Prefixes:
* Illogical: Means lacking logic or reason.
* Alogical: Means not based on logic or reason (can be synonymous with illogical).
* Pseudological: Means falsely claiming to be logical or using misleading logic.
* Paralogical: Means seemingly logical, but actually flawed or incorrect.
* Hyperlogical: Means excessively or overly logical, to the point of being unreasonable or inflexible.
Suffixes:
* Logically: Indicates that something is done in a logical manner.
* Logician: A person who is skilled in logic or reason.
* Logicality: The quality of being logical or reasonable.
You can also combine prefixes and suffixes to create more complex words:
* Illogically: In a way that is not logical.
* Pseudologically: Using false or misleading logic.
Ultimately, the best prefix or suffix to use will depend on the specific meaning you want to convey.