arXiv:2409.07119v1 Announce Type: new
Abstract: We consider credibility-limited revision in the framework of belief change for epistemic spaces, permitting inconsistent belief sets and inconsistent beliefs. In this unrestricted setting, the class of credibility-limited revision operators does not include any AGM revision operators. We extend the class of credibility-limited revision operators in a way that all AGM revision operators are included while keeping the original spirit of credibility-limited revision. Extended credibility-limited revision operators are defined axiomatically. A semantic characterization of extended credibility-limited revision operators that employ total preorders on possible worlds is presented.
Analysis of Credibility-Limited Revision in Belief Change
In the field of belief change, credibility-limited revision is an important concept that deals with revising beliefs in the presence of inconsistencies, both in belief sets and individual beliefs. This article explores the multi-disciplinary nature of credibility-limited revision and discusses its relationship with AGM revision operators.
Credibility-limited revision allows for the relaxation of traditional assumptions within belief change frameworks, where consistency of beliefs is typically a fundamental requirement. By permitting inconsistent belief sets and beliefs, credibility-limited revision acknowledges the complexities and nuances of real-world reasoning processes.
Implications for AGM Revision Operators
The article highlights that, in the unrestricted setting of credibility-limited revision, no AGM revision operators are included in the class of credibility-limited revision operators. AGM revision operators are a well-established framework in belief change and have been extensively studied and applied in various domains.
However, the authors of this article propose an extension to the class of credibility-limited revision operators to include all AGM revision operators while still maintaining the essence and principles of credibility-limited revision. This extension showcases the interplay and synergy between different concepts within belief change, creating opportunities for cross-pollination of ideas and methodologies.
The extension of credibility-limited revision operators is defined axiomatically, providing a formal framework for reasoning about belief change in the presence of inconsistencies. This adds a layer of structure and rigor to the concept, facilitating its application in practical scenarios.
Semantic Characterization through Total Preorders
A key aspect of this article is the presentation of a semantic characterization of extended credibility-limited revision operators using total preorders on possible worlds. This approach connects the formal models of belief change with the rich semantics of possible worlds, offering a bridge between symbolic reasoning and philosophical interpretations.
By employing total preorders, the authors demonstrate how the concepts of credibility-limited revision can be grounded in a well-defined mathematical framework. This not only adds clarity and precision to the discourse but also enables further exploration and refinement of these ideas using tools and techniques from various disciplines.
Conclusion
The study of credibility-limited revision in the context of belief change showcases the multi-disciplinary nature of this field. By incorporating insights from philosophy, formal logic, and computational modeling, this article expands the boundaries of belief change theory and opens up new avenues for research and application.
The proposed extension of credibility-limited revision operators, which includes all AGM revision operators, and the semantic characterization using total preorders provide valuable contributions to the existing body of literature. They enhance our understanding of belief change processes and offer practical tools for handling inconsistencies in real-world reasoning scenarios.
Overall, this article serves as a thought-provoking exploration of credibility-limited revision and its relationship with AGM revision operators, emphasizing the importance of multi-disciplinary approaches in advancing the field of belief change.