Peter Gärdenfors

Knowledge in flux : modeling the dynamics of epistemic states

Knowledge in Flux presents a theory of rational changes of belief, focusing particularly on revisions that occur when the agent receives new information that is inconsistent with the present epistemic state.

Nonmonotonic inference based on expectations

Abstract We show how nonmonotonic inferences may elegantly be interpreted in terms of underlying expectations . The fundamental idea is that when we reason, we make use of not only the information that we firmly believe, but also expectations that guide our beliefs without quite being part of them. We propose two ways of modelling the expectations used in nonmonotonic reasoning: by expectation sets, equipped with selection functions, and by expectation relations. For each of these we prove representation theorems and establish relations with several other modellings in the area, including Poole systems and preferential models. We also show that by using the notion of expectation, one can unify the treatment of the theory of belief revision and that of nonmonotonic inference relations. This is accomplished by viewing the relation of “epistemic entrenchment” used in Gardenfors [18] and Gardenfors and Makinson [20] as a kind of expectation ordering. Thus we see belief revision and nonmonotonic reasoning as basically the same process, albeit used for two different purposes.

Relations between the logic of theory change and nonmonotonic logic

The purpose of this paper is to investigate the close relations between the logic of theory change (alias belief revision) on the one hand, and nonmonotonic logic on the other. The connection is most manifest at the level of general conditions on nonmonotonic inference operations, compared to those on theory revision operations. It also appears between some of the specific constructions that have been used in the literature to generate such operations.

Knowledge, belief, and strategic interaction: The dynamics of belief systems: Foundations versus coherence theories

1. The PROBLEM OF belief revision In this article I want to discuss some philosophical problems one encounters when trying to model the dynamics of epistemic states. Apart from being of interest in themselves, I believe that solutions to these problems will be crucial for any attempt to use computers to handle changes of knowledge systems. Problems concerning knowledge represen tation and the updating of such representations have become the focus of much recent research in artificial intelligence (AI). Human beings perpetually change their states of knowledge and belief in response to various cognitive demands. There are several different kinds of belief changes. The most common type occurs when we learn some thing new — by perception or by accepting the information provided by other people. This kind of change will be called an expansion of a belief State. Sometimes we also have to revise our beliefs in the light of evidence that contradicts what we had earlier mistakenly accepted, a process which will here be called a revision of a belief state. And sometimes, for example when a measuring instrument is malfunctioning, we discover that the reasons for some of our beliefs are invalid and so we have to give up those

Conceptual spaces as a framework for knowledge representation

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a varietyof non-sy mbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent theylack a higher-level theoryof representation. In this paper, conceptual spaces are suggested as an appropriate framework for non-symbolic models. Conceptual spaces consist of a number of “qualitydimensions” that often are derived from perceptual mechanisms. It will be outlined how conceptual spaces can represent various kind of information and how theycan be used to describe concept learning. The connections to prototype theory will also be presented.

POSITIONALIST VOTING FUNCTIONS

Positionalist voting functions are those social choice functions where the positions of the alternatives in the voters preference orders crucially influence the social ordering of the alternatives. An important subclass consists of those voting functions where numbers are assigned to the alternatives in the preference orders and the social ordering is computed from these numbers. Such voting functions are called representable. Various well-known conditions for voting functions are introduced and it is investigated which representable voting functions satisfy these conditions. It is shown that no representable voting function satisfies the Condorcet criterion. This condition and Arrows independence condition, which are typical non-positionalist conditions, are shown to be incompatible. The Borda function, which is a well-known positionalist voting function, is studied extensively, conditions uniquely characterizing it are given and some modifications of the function are investigated.

Cognition, Education and Communication Technology

Contents: Preface. P. Johansson, P. Gardenfors, Introduction to Cognition, Education, and Communication Technology. D.L. Schwartz, T. Martin, N. Nasir, Designs for Knowledge Evolution: Towards a Prescriptive Theory for Integrating First- and Second-Hand Knowledge. L. Plowman, Getting the Story Straight: The Role of Narrative in Teaching and Learning With Interactive Media. L.B. Resnick, A. Lesgold, M.W. Hall, Technology and the New Culture of Learning: Tools for Education Professions. W.J. Clancey, Modeling the Perceptual Component of Conceptual Learning: A Coordination Perspective. D. Kirsh, Metacognition, Distributed Cognition, and Visual Design. M. Scaife, Y. Rogers, External Cognition, Innovative Technologies, and Effective Learning. J. Ivarsson, R. Saljo, Seeing Through the Screen: Human Reasoning and the Development of Representational Technologies. M.C. Linn, WISE Design for Lifelong Learning: Pivotal Cases. T. de Jong, J. Beishuizen, C. Hulshof, F. Prins, H. van Rijn, M. van Someren, M. Veenman, P. Wilhelm, Determinants of Discovery Learning in a Complex Simulation Learning Environment.

A representation theorem for voting with logical consequences

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrows impossibility theorem.

Belief revision and nonmonotonic logic: two sides of the same coin?

Belief revision and nonmonotonic logic are motivated by quite different ideas. The theory of belief revision deals with the dynamics of belief states, that is, it aims at modelling how an agent or a computer system updates its state of belief as a result of receiving new information. Of particular interest is the case where the new information is incompatible with the old state of belief. Nonmonotonic logic, on the other hand, is concerned with a systematic study of how we jump to conclusions from what we believe. By using default assumptions, generalizations etc. we tend to believe in things that do not follow from our knowledge by the classical rules of logic. A thorough understanding of this process is desirable since we want AI-systems to be able to perform the same kind of reasoning. Despite the differences in motivation for the theories of belief revision and nonmonotonic logic, I argue in this paper that the formal structures of the two theory areas, as they have developed, are surprisingly similar. My aim is to show that it is possible to translate concepts, models, and results from one area to the other. Establishing such a translation will hopefully lead to a cross-fertilization of the two research areas. The translation between belief revision and nonmonotonic logic was first given in Makinson and G~rdenfors (1990).

The emergence of meaning

According to the realistic approach to semantics the meaning of an expression is something out there in the world. In technical terms, a semantics for a language is seen as a mapping from the grammatical structures to things in the world (or in several possible worlds). Often meanings are defined in terms of truth conditions. A consequence of this approach is that the meaning of an expression is independent of how individual users understand it.