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Nonmonotonic Reasoning with Defeasible Rules on Feasible and Infeasible Worlds

其他書名	Exploring a Landscape of Inductive Inference Operators
出版	IOS Press, Incorporated, 2024-08-08
主題	Computers / Artificial Intelligence / General
ISBN	16436852959781643685298
URL	http://books.google.com.hk/books?id=go_q0AEACAAJ&hl=&source=gbs_api

註釋It is often necessary for an intelligent agent in a complex environment to draw conclusions from incomplete and uncertain information. One established way to represent uncertain beliefs is by means of conditionals (B|A) formalizing defeasible rules of the form "if A then usually B". Semantic structures for conditional beliefs are often built upon propositional interpretations known as possible worlds. To formalize the process of inference, the notion of inductive inference operators by Kern-Isberner, Beierle, and Brewka is used. This maps a set of given conditionals (called a belief base) to an inference relation containing all the inferences an agent can draw from the set. Investigating how an agent should draw inferences from defeasible rules is part of the research field of nonmonotonic reasoning, a sub-field of knowledge representation, reasoning and artificial intelligence. Various definitions of consistency have been used in the literature, and in this book, two notions of consistency called weak and strong consistency are contrasted. One of the main topics covered here is inductive inference from weakly consistent belief bases. It is observed that weakly consistent belief bases can require some worlds to be completely infeasible in the induced inference relations, while strongly consistent belief bases allow every world to be at least somewhat feasible. Among the postulates put forward for nonmonotonic inference, there are some that deal with syntax splitting, the idea being that if a belief base contains completely independent information on different topics, then inference operators should treat these parts independently. Previously introduced syntax-splitting postulates assumed all belief bases to be strongly consistent. Here, extended versions of these syntax-splitting postulates are introduced that also cover inference from weakly consistent belief bases. This book also investigates the properties of the recently defined inductive inference operator system W. This is evaluated with regard to different postulates for inference relations, and it is demonstrated that system W fully complies with syntax splitting and even with the more general conditional syntax splitting. The inductive inference operators system W and c-inference were initially defined only for strongly consistent belief bases. Inference is extended to both operators to cover weakly consistent belief bases and thus to handle inference with infeasible worlds. Extended versions of system W and c-inference are evaluated with respect to their properties, and in particular to demonstrate that extended system W and extended c-inference still comply with syntax splitting. Relationships among inductive inference operators are also investigated, and operations proposed that generate inductive inference operators from given inference operators, using them to introduce approximations of system W. The relationships between inductive inference operators like (extended) c-inference, (extended) system Z, (extended) system W, approximations of system W, and lexicographic inference are investigated, leading to a landscape of inductive inference operators and their interrelationships. Characterizations of inductive inference operators are also given that extend rational closure in terms of properties on their underlying semantic structures --