Scientific Discovery on Positive Data via Belief Revision

A model of inductive inquiry is defined within a first-order context. Intuitively, the model pictures inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure (the real world) from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revision allows scientists to solve a wide class of problems.     

Conditional Probability and Defeasible Inference

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. The research of both authors was supported in part by a grant from NSF, and, for Parikh, also by support from the research foundation of CUNY.     

学前儿童对事实、信念、愿望和情绪间关系的认知

76名3至5岁儿童接受了区分事实和信念、根据信念推测他人愿望、根据愿望推测他人情绪等实验任务,通过考查学前儿童对事实、信念、愿望和情绪间关系的认知,探察学前儿童心理理论发展的特点。结果显示3岁儿童在区分信念和事实时,出现错报事实或错报信念两种错误,而不单纯是现实主义偏向错误;在推测他人愿望时,部分3岁和4岁儿童虽然能够正确报告他人的信念却不能正确推测他人愿望,愿望认知发展有其复杂性的一面。学前儿童主要依据愿望推测他人情绪,儿童对信念和愿望的认知水平制约儿童对他人情绪的理解。     

Blame and Responsibility

This paper looks at judgments of guilt in the face of alleged wrong-doing, be it in public or in private discourse. Its concern is not the truth of such judgments, although the complexity and contestability of such claims will be stressed. The topic, instead, is what sort of activities we are engaged in, when we make our judgments on others' conduct. To examine judging as an activity it focuses on a series of problems that can occur when we blame others. On analysis, we see that these problems take the form of performative contradictions, so that the ostensible purposes of assigning guilt to others are undermined.There is clear evidence from social psychology that blame is especially frequently and inappropriately attributed to individuals in modern Western societies. On the other hand, it has often been observed how suspicious we are about the activity of judging – thus a widespread perception that a refusal to judge is somehow virtuous. My suggestion is that the sheer difficulty of attributions of responsibility, in the face of a complex and often arbitrary moral reality, frequently defeats us. This leads to a characteristic set of distortions when we blame, so that it is no surprise that we have become suspicious of all blaming activities.Yet, the paper argues, these problems need not arise when we hold others responsible. This paper therefore investigates what, exactly, can be questionable about attempts to assign guilt, and the structural logic that lies behind these problems – what will be called, adapting a term from social psychology, a belief in a just world. Such a belief takes for granted what needs to be worked for through human activity, and therefore tends to be counter-productive in dealing with misdeeds and adverse outcomes.     

外表真实区别、表征变化和错误信念的任务分析

自20世纪80年代以来,“心理理论”已成为发展心理学的研究热点和最活跃、最多产的领域。为了分析和比较“心理理论”的实验任务,该研究以济南市3所幼儿园中的233名3—6岁儿童为有效被试。进行了“意外转移。和“欺骗外表”两种心理理论实验任务。得出如下主要结论：(1)意外转移任务中内隐错误信念显著难于标准错误信念,易化错误信念与标准错误信念的难度不存在显著差异。(2)欺骗外表任务中外表真实区别难度显著低于表征变化和错误信念。(3)意外转移任务的错误信念显著难于欺骗外表任务的错误信念。     

Selective Revision

We introduce a constructive model of selective belief revision in which it is possible to accept only a part of the input information. A selective revision operator ο is defined by the equality K ο α = K * f(α), where * is an AGM revision operator and f a function, typically with the property ⊢ α → f(α). Axiomatic characterizations are provided for three variants of selective revision. This revised version was published online in June 2006 with corrections to the Cover Date.     

Why we Believe

The radical probabilist counsels the prudent never to put away uncertainty, and hence always to balance judgment with probabilities of various sizes. Against this counsel I shall advise in favor of the practice of full belief — at least for some occasions. This advice rests on the fact that it is sometimes in a person's interests to accept certain propositions as a means of bringing it about that others recognize oneself as having accepted those propositions. With the pragmatists, therefore, I shall reject the view that belief formation must in every instance be a truth-directed affair. Unlike the pragmatists, however, I shall conclude that the enterprise of belief formation is not directed exclusively, or even primarily, at attaining knowledge. In other words, pursuit of that which it profits to believe, on the one hand, and pursuit of knowledge on the other, are distinct enterprises, which overlap (when they do) only accidentally. This revised version was published online in August 2006 with corrections to the Cover Date.     

Foundational belief change

This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann'sminimal base contraction operation, even under quite strong restrictions, fails to satisfy the supplementary postulates of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be described as involving a modification of safe (base) contraction so as to make it maxichoice.     

Test theory without true scores?

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. This shows how an underlying order is defined, and was used to provide the basis for a tailored testing procedure. It also was used to define a number of measures of test consistency. Test items provide person dominance relations, and the relations provided by one item can be in one of three relations with a second one: redundant, contradictory, or unique. Summary statistics concerning the number of relations of each kind are easy to get and provide useful information about the test, information which is related to but different from the usual statistics. These concepts can be extended to form the basis of a test theory which is based on ordinal statistics and frequency counts and which invokes the concept of true scores only in a limited sense.1979 Psychometric Society presidential address.I want to recognize the contributions which others have made to whatever I have accomplished. First to mention here are my teachers: principally Harold Gulliksen, Ledyard Tucker, and the late Edith Jay. Second, I would like to recognize the importance of my graduate students. Tom Reynolds has been especially important in developing the ideas that I will talk about here today, but at various times, the others have made major contributions in this and other topics. I would like to express also a debt to my family, primarily my wife, Rosemary, who herself has a longterm interest in the psychometric area. Finally, I must acknowledge the financial support of the NIMH some time ago, the Office of Naval Research, until about a year ago, and of the James McKeen Cattell Fund this past year.