Algebraic Linguistics

It came to me today that because of the way language is built, it could be structured in sentences similar to an algebraic equation. Words could be grouped in parentheses to show their relation to one another, with modifiers between word groups to show how they work together. For example, "(the dog) bit (the man)" or with modifiers, "[ (black) x (dog) ] bit(hard) [ (tall) x (man) ]". Admittedly it's a bit awkward in English, but a language specifically designed for this could work well--and would at least be very precise. Sentence structure could be expressed in formulas, such as "if (X) then (Y)" or, as in Latin, "[ (X) et (Y) ]=[ (XY)que ]".

For a longer example, here is the original sentence I had in mind, from the blurb on the back of "Founding Brothers": "In this landmark work of history, the National Book Award-winning author of American Sphinx explores how a group of greatly gifted but deeply flawed individuals..." or, translated, "in [ ( {this} {landmark} x {work} ) of (history) ] , [ ( {the National Book Award} + {winning} ) x (author) of (American Sphinx) ] explores how [ (a group) of ( {greatly gifted} - {deeply flawed} ) x (individuals) ] ... "

Then again, perhaps I should just leave well enough alone.