I have just started studying logic and wish to find some example arguments by famous philosophers broken down very plainly into their premises and conclusions, along with the logical notation to the argument.
1) The famous logician Kurt Goedel left behind a formalized "proof" for the ontological argument of Anselm of Canterbury.
Anselm gave a "proof" that the term "a being than which none greater can be conceived" must refer to some existing being, i.e., that there must exist a being than which none greater can be conceived.
See the following lecture by the logician Brendel for a formalization of Goedels "proof"
It closes with a critical assessment of what Goedel's formalization proves and what it does not prove.
2) You may also read Gettier's presentation of the "Gettier example" in
The Gettier example is considered a counter-example against a widely hold definition of knowlegde as justified true belief. Gettier's formalization is not so extensive like Goedel's argument.
Some parts of Wittgenstein's "Tractatus Logical-Philosophicus" are written in purely logical notation and Wittgenstein's view at the time (he moved away from it later) was called logical atomism: he wanted to break down all meaningful statements into basic atomic logical sentences. Bertrand Russell was also a proponent of this view. See Russell's famous "the present present king of France" example.
John Hospers's Introduction to Philosophical Analysis was written as an introductory textbook, with a strong emphasis on providing logical analyses of important arguments. link
There's also a book called Just the Arguments which I think provides nice little argument analyses from the great philosophers. link
I haven't used either text myself, so I can't vouch for the quality, but they seem to fit the description you're looking for.