Begging the Question used recursively. A is true because B is true. B is true because A is true. If A, then B; if B, then A. The proof for the statements being asserted simply circles around and around, with nothing in it that isn't being proved by itself. This is a logical fallacy, because it disallows the possibility that both statements are false and, like Begging the Question, presupposes the truth of the thing it's supposed to be providing an argument to prove the truth of. To summarize, the one using it thinks that their claim proves itself; any argument that uses circular reasoning can be boiled down to "it's true because it's true."

If A or B have independent proofs that are "outside the loop", it is no longer circular reasoning.

The simplest form of this is a tautology (like defining "sports writer" as "a writer who writes about sports"). See also Shaped Like Itself and Famous for Being Famous. A similar concept is a logic loop, a type of Logic Bomb where a series of thoughts leads to itself. The Tautological Templar lives by this trope, assuming that they're inherently good and therefore everything they say or do is inherently good, too.

Looks like this fallacy, but isn't.

• Algorithms that describe decision-making processes often loop back to the decision point, but being decisions, they have more than one possible circle. These algorithms, while circular, describe a process rather than making an argument.
• As mentioned above, a logic loop is kind of like circular reasoning but in the other way. Instead of “A is true because B is true because C is true because A is true” (circular reasoning) it's “A is true; therefore B is true; therefore C is true; therefore A is true.” While not a fallacy,^note Since A is assumed/ proven to be true by data outside the loop a logic loop is a Logic Bomb and it's best to steer machines away from them. Most humans will recognize the futility of the exercise once one loop has been completed but most machines can't.
• Axioms are considered self-evidently valid, and thus are accepted as "true because they are true". (For example, “A = A” or “The whole is greater than the part”, or "If A = B and B = C then A = C".) This is not fallacious because axioms form the basis for other logical arguments. We're not trying to prove axioms; we're using them to prove other things.
• Shaped Like Itself is when something is described recursively, as in “an apple-colored apple” or “a round circle.” This may indicate vague thinking, but isn’t inherently fallacious since we’re describing rather than proving anything.
• Circular Definition: Definitions reference other definitions (a cat is an animal, an animal is a living being, etc.), but this cannot go on forever. So, at some point, you end up defining thing A as thing B and then thing B in terms of thing A. This might look like circular reasoning, but the truth is that some stuff you have to deem undefinable and move on.

Examples: