Have a look at the logic module's code. Especially the 'boolalg.py' and 
'inference.py' files. Once you work with the code and use it for some 
primary tasks, you will get used to it.
Solve a few bugs first, many are there on the bugs tracker.
About GSoC, you can probably try your hand at the idea of implementing FOL 
in sympy.logic. I had wanted to implement it some time back, but couldn't 
due to time constraints. I guess implementing even the basics of predicate 
logic with sympy's architecture would take quite some time. Things like 
inference could be taken care of later. See Prolog's way of doing things, 
that may give you some ideas.


On Saturday, January 18, 2014 12:43:55 PM UTC+5:30, Dhruvesh Parikh wrote:
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