I am planning to do a research paper in the definite articles of my dialect. Can anyone provide me with any framework that is suitable for analyzing the definite articles?
I strongly recommend looking at systemic functional linguistics. SFL can offer a few different perspectives. At the syntax level, which SFL calls lexicogrammar, it would be useful to look at the use of the nominal group structure. At another level, which SFL calls discourse semantics, it would be useful to look at the system of reference e.g. https://books.google.com.au/books?id=9BqCtpYdeiwC&pg=PA34&lpg=PA34&dq=Systemic+Functional+Linguistics+tracking+definite+articles&source=bl&ots=2tfAH-_agz&sig=eIwNIcTpHcOqVgLegUT8bA1KvuI&hl=en&sa=X&ved=0ahUKEwj3263w-rfLAhVXwWMKHRE6B9QQ6AEIGzAA#v=onepage&q=Systemic%20Functional%20Linguistics%20tracking%20definite%20articles&f=false
For a starter, you may want to look at WALS http://wals.info/chapter/37 and references therein.