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: 
Just to stress the importance of the "similarity" concept. 

Data mining (AI, machine learning, modelling etc) is about bringing some function to either it's maximum or minimum value. Take the best optimization/learning/mining algorithm and a wrong function and you get a complete garbage. Note that we use "value" and not "valueS". That's because there is no (to my best knowledge) algorithm (computational or other) that is capable of optimizing more than one value. However, in our Universe, complex optimizations are more frequent than one-dimensional ones (we want to be rich AND young AND healthy). That is why there a plethora of similarity and other scoring functions exists. And that is why none of them is "the right one"
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