Semantics of Belief Change Operators for Intelligent Agents: Iteration, Postulates, and Realizability
One of the core problems in artificial intelligence is the modelling of human reasoning and intelligent behaviour. The representation of knowledge, and reasoning about it, are of crucial importance in achieving this.
This book, Semantics of Belief Change Operators for Intelligent Agents: Iteration, Postulates, and Realizability, addresses a number of significant research questions in belief change theory from a semantic point of view; in particular, the connection between different types of belief changes and plausibility relations over possible worlds is investigated. This connection is characterized for revision over general classical logics, showing which relations are capturing AGM revision. In addition, those classical logics for which the correspondence between AGM revision and total preorders holds are precisely characterized. AGM revision in the Darwiche-Pearl framework for belief change over arbitrary sets of epistemic states is considered, demonstrating, especially, that for some sets of epistemic states, no AGM revision operator exists. A characterization of those sets of epistemic states for which AGM revision operators exist is presented. The expressive class of dynamic limited revision operators is introduced to provide revision operators for more sets of epistemic states. Specifications for the acceptance behaviour of various belief-change operators are examined, and those realizable by dynamic-limited revision operators are described. The iteration of AGM contraction in the Darwiche-Pearl framework is explored in detail, several known and novel iteration postulates for contraction are identified, and the relationships among these various postulates are determined.
With a convincing presentation of ideas, the book refines and advances existing proposals of belief change, develops novel concepts and approaches, rigorously defines the concepts introduced, and formally proves all technical claims, propositions and theorems, significantly advancing the state-of-the-art in this field.