zohra Smaili, et al. OPA2Vec: combining formal and informal content of biomedical on- tologies to improve similarity-based prediction. Bioinfor- matics, 11 2018.","title":"Fatima Zohra Smaili, et al. OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction","authors":"Smaili","year":"2018","venue":"Bioinformatics","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Smith et al., 2007] Barry Smith, et al. The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration. Nat Biotech, 25(11):1251-1255, 2007.","title":"The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration","authors":"Smith","year":"2007","venue":"Nat Biotech","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Subramanian et al., 2005] Aravind Subramanian, et al. Gene set enrichment analysis: A knowledge-based ap- proach for interpreting genome-wide expression profiles. Proceedings of the National Academy of Sciences of the United States of America, 102(43):15545-15550, 2005.","title":"Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles","authors":"Aravind Subramanian","year":"2005","venue":"Proceedings of the National Academy of Sciences of the United States of America","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wang et al., 2017] Quan Wang, et al. Knowledge graph embedding: A survey of approaches and applications. IEEE Transactions on Knowledge and Data Engineering, 29(12):2724-2743, Dec 2017.","title":"Knowledge graph embedding: A survey of approaches and applications","authors":"Quan Wang","year":"2017","venue":"IEEE Transactions on Knowledge and Data Engineering","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zemojtel et al., 2016] Tomasz Zemojtel, et al. The Human Phenotype Ontology in 2017. Nucleic Acids Research, 45(D1):D865-D876, 11 2016.","title":"The Human Phenotype Ontology in 2017","authors":"Tomasz Zemojtel","year":"2016","venue":"Nucleic Acids Research","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}