Logic (noun)

1. Reasoning conducted or assessed according to strict principles of validity.
2. A particular system or set of principles of reasoning.
3. The process of thinking about something in a reasonable and sensible way.
4. The branch of mathematics and philosophy concerned with the study of reasoning and argument.

Origin:

Late middle english: via latin from greek logikē (tekhnē) "(art) of reason", from logos "word, reason".

Examples:

1. The argument lacks logic.
2. The logic of the situation.
3. The logic of his decision.
4. The logic of a computer program.
5. The principles of logic and mathematics.