Circular Reasoning
The most well known examples of circular reasoning are cases of the Fallacy of Begging the Question. Here the circle is as short as possible. However, if the circle is very much larger, including a wide variety of claims and a large set of related concepts, then the circular reasoning can be informative and so is not considered to be fallacious.
For example, a dictionary contains a large circle of definitions that use words which are defined in terms of other words that are also defined in the dictionary. Because the dictionary is so informative, it is not considered as a whole to be fallacious. However, a small circle of definitions is considered to be fallacious.
In properly-constructed recursive definitions, defining a term by using that same term is not fallacious. For example,
here is an appropriate recursive definition of the term “a stack of coins.”
Basis step: Two coins, with one on top of the other, is a stack of coins.
Recursion step: If p is a stack of coins, then adding a coin on top of p produces a stack of coins. For a deeper discussion of circular reasoning see