Question: In the field of Data Mining, is there a specific sub-discipline called 'Similarity'? If yes, what does it deal with. Any examples, links, references will be helpful.

Also, being new to the field, I would like the community opinion on how closely related Data Mining and Artificial Intelligence are. Are they synonyms, is one the subset of the other?

Thanks in advance for sharing your knowledge.

Answer: 
Similarity is a concept that is used in several data mining tasks such as clustering, classification. Dependings on what kind of data you have, you may used different similarity measures such as cosine similarity for text documents, euclidian distance, etc
There are lots of similarity measurement used in data mining. for text mining, to find similarity in texts, cosine similarity, jaccard similarity widely used

For reference, you can see raghavan and amnnings information retrieval book