Normal Forms of Conditional Belief Bases Respecting Inductive Inference

Abstract

Normal forms of syntactic entities play an important role in many different areas in computer science. In this paper, we
address the question of how to obtain normal forms and minimal normal forms of conditional belief bases in order to,
e.g., ease reasoning with them or to simplify their comparison. We introduce notions of equivalence of belief bases
taking nonmonotonic inductive inference operators into account. Furthermore, we also consider renamings of belief
bases induced by renamings of the underlying signatures. We show how renamings constitute another dimension of normal
forms. Based on these different dimensions, we introduce and illustrate various useful normal forms and show their properties, advantages, and interrelationships.