Definition:
illogical refers to an action or statement that does not make sense or violates accepted principles of reasoning. Illogical can also refer to concepts that are absurd, unreasonable, or ill-founded.
Rules:
illogical generally describes an action, statement, or rule that goes against traditional principles of reasoning. It does not have to be false, it just makes no sense according to the accepted norms of reasoning.
Examples:
1. The illogical argument confounded his opponent.
2. She refused to accept the illogical consequences of the policy.
3. His analysis of the situation was illogical at best.