Which type of reasoning is usually based on laws, rules, principles, generalizations, or definitions?

Deductive reasoning. Deductive reasoning is based on laws, rules, principles, generalizations, or definitions. It is a logical process in which a conclusion is based on multiple premises, (a premise is an assumption that something is true), that are generally assumed true.

For example:

The catalog states that all entering freshmen must take a mathematics placement test.

You are a entering freshmen.

Conclusion: You will have to take the entering mathematics placement test.

The opposite of deductive reasoning is inductive reasoning, in which the premises seek to supply strong evidence for (Not absolute proof of) the truth of the conclusion.