* Irrational: Meaning not rational, illogical, or unreasonable.
* Superrational: Meaning extremely rational, perhaps to a fault.
* Hyperrational: Similar to superrational, emphasizing excessive rationality.
* Nonrational: Meaning lacking rationality or not based on reason.
* Arational: Meaning without rationality, often implying a state of being beyond or outside reason.
The best prefix to use will depend on the specific context and the intended meaning.