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What are the rules on statutory interpretation adopted by the courts?
What are the problems encountered in each of these rules?
Well, generally judges are dealing either with statutes or common law. Congress may formally make law by statute, essentially formulating the boundaries of the law on that given topic and leaving courts to interpret their intention. In areas where statutes have not been written, courts rely upon their previous rulings (common law).
Just because a law has been reduced to a statute does not necessarily mean that courts don't have a difficult task going forward. They must determine, as I mentioned, what was intended by the language. They will look to the text itself and spend a lot of time bickering over every "and" or "or." They will look to what they believe to be the intent driving the statute, and may look to prior law, other related law, or the records of the discussions that transpired in making the law.
Wikipedia (http://en.wikipedia.org/wiki/Statutory_interpretation) mentions three major types of statutory interpretation. (1) Textual, where the judges are looking strictly at the text itself, (2) Substantive, where judges are concerned about what results different readings of the text will produce, and (3) Deference, where judges defer to other agencies for example.
This article (http://digitalcommons.law.yale.edu/cgi/viewcontent.cgi?article=2967&context=fss_papers) offers two categories: (1) Looking to the text itself or (2) looking outside the text.
I'm not sure what areas you were provided, if any, but this should give you a good start. And the pros and cons of each should also be slightly apparent. One major issue is the tension between courts and the legislature. Do courts sometimes overstep their bounds by pretending to know what legislatures were thinking? Are they given an impossible task? Are they merely interpreting law or in a way making law?