Contracting Intuitionistic Theories

I reformulate the AGM-account of contraction (which would yield an account also of revision). The reformulation involves using introduction and elimination rules for relational notions. Then I investigate the extent to which the two main methods of partial meet contraction and safe contraction can be employed for theories closed under intuitionistic consequence. I would like to thank the organisers, Heinrich Wansing, Sergei Odintsov and Yaroslav Shramko, of the Dresden Workshop on Constructive Negation, July 2–4, 2004, for providing the opportunity to present the ideas in this paper for the first time to a constructively critical audience. I am grateful to Sven Ove Hansson for useful comments on an earlier draft. A special note of thanks is owed also to Joongol Kim, who spotted a mistake in an earlier attempt of mine to prove a stronger form of Theorem 8.6. The results in this paper were presented to the Central Division Meeting of the American Philosophical Association in Chicago in April 2005.     

信念修正的AGM理论

信念修正问题是一个富有活力的,正在发展的研究主题。这个主题包括了一大批背景不同、形态各异的理论。阿尔罗若(C．E．Alchourron)、加德福斯(P．Gardenfors)和梅金森(D．Markinson)共同建立的信念修正理论(简称AGM理论)是其中形成比较早的、影响最大的理论。本文说明信念修正的基本概念,并且对AGM理论进行述评.     

Utility independence of multiattribute utility theory is equivalent to standard sequence invariance of conjoint measurement

Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain.     

冲突情境下幼儿的选择性信任和信念修正

幼儿如何选择性地采信他人提供的信息、获取知识, 是幼儿社会认知发展研究的重要问题。除客观的信息内容外, 信息传递者的特征也影响幼儿的选择性信任。另外, 在不确定情境下, 他人证言与幼儿已有信念可能存在冲突, 在二者冲突的情境下, 幼儿是否可以采信他人的证言, 并最终改变幼儿的已有判断是以往研究忽略的问题。本研究考察了当母亲证言与幼儿已有信念冲突时, 不同程度的冲突情境(面对不同比例的合成动物时)对幼儿选择性信任和信念修正的影响。研究采用冲突信息源范式, 向74名4~6岁幼儿呈现对不同比例合成动物(50%-50%任务 vs 75%-25%任务)命名的证言, 考察幼儿对信息提供者的询问意愿、对证言的信任情况和在证言前后对合成动物的判断(信念修正)。信息提供的一方为母亲(提供相似度低的动物名称), 另一方为陌生人(提供相似度高的动物名称)。结果发现, 幼儿的选择性信任和信念修正受到母亲证言与已有信念冲突程度的影响。在低冲突情境下, 幼儿对母亲证言的询问意愿和外显信任均高于高冲突情境。幼儿的信念修正存在年龄差异, 在低冲突情境下, 年长幼儿比年幼幼儿更倾向于改变已有信念, 在高冲突情境下, 年长的幼儿比年幼幼儿更不愿意改变已有信念。本研究结果表明, 当母亲的证言与幼儿已有信念冲突时, 中国幼儿可以区分不同程度的冲突情境, 并且可以根据冲突的程度进行选择性信任和信念修正。     

A Practical Approach to Revising Prioritized Knowledge Bases

This paper investigates simple syntactic methods for revising prioritized belief bases, that are semantically meaningful in the frameworks of possibility theory and of Spohn's ordinal conditional functions. Here, revising prioritized belief bases amounts to conditioning a distribution function on interpretations. The input information leading to the revision of a knowledge base can be sure or uncertain. Different types of scales for priorities are allowed: finite vs. infinite, numerical vs. ordinal. Syntactic revision is envisaged here as a process which transforms a prioritized belief bases into a new prioritized belief base, and thus allows a subsequent iteration.     

Reasons for sequence preferences

Much research shows that when it comes to preferences over sequences of money, such as a monthly paycheck, people do not always maximize present value. Rather, they often choose the lower‐valued of a pair of sequences, especially when it has attractive properties such as an increasing trend. To unearth the reasons for sequence preferences we conducted a verbal‐protocol analysis of choices between money sequences, including lifetime and one‐year earnings and one‐year lottery winnings, as well as lifetime health sequences. Participants thought aloud while choosing between visual representations of sequences. Their verbalizations contained reference to a wide range of previously hypothesized, as well as new, reasons for choice. These reasons were also correlated in sensible ways with the choices made. There was some evidence of solid economic reasoning (which we called maximization), although this was largely restricted to choices for one‐year earnings. More commonly, respondents did not distinguish between earnings and consumption, and thought about money as if they would automatically spend it at the rate it was received. This meant the most frequently given reason was what we called appropriateness—how well the money received at a given point matched the desired consumption at that point. Other common explanations include the expectedness of a sequence (we argue this is mediated by appropriateness), the way that parts of the sequence constitute reference points for other parts, and the ease with which incoming money can be managed (convenience). Copyright © 2002 John Wiley & Sons, Ltd.     

Recovery Recovered

The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more closely to the identification of the beliefs contracted away in each counterexample case. Since, on our view, speakers" belief contraction intentions are often more complicated than they may first appear, we are led to develop apparatus for thinking about the communication and identification of those intentions. Our argument refocuses attention on the difficult question of how to apply the AGM theory to particular cases.     

Representing,Running, and Revising Mental Models: A Computational Model

People use commonsense science knowledge to flexibly explain, predict, and manipulate the world around them, yet we lack computational models of how this commonsense science knowledge is represented, acquired, utilized, and revised. This is an important challenge for cognitive science: Building higher order computational models in this area will help characterize one of the hallmarks of human reasoning, and it will allow us to build more robust reasoning systems. This paper presents a novel assembled coherence (AC) theory of human conceptual change, whereby people revise beliefs and mental models by constructing and evaluating explanations using fragmentary, globally inconsistent knowledge. We implement AC theory with Timber , a computational model of conceptual change that revises its beliefs and generates human‐like explanations in commonsense science. Timber represents domain knowledge using predicate calculus and qualitative model fragments, and uses an abductive model formulation algorithm to construct competing explanations for phenomena. Timber then (a) scores competing explanations with respect to previously accepted beliefs, using a cost function based on simplicity and credibility, (b) identifies a low‐cost, preferred explanation and accepts its constituent beliefs, and then (c) greedily alters previous explanation preferences to reduce global cost and thereby revise beliefs. Consistency is a soft constraint in Timber ; it is biased to select explanations that share consistent beliefs, assumptions, and causal structure with its other, preferred explanations. In this paper, we use Timber to simulate the belief changes of students during clinical interviews about how the seasons change. We show that Timber produces and revises a sequence of explanations similar to those of the students, which supports the psychological plausibility of AC theory.     

Constraints for Input/Output Logics

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourrón/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step.