We show in this paper that the AGM postulates are too week to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. Keywords: Iterated revision, AGM postulates, conditional beliefs, probabilistic conditioning, epistemic states, ...

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We propose a general framework in which to study belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes ' if he knows that ' is true in all the worlds he considers most plausible. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin [HF89] for modeling knowledge in multi-agent systems. We show that our framework is quite expressive and lets us model in a natural way a number of different scenarios for belief change. For example, we show how we can capture an analogue to prior probabilities, which can be updated by "conditioning". In a related ...

We study the problem of combining updates ---a special instance of theory change--- and counterfactual conditionals in propositional knowledgebases. Intuitively, an update means that the world described by the knowledgebase has changed. This is opposed to revisions ---another instance of theory change--- where our knowledge about a static world changes. A counterfactual implication is a statement of the form `If A were the case, then B would also be the case', where the negation of A may be derivable from our current knowledge. We present a decidable logic, called VCU 2 , that has both update and counterfactual implication as connectives in the object language. Our update operator is a generalization of operators previously proposed and studied in the literature. We show that our operator satisfies certain postulates set forth for any reasonable update. The logic VCU 2 is an extension of D. K. Lewis' logic VCU for counterfactual conditionals. The semantics of VCU 2 is that of a m...

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a “virtual” manner, using uniterated revision.

This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI-99, and is intended to supplement the lecture with technical details and pointers to more elaborate discussions in the literature. The ruling conception will be to treat causation as a computational schema devised to identify the invariant relationships in the environment, so as to facilitate reliable prediction of the effect of actions. This conception, as well as several of its satellite principles and tools, has been guiding paradigm for several research communities in AI, most notably those connected with causal discovery, troubleshooting, planning under uncertainty and modeling the behavior of physical systems. My hopes are to encourage a broader and more effective usage of causal modeling by explicating these common principles in simple and familiar mathematical form. Af...

Belief revision and belief update have been proposed as two types of belief change serving different purposes, revision intended to capture changes in belief state reflecting new information about a static world, and update intended to capture changes of belief in response to a changing world. We argue that routine belief change involves elements of both and present a model of generalized update that allows updates in response to external changes to inform an agent about its prior beliefs. This model of update combines aspects of revision and update, providing a more realistic characterization of belief change. We show that, under certain assumptions, the original update postulates are satisfied. We also demonstrate that plain revision and plain update are special cases of our model. We also draw parallels to models of stochastic dynamical systems, and use this to develop a model that deals with iterated update and noisy observations in (qualitative settings) that is analogous to Bayesian updating in a quantitative setting. Some parts of this report appeared in preliminary form in “Generalized Update: Belief Change in Dynamic Settings,” Proc. of Fourteenth International Joint Conf. on Artificial Intelligence (IJCAI-95), Montreal, pp.1550–1556 (1995).

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper [Friedman and Halpern 1997a], we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update [Katsuno and Mendelzon 1991a] depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revi...

Research in belief revision has been dominated by work that lies firmly within the classic AGM paradigm, characterized by a well-known set of postulates governing the behavior of “rational” revision functions. A postulate that is rarely criticized is the success postulate: the result of revising by an observed proposition'results in belief in'. This postulate, however, is often undesirable in settings where an agent’s observations may be imprecise or noisy. We propose a semantics that captures a new ontology for studying revision functions, which can handle noisy observations in a natural way while retaining the classical AGM model as a special case. We present a characterization theorem for our semantics, and describe a number of natural specialcases that allow ease of specification and reasoning with revision functions. In particular, by making the Markov assumption, we can easily specify and reason about revision.

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