A binary relation is defined as a set of ordered pairs of objects where some common "relation" holds true across all ordered pairs in the set.

For example, the relation "is greater than" across the set $\{1, 2, 3\}$ would give $\mathbb{S}=\{(3, 1), (2, 1), (3, 2)\}$.

University of Connecticut

On the frontier of deep learning applications, research is being done on the representation of knowledge in relational manners to learn reasoning.

Knowledge Representation, Reasoning and Question Answering

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

Binary Relations

A relational database is a database that explicitly stores information on relations between entities that are significant in our model. While regular training data allows the model to infer and learn relationships, a relational database explicitly states the relations significant for the problem at hand.

A knowledge base is any database intended to convey "commonsense" knowledge that humans normally know from day-to-day experiences for a deep learning model. Significant knowledge bases include *Freebase*, *OpenCyc*, *WordNet*, *Wikibase*, and *GeneOntology*. 

Relational Databases and Knowledge Bases

The most common practical application of knowledge representation and relational learning is **link prediction**. 

Link prediction is the act of attempting to use a given knowledge base to predict missing relations in the knowledge base. It is a form of generaliation to predict new facts based on old ones.

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