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I am told "Watson also has a Proprietary Knowledge Graph trained on billions of web pages, understanding millions of “types” in text." Where can I access this Knowledge Graph? I would want to query it. I want to add to it. I want to see what inference it makes on information I add.

Ed Pell
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As written in your question, it is a Proprietary knowledge graph. If I were IBM, I would like it to be stored very privately and unaccessible. This knowledge graph is a main asset of Watson, and therefore opening it to public would result in companies using this graph without buying Watson.

This knowledge graph is probably using some semantic web (or similar) technologies to build ontologies and vocabularies representing some fields like oncology, medicine, etc. You may be interested in DBPedia project. It basically is a knowledge graph built from wikipedia data. It is open and can be queried thanks to SPARQL.

To understand better semantic web principles and inferences you can do with it, you should start to learn more about RDF, RDFS, OWL.

Community
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Grégoire G.
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IBM Watson's knowledge graph is not open sourced but YAGO (multilingual knowledge base from Wikipedia, Wordnet, and Geonames) is, which was part of the IBM Watson system that defeated Jeopardy champions. Visit YAGO's GitHub page for more information regarding how to use it and querying the knowledge base.

DBpedia,WikiData and Freebase are good alternatives of YAGO

If you are interested to know more about knowledge graph or like to build your own then refer this.

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To clarify, Watson's Jeopardy showcase wasn't just about YAGO it was a combination of YAGO and DBpedia.

I respond as a collaborator who made this data available to the IBM Watson project at the time.

Some reference links, for additional context.