this paper, we argue that no such set of postulates will be adequate for every application. In particular, we make a fundamental distinction between two kinds of modifications to a knowledge base. The first one, update, consists of bringing the knowledge base up to date when the world described by it changes. For example, most database updates are of this variety, e.g. "increase Joe's salary by 5%". Another example is the incorporation into the knowledge base of changes caused in the world by the actions of a robot (Ginsberg and Smith 1987, Winslett 1988, Winslett 1990) . We show that the AGM postulates must be drastically modified to describe update. The second type of modification, revision, is used when we are obtaining new information about a static world. For example, we may be trying to diagnose a faulty circuit and want to incorporate into the knowledge base the results of successive tests, where newer results may contradict old ones. We claim the AGM postulates describe only revision.

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, ...

This work proposes an axiomatic characterization of merging operators. It underlines the differences between arbitration operators and majority operators. A representation theorem is stated showing that each merging operator corresponds to a family of partial preorders on interpretations. Examples of operators are given. They show the consistency of the axiomatic characterization. A new merging operator 4GMax is provided. It is proved that it is actually an arbitration operator. 1 Introduction In a growing number of applications, we face conflicting information coming from several sources. The problem is to reach a coherent piece of information from these contradicting ones. A lot of different merging methods have already been given [BI84, LMa, BKM91, BKMS92, Sub94]. Instead of giving one particular merging method we propose, in this paper, a characterization of such methods following the rationality of the postulates they satisfy. We shall call merging operators those meth...

We consider the problem of merging several belief bases in the presence of integrity constraints.

: Revision and update operators add new information to some old information represented by a logical theory. Katsuno and Mendelzon show that both revision and update operators can be characterized as accomplishing a minimal change in the old information to accommodate the new information. Arbitration operators add two or more weighted informations together where the weights indicate the relative importance of the informations rather than a strict priority. This paper shows that arbitration operators can be also characterized as accomplishing a minimal change. The operator of model-fitting is also defined and analyzed in the paper. 1 Introduction Arbitration is the process of settling a conflict between two or more persons. Arbitration occurs in many situations. For example, settling a labor dispute by an outsider, reaching a verdict in a trial, evaluating several alternative research hypotheses, negotiating an international peace agreement, or setting the price of a product in a compe...

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: Katsuno and Mendelzon divide theory change, the problem of adding new information to a logical theory, into two types: revision and update. We propose a third type of theory change: arbitration. The key idea is the following: the new information is considered neither better nor worse than the old information represented by the logical theory. The new information is simply one voice against a set of others already incorporated into the logical theory. From this follows that arbitration should be commutative. First we define arbitration by a set of postulates and then describe a model-theoretic characterization of arbitration for the case of propositional logical theories. We also study weighted arbitration where different models of a theory can have different weights. 1 Introduction The problem of updating logical theories is a common fundamental concern to databases, to Artificial Intelligence [McC68, Rei92], and to belief revision [Mak85, Gar88]. It is well-known that giving semant...

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 investigate the semantic foundations of a method for modeling agents as entities with a mental state which was suggested by McCarthy and by Newell. Our goals are to formalize this modeling approach and its semantics, to understand the theoretical and practical issues that it raises, and to address some of them. In particular, this requires specifying the model's parameters and how these parameters are to be assigned (i.e., their grounding). We propose a basic model in which the agent is viewed as a qualitative decision maker with beliefs, preferences, and decision strategy; and we show how these components would determine the agent's behavior. We ground this model in the agent's interaction with the world, namely, in its actions. This is done by viewing model construction as a constraint satisfaction problem in which we search for a model consistent with the agent's behavior and with our general background knowledge. In addition, we investigate the conditions under which a mental st...