Belief revision and belief update have been proposed as two types of belief change serving different purposes. Belief revision is intended to capture changes of an agent’s belief state reflecting new information about a static world. Belief update is intended to capture changes of belief in response to a changing world. We argue that both belief revision and belief update are too restrictive; routine belief change involves elements of both. We present a model for generalized update that allows updates in response to external changes to inform the 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, in a way that formally verifies the intuition that revision is suitable for “static ” belief change. 1

As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing explanations. We examine two representative approaches to explanation in the literature--- one due to G ardenfors and one due to Pearl---and show that both suffer from significant problems. We propose an approach to defining a notion of "better explanation" that combines some of the features of both together with more recent work by Pearl and others on causality. 1 INTRODUCTION Probabilistic inference is often hard for humans to understand. Even a simple inference in a small domain may seem counterintuitive and surprising; the situation only gets worse for large and complex domains. Thus, a system doing probabilistic inference must be able to explain its findings and recommendations to evoke confidence on the part of the user. Indeed, in experiments wi...

Model checking is a fruitful application of computational logic with high relevance to the verification of concurrent systems. While model checking is capable of automatically testing that a concurrent system satisfies its formal specification, it can not precisely locate an error and suggest a repair, i.e., a suitable correction, to the system. In this paper, we tackle this problem by using principles from AI. In particular, we introduce the abstract concept of a system repair problem, and exemplify this concept on repair of concurrent programs and protocols. For the development of our framework, we formally extend the concept of counterexample, which has been proposed in model checking previously, and provide examples which demonstrate the need for such an extension. Moreover, we investigate into optimization issues for the problem of finding a repair, and present techniques which gain in some cases a considerable reduction of the search space for a repair.

This paper presents an operative measure of reinforcement for constructive learning methods, i.e., eager learning methods using highly expressible (or universal) representation languages. These evaluation tools allow a further insight in the study of the growth of knowledge, theory revision and abduction. The final approach is based on an apportionment of credit wrt. the ‘course ’ that the evidence makes through the learnt theory. Our measure of reinforcement is shown to be justified by cross-validation and by the connection with other successful evaluation criteria, like the MDL principle. Finally, the relation with the classical view of reinforcement is studied, where the actions of an intelligent system can be rewarded or penalised, and we discuss whether this should affect our distribution of reinforcement. The most important result of this paper is that the way we distribute reinforcement into knowledge results in a rated ontology, instead of a single prior distribution. Therefore, this detailed information can be exploited for guiding the space search of inductive learning algorithms. Likewise, knowledge revision may be done to the part of the theory which is not justified by the

Abduction is a topic that attracts much interest in AI and automated reasoning research. Different approaches have been devised, that give a formalized account of explanatory reasoning, propose methods to compute explanations, frame abduction in the context of logic programming. However, the logical nature of abduction is still far from being clear and different specifications of the key underlying concepts have been given, that make it difficult to speak of abduction as a single welldefined form of reasoning. This work is a preliminary discussion on the logical nature of abductive reasoning, emphasizing the fundamental difference between abductive and deductive inference. Some logical properties of the inference to the "best explanation" are put forward and analyzed when the underlying logic is any extension of classical propositional logic (first order logic, modal logic) or a non monotonic system. Keywords: abduction, explanation, preference, nonmonotonic logic 1 Introduction Abdu...

The Katsuno and Mendelzon (KM) theory of belief update has been proposed as a reasonable model for revising beliefs about a changing world. However, the semantics of update relies on information which is not readily available. We describe an alternative semantical view of update in which observations are incorporated into a belief set by: a) explaining the observation in terms of a set of plausible events that might have caused that observation; and b) predicting further consequences of those explanations. We also allow the possibility of conditional explanations. We show that this picture naturally induces an update operator conforming to the KM postulates under certain assumptions. However, we argue that these assumptions are not always reasonable, and they restrict our ability to integrate update with other forms of revision when reasoning about action.

Abduction is an inference mechanism where given a knowledge base and some observations, the reasoner tries to find hypotheses which together with the knowledge base explain the observations. A reasoning based on such an inference mechanism is referred to as abductive reasoning. Given a theory and some observations, by filtering the theory with the observations, we mean selecting only those models of the theory that entail the observations. Entailment with respect to these selected models is referred to as filter entailment. In this paper we give necessary and sufficient conditions when abductive reasoning with respect to a theory and some observations is equivalent to the corresponding filter entailment. We then give sufficiency conditions for particular knowledge representation formalisms that guarantee that abductive reasoning can indeed be done through filtering and present examples from the knowledge representation literature where abductive reasoning is done through filtering. We...

This paper describes a change theory based on abductive reasoning. We take the AGM postulates for revisions, expansions and contractions, and Katsuno and Mendelzon postulates for updates and incorporate abduction into them. A key feature of the theory is that presents a unified view of standard change operators and abductive change operators rather than a new and independent change theory for abductive changes. Abductive operators reduce to standard change operators in the limiting cases. 1 Introduction Many actions taken by rational agents can be explained based on a cause--effect reasoning of the agent. There are actions that are taken to produce an effect. For example, we will put money in a parking-meter to avoid paying a fine to the city. Feeding the meter causes not getting a parking ticket as an effect. There are also actions that occur after an explanation or cause is derived from an observation or effect. The process of finding explanations from observations is usually referr...

Abstract: This paper presents a theoretical and general differentiation among descriptional induction, explanatory induction and abduction. Descriptional induction is based on the idea of compression (justified by mean- or cross-validation). Explanatory induction is characterised by a 'balanced ' compression (exception-free validation). Finally, abduction is the more elusive notion, where the validation comes from a background theory. Since this background theory can also be used in both kinds of induction, we must distinguish between an auxiliary use and a necessary or ‘consilient ’ use of the background knowledge. We introduce many new concepts and formalisations for this goal, mainly the idea of ‘intrinsic exception or anomaly’, consilience and an operative measure of reinforcement for logic programs. Finally, the difference between induction and abduction is seen in the context of growth of knowledge and theory revision.

This paper describes a symbolic representation of the data provided by the stereo-vision system of a mobile robot. The representation proposed is constructed from qualitative descriptions of transitions in the depth information given by the stereograms. The goal of this paper is to investigate the consequences in the depth transitions of qualitative spatial events such as the relative motion between objects, spatial occlusion and object's deformation (expansion and contraction). This causal relationship between spatial events and depth transitions forms a background theory for an abductive process of sensor data assimilation.