Nonmonotonic Reasoning with Defeasible Rules on Feasible and Infeasible Worlds : Exploring a Landscape of Inductive Inference Operators

The modeling of intelligent behavior has been a central topic for researchers since artificial intelligence emerged as a research field. The use of classical logic in representing the knowledge and beliefs of an intelligent agent implies that inferences remain valid irrespective of additional information, and that the set of conclusions grows monotonically with the amount of available information. In reality, however, decisions must be made and planning actions must be taken in the presence of uncertain and incomplete information, meaning that previously obtained inferences may have to be withdrawn in the light of new information. Nonmonotonic logic provides the means to model such behavior. This book, Nonmonotonic Reasoning with Defeasible Rules on Feasible and Infeasible Worlds, explores the area of nonmonotonic reasoning from conditional belief bases, in which postulates describe desirable properties of nonmonotonic reasoning, and many inference methods, differing in which of these postulates they satisfy, are applied. The author employs the notion of inductive inference operators, which map a belief base (a set of given conditionals) to an inference relation containing all the inferences an agent can draw from the set. Two notions of consistency – weak and strong – are contrasted, and the topic of inductive inference from weakly consistent belief bases is examined. The book addresses the challenging problems of nonmonotonic reasoning from conditional belief bases with convincing and rigorously proven theoretical results, placed in a scientific context. It will be of interest to all those working in the area of logic-based knowledge representation.