* Il-: Meaning "not" or "the opposite of". Example: illogical (not logical).
* A-: Meaning "not" or "without". Example: alogical (not logical, lacking logic).
* Non-: Meaning "not" or "the opposite of". Example: non-logical (not logical).
* Un-: Meaning "not" or "the opposite of". Example: unlogical (though less common, it's possible).
* Pseudo-: Meaning "false" or "imitation". Example: pseudo-logical (appearing logical but not actually being so).
The best prefix to use depends on the specific context and the nuance you want to convey.