Finding meaningful sub-sentences from a sentence

You can use dependency parser provided by Stanford CoreNLP. Collapsed output of your sentence will look like below.

nsubj(going-3, I-1)
xsubj(do-5, I-1)
aux(going-3, am-2)
root(ROOT-0, going-3)
aux(do-5, to-4)
xcomp(going-3, do-5)
det(seminar-7, a-6)
dobj(do-5, seminar-7)
prep_on(seminar-7, NLP-9)
prep_at(do-5, -11)
prep_in(do-5, Austin-13)
amod(month-15, next-14)
tmod(do-5, month-15)

The last 5 of your sentence output are optional. You can remove one or more parts that are not essential to your sentence.
Most of this optional parts are belong to prepositional and modifier e.g : prep_in, prep_do, advmod, tmod, etc. See Stanford Dependency Manual.

For example, if you remove all modifier from the output, you will get

I am going to do a seminar on NLP at SXSW in Austin.

There's a paper titled "Using Discourse Commitments to Recognize Textual Entailment" by Hickl et al that discusses the extraction of discourse commitments (sub-sentences). The paper includes a description of their algorithm which in some level operates on rules. They used it for RTE, and there may be some minimal levels of deduction in the output. Text simplification maybe a related area to look at.