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1.
Used by ignoramuses who can't spell "quadrilogy" or "tetralogy", which are the commonly-accepted terms for a compound work consisting of four distinct works.
I tried to download the Lethal Weapon quadrology, but nobody had any idea what I was talking about.
by piedpiper34 April 30, 2012
 
2.
a set of four related items or works, most often used in reference to movies, music, or literature
We had a movie marathon and watched National Lampoon's Vacation quadrology.
by twhinkle January 14, 2008