The AGM model is the most remarkable framework for modeling belief revision. However, it is not perfect in all aspects. Paraconsistent belief revision, multi-agent belief revision and non-prioritized belief revision are three different extensions to AGM to address three important criticisms applied to it. In this article, we propose a framework based on AGM that takes a position in each of these categories. Also, we discuss some features of our framework and study the satisfiability of AGM postulates in this new context.
Federal University of Bahia(巴伊亚联邦大学);Pontifical Catholic University of Rio Grande do Sul(南里奥格兰德天主教大学);Federal University of Rio Grande do Sul(南里奥格兰德联邦大学)
AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich and expressive semantic frameworks. While the connections of AGM-like operations and their encoding in dynamic doxastic logics have been studied before by the work of Segerberg, most works on the area of Dynamic Epistemic Logics (DEL) have not, to our knowledge, attempted to use those logics as tools to investigate mathematical properties of belief change o…
Iterated Belief Change is the research area that investigates principles for the dynamics of beliefs over (possibly unlimited) many subsequent belief changes. In this paper, we demonstrate how iterated belief change is connected to computation. In particular, we show that iterative belief revision is Turing complete, even under the condition that broadly accepted principles like the Darwiche-Pearl postulates for iterated revision hold.
An Abstract Worlds Semantic Framework for Belief Change Operators
Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires(布宜诺斯艾利斯大学计算机系);Instituto de Investigación en Ciencias de la Computación UBA-CONICET(UBA-CONICET计算科学研究所);Artificial Intelligence Research Institute (IIIA-CSIC)(人工智能研究 institute (IIIA-CSIC))
On Lockean beliefs that are deductively closed and minimal change
Artificial Intelligence Research Institute (IIIA - CSIC)(人工智能研究 institutes(IIIA - CSIC));Centre de Recherche en Informatique de Lens (CRIL)(信息学研究中心(CRIL));Department of Mathematics, University of Barcelona (UB)(数学系,巴塞罗那大学(UB))
Consider the following belief change/merging scenario. A group of information sources gives a sequence of reports about the state of the world at various instances (e.g. different points in time). The true states at these instances are unknown to us. The sources have varying levels of expertise, also unknown to us, and may be knowledgeable on some topics but not others. This may cause sources to report false statements in areas they lack expertise. What should we believe on the basis of these reports? We provide a framework in which to explore this problem, based on an extension of proposition…
FernUniversität in Hagen(哈根远程大学);TU Dortmund University(多特蒙德工业大学)
The research on non-prioritized revision studies revision operators which do not accept all new beliefs. In this paper, we contribute to this line of research by introducing the concept of dynamic-limited revision, which are revisions expressible by a total preorder over a limited set of worlds. For a belief change operator, we consider the scope, which consists of those beliefs which yield success of revision. We show that for each set satisfying single sentence closure and disjunction completeness there exists a dynamic-limited revision having the union of this set with the beliefs set as sc…
How Do People Revise Inconsistent Beliefs? Examining Belief Revision in Humans with User Studies
Washington University in St. Louis(华盛顿大学圣路易斯分校);Imperial College London(伦敦帝国学院);Artificial Intelligence Research Institute (IIIA-CSIC)(人工智能研究所(IIIA-CSIC))
TU Dresden(德累斯顿工业大学);FernUniversität in Hagen(哈根远程大学)
The AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. We generalize the approach of Katsuno and Mendelzon (KM) for characterizing AGM base revision from propositional logic to the setting of (multiple) base revision in arbitrary monotonic logics. Our core result is a representation theorem using the assignment of total - yet not transitive - "preference" relations to belief bases. We also provide a characterization of all logics for which our result can be strengthened to preorder assignments (as in KM's original wo…
Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision, the second a contraction and the third a refinement of the previous beliefs. The ten operators considered in this article are shown to be all reducible to three: lexicographic revision, refineme…
Descriptor revision by Hansson is a framework for addressing the problem of belief change. In descriptor revision, different kinds of change processes are dealt with in a joint framework. Individual change requirements are qualified by specific success conditions expressed by a belief descriptor, and belief descriptors can be combined by logical connectives. This is in contrast to the currently dominating AGM paradigm shaped by Alchourrón, Gärdenfors, and Makinson, where different kinds of changes, like a revision or a contraction, are dealt with separately. In this article, we investigate the…