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Ebook: Semantics of Belief Change Operators for Intelligent Agents: Iteration, Postulates, and Realizability
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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.
In Artificial Intelligence, a core problem is the modelling of human reasoning and intelligent behaviour, and the representation of knowledge and reasoning about it are of fundamental importance for this. In particular, the agent paradigma makes this observation evident. An intelligent agent must be able to built up a complete epistemic state from her knowledge and beliefs in order to reason plausibly, to draw inferences, and for planning her actions. Normally, an autonomous intelligent agent does not live in a static, but in a changing and dynamically evolving environment. Such an agent must adapt her beliefs and epistemic state to new information she receives. The theory of belief change deals with these kinds of changes, and Kai Sauerwald’s dissertation addresses several important and significant research questions in belief change theory.
A fundamental result of revision theory is that plausibility orderings, given by total preorders over possible worlds, characterize belief revision. Kai Sauerwald analyzes this connection for general classical logics and characterizes precisely those conditions in which the relationship between total preorders and belief revision still holds. Moreover, he investigates a relaxation of the principle of minimal change for non-prioritized revision, yielding revision operators in complex epistemic settings where classical revision theory provides no operators. For iterated belief changes, Kai Sauerwald analyzes a whole landscape of different iteration principles for contraction. For each principle, he identifies characterizations from the viewpoint of changing plain beliefs, from the viewpoint of changing conditional beliefs, and from the viewpoint of changing plausibility orderings.
Throughout the whole thesis, Kai Sauerwald convincingly presents his ideas, refines and advances existing proposals of belief change, developes novel concepts and approaches, rigorously defines the introduced concepts, and formally proves all technical claims, propositions, and theorems. Given the numerous remarkable results to belief change theory, with his thesis, Kai Sauerwald significantly advances the state of the art in this field.
Hagen, August 2022
Christoph Beierle