An inquiry is any process that has the aim of augmenting knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...

, resolving doubt
Doubt, a status between belief and disbelief, involves uncertainty or distrust or lack of sureness of an alleged fact, an action, a motive, or a decision. Doubt brings into question some notion of a perceived "reality", and may involve delaying or rejecting relevant action out of concerns for...

, or solving a problem
A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal...

. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.

When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism.