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The definition is a common form of human expert knowledge, a building blockof formal science and mathematics, a foundation for database theory and issupported in various forms in many knowledge representation and formalspecification languages and systems. This paper is a formal study of some ofthe most common forms of inductive definitions found in scientific text:monotone inductive definition, definition by induction over a well-foundedorder and iterated inductive definitions. We define a logic of definitionsoffering a uniform formal syntax to express definitions of the different sorts,and we define its semantics by a faithful formalization of the inductionprocess. Several fundamental properties of definition by induction emerge: thenon-determinism of the induction process, the confluence of inductionprocesses, the role of the induction order and its relation to the inductiverules, how the induction order constrains the induction process and,ultimately, that the induction order is irrelevant: the defined set does notdepend on the induction order. We propose an inductive construction capable ofconstructing the defined set without using the induction order. We investigateborderline definitions of the sort that appears in definitional paradoxes.

A Logical Study of Some Common Principles of Inductive Definition and its Implications for Knowledge Representation