Revision theory is a subfield of philosophical logic. It consists of a general theory of definitions, including (but not limited to) circular and interdependent concepts. A circular definition is one in which the concept being defined occurs in the statement defining it—for example, defining a G as being blue and to the left of a G. Revision theory provides formal semantics for defined expressions, and formal proof systems study the logic of circular expressions.
Definitions are important in philosophy and logic. Although circular definitions have been regarded as logically incorrect or incoherent, revision theory demonstrates that they are meaningful and can be studied with mathematical and philosophical logic. It has been used to provide circular analyses of philosophical and logical concepts.
Revision theory is a generalization of the revision theories of truth developed Anil Gupta, Hans Herzberger, and Nuel Belnap. In the revision theories of Gupta and Herzberger, revision is supposed to reflect intuitive evaluations of sentences that use the truth predicate. Some sentences are stable in their evaluations, such as the truth-teller sentence,
Assuming the truth-teller is true, it is true, and assuming that it is false, it is false. Neither status will change. On the other hand, some sentences oscillate, such as the liar,
On the assumption that the liar is true, one can show that it is false, and on the assumption that it is false, one can show that it is true. This instability is reflected in revision sequences for the liar.
The generalization to circular definitions was developed by Gupta, in collaboration with Belnap. Their book, The Revision Theory of Truth, presents an in-depth development of the theory of circular definitions, as well as an overview and critical discussion of philosophical views on truth and the relation between truth and definition.
The philosophical background of revision theory is developed by Gupta and Belnap. Other philosophers, such as Aladdin Yaqūb, have developed philosophical interpretations of revision theory in the context of theories of truth, but not in the general context of circular definitions.