因果信念调整中反例信息的解释机制
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摘要
信念调整指的是一个理性主体将信念从一种状态转变为另一种状态的过程。具体地说,它是人们在发现新信息和原有信念系统不一致后,确定原有信念的哪一部分和新信息相冲突并对原有信念的某一部分作出调整和改变,以接受新的信息,适应新环境的过程(Elio,＆Pelletier,1997).
关于信念调整的机制,哲学和人工智能理论提出了两个基本原则：最小化改变原则和信念牢固性原则。前者强调,在遇到不一致信息时,人们会对原来的信念作出最小化,最保守的调整和修正,从而尽可能多地保留原来的信念(Gardenfors,1988；Harman,1986；James,1907).后者指出,信念在人的知识体系里,其牢固程度有所差异。当必须要放弃或改变一些信念的时候,人们会选择放弃那些最不重要的信息(Gardenfors,1992).以上两个原则的共同问题是,缺少明确的操作化定义,缺少一种合理的测量最小化改变和信念牢固性的手段,最重要的是缺少实证数据的支持。
心理模型理论是目前信念调整领域中第一个完整而系统的心理学理论。它强调,信念是通过心理模型的可能性的方式来表征的,这种表征方式决定了人们信念调整的过程(Johnson.Laird,& Byrne,2002；Johnson-Laird,Girotto,& Legrenzi,2004)。当人从不一致信念推理到一致信念的时候,要经过3个计算过程,每一个过程中,人们分别遵守相应的原则：首先人们会用模型一致性原则来检测不一致信息,然后是遵循不匹配原则作出修正哪一部分信念的决定,最后是产生解释以最终解决信念的冲突(Johnson-Laird,Girotto,& Legrenzi,2004).心理模型理论存在的问题是,它认为信念的表征和信念调整的过程是确定性的,非概率性的。它夸大了理性在信念调整中的作用,它采用二分思想,把人的信念调整看做是个或者否定大前提或者否定小前提的的过程,不符合人们实际的心理过程。此外,该理论还弱化了解释的作用。
解释机制假说是继心理模型理论之后,关于信念调整的第二个心理学解释。它认为,当遇到不一致信息之后,人们会主动建构解释,并将它作为一个新成分,引入原有因果结构,人们正是基于这种新的因果结构进行信念调整的(Walsh,& Sloman,2004,2008; Walsh, Johnson-Laird,2009).解释机制假说目前缺少对信念调整过程或阶段的研究,尤其缺少理论观点的系统构建。
基于以往关于信念调整的研究,本研究通过5个实验,围绕“一个中心两个基本点”——以信念调整的机制为中心,以解释对信念调整的决定性影响和解释建构的阶段为两个基本点,逐步探索因果信念表征的可能形式,因果信念调整的机制及其可能的过程和阶段,从而检验以往关于信念调整的理论,并在此基础上,发展信念调整的心理学理论模型。
为了初步探讨解释是否会对因果信念修正的过程产生作用,研究一在传统的信念调整的任务中操纵了因果结构和新信息的呈现顺序,对比和检验了心理模型理论和解释机制假说。实验一中被试的任务是,在知觉到不一致信息后选择修改大前提或者小前提。实验自变量为：因果结构,包括肯定的因果结构(cause:A发生了导致B发生)和否定的因果结构(prevent:A发生了阻止B发生)；分类前提和事实的呈现顺序,包括肯定前件式(先呈现分类前提再呈现事实,A-not B)和否定后件式(先呈现事实再呈现分类前提not B-A)。实验因变量为被试选择修改大前提的分数。实验一的结果与心理模型理论(Hasson,& Johnson-Laird,2003)预测不一致的是,因果结构和呈现顺序之间的交互作用差异不显著,被试在所有条件下都有修改大前提的强烈倾向,这种倾向在否定的因果结构(prevent)中比在肯定的因果结构中更为明显,肯定前件式和否定后件式这两种呈现顺序对被试修改大前提的倾向没有显著影响。实验结果初步支持基于因果模型理论的解释机制假说,而不支持心理模型理论。
为了进一步确定解释对信念调整过程的决定性影响,研究二直接操纵针对不同前提的反例的解释可获得性高低。本研究中被试的任务是,在检测到不一致信息后,需要选择修改大前提或者类别前提或者两者都修改或者两者都不修改,实验记录被试在每个选项中的分数。实验二和实验三分别采用熟悉和假设性的实验材料,自变量为针对不同前提反例的解释可获得性。在选择任务之后,被试还需要对题项中的冲突信息给出解释,实验者对被试给出的解释进行分类。实验结果发现,无论是熟悉的还是假设性的实验材料中,无论是在选择任务中还是在解释任务中,对前提反例的解释可获得性的操纵可以直接影响被试对原有信念的调整模式,提高针对某类前提的反例的解释可获得性可增强修改某类前提的倾向。此外,熟悉和假设性任务下反应模式的一致性说明了目前的信念牢固性原则对信念调整的解释力比较小。
前两个研究基本上可以从功能上证明,前提反例的解释可获得性决定人们信念调整的结果,要最终确定解释和信念调整反应之间的因果关系,时间上,解释的构建必须发生在信念调整决策之前。因此,研究三的目的是在新的实验范式基础上探索解释构建发生在信念调整中的哪一个阶段。以下两个实验分别研究了不同概率命题的信念调整任务中,人们建构解释可能发生的阶段。
实验四的自变量为：大前提的概率高低(那些包含了很少失效条件的命题为高概率命题,那些包含了很多失效条件的命题为低概率命题)和解释的时间(在大前提出现之前让被试对可能的反例进行解释或者在矛盾信息出现之后让被试对出现的反例进行解释)。实验因变量为：解释产生之前和之后对同一因果信念的概率判断值。实验结果发现,在高概率命题中,大前提之前要求被试对其可能的反例进行解释会降低之后对此前提的概率判断,而在低概率命题中,前提的概率判断因此受到的影响就会小很多。无论是在高概率的信念中还是低概率的信念中,无论是大前提之前给出反例解释还是之后给出解释,只要后面出现关于反例的新信息,被试都会降低针对原来大前提的概率判断。不过,高概率信念条件下的信念调整幅度显著高于低概率信念条件下的信念调整幅度。实验四的结果说明,原有信念概率的高低是影响信念调整的一个重要因素,进一步证实人们的信念表征更可能是概率性的。人们对低概率前提的表征中可能包含了反例的解释,对于高概率的信念,因为其反例的解释可获得性相对比较低,需要附加的任务才可以增加被试提取反例解释的主观努力。另外,人们对解释在信念调整中的作用的评估可能是一个动态过程。
实验五采用单因多果的因果结构(A发生导致B发生；A发生导致C发生),以一般性的规则信念为材料,要求被试在知道原因发生和一个结果发生或者没有发生后判断另一个结果发生的概率大小(P(C/A,B)(一致条件下)或者P(C/A,-B)(不一致条件下))。实验自变量为：新信息的一致性(和原有信念一致的或者不一致的信息)和解释提示问题的相关性(直接询问导致新信息一致性原因的问题为相关问题,否则为不相关问题)。实验因变量为：前后对结果的概率判断,对新信息的阅读时间(RT1)以及第二次判断概率的时间(RT2)。实验结果发现,在概率判断上,当之后出现的新信息是反例时,人们会降低原因所导致的各个结果的概率。当之后出现的新信息是正向例子时,人们会提高原因所导致的各个结果的概率。在反应时上,无论后面解释提示的问题是否是相关问题,人们阅读不一致信息的时间要长于一致信息的时间。在最后判断条件概率P(C/A,-B)或者P(C／A,B)时,不一致条件下,两种问题类型条件下判断反应时没有显著差异。致条件下,问题不相关条件下的判断反应时要长于问题相关条件下的判断反应时。实验五的结果说明,人们会在遇到不一致信息时,马上搜寻解释,而不会在遇到一致信息时,有意去解释原因导致结果的机制。但之后的信念调整任务,比如判断条件概率P(C/A,B)会迫使被试在遇到一致信息后进一步思考因果机制。
研究三发现了人们构建解释发生在信念表征阶段或者阅读矛盾信息时,即人们是在决定如何修改信念之前构建解释的。研究三在时间上确定了解释可获得性和信念调整反应之间的因果关系。
以上三个研究不能很好地支持以往关于信念调整的理论解释,本文因此提出了基于因果模型理论的解释机制假说：人们对因果信念的表征基于的是因果结构,而不是心理模型。对于因果信念,无论是最开始的信念表征还是遇到新信息后的信念调整过程,都更可能是概率性的,而非确定性的。人们很少会直接否定一个前提,而更多地是去修改或者调整前提的概率。从加工阶段上来看,在遇到新信息后,人们先评价不一致信息,然后构建解释,最后根据所产生的解释对原有信念的强度进行重新的调整。从加工机制上来看,解释的性质决定了人们信念调整的模式。对于低强度的信念,人们在表征大前提的时候可能就包含了反例和反例解释。对于高强度的信念,人们是在遇到矛盾信息之后构建解释的。
Belief revision is a process during which a rational agent change the belief state from inconsistency into consistency. Specifically, it is a process in which people first detect an inconsitency between new information and the original belief system, then decide which of the belief set to be revised after finding out a certain part of the belief conflicts with the new information, and eventually to accept the new information so that to adapt to the new enviroment.
Concerning the mechansim of the belief revision, two basic principles had been proposed in philosophy and artificial intelligence:minimal change principle and entrenchment account. The former pointed out, people would make the minimal or the most conservative change of the original belief after detecting an inconsistency so that to maintain as much of the original belief as they can (Gardenfors,1988; Harman, 1986; James,1907).The latter claimed that some beliefs might be more entrenched than others in people's minds and thus more resistant to being abandoned (Gardenfors,1992). Both of the two accounts have been criticized for being lack of a clear operational definition, a proper measurement of the minimal change and entrechment of the belief and above all, they are in shortage of enough supporting data.
Mental model theory has been so far the first psychological account of belief revision, which claimed that, people represent beliefs by constructing sets of mental models in which each model represents a possiblity. Belief revision is built on the representation of the beliefs (Johnson-Laird,& Byrne,2002; Johnson-Laird, Girotto, & Legrenzi,2004). The theory distinguished three main computations, in each of which one principle is supposed to be employed when people reason from inconsistency to consistency:first people must detect an inconsistency within a set of propositions by using the principle of modeling consistency; Second, people use the mismatch principle to decide which of the original belief to be revised. Third, people use the principle of causal knowledge to generate an explantion so that they can eventually resolve the inconsistency (Johnson-Laird, Girotto,& Legrenzi,2004).The problems of the theory lie in threefolds:it adopts an all-or-nothing manner in the representation of the belief as well as in the belief revision process; it overstates the role of rationality in belief revision, and in the meantime, it may underestimate the role of explanation in the process of belief revision.
The explanation hypothesis has been another psychological account of belief revision. It suggested people resolve an inconsistency by explaining its origin. Explanations would be introduced as a new element into the causal structure after an inconsistency arises and people revise their causal beliefs on the basis of the new structure (Walsh,& Sloman,2004,2008; Walsh, Johnson-Laird,2009). The hypothesis fails to investigate the process of the belief revision, neither does it systematically build its theoretical structure on sufficient data.
Based on the previous belief revision studies, this research focused on the mechanism of belief revision by answering two basic questions-how explanations determine belief revision response and when explanations are generated. Consisting of 5 experiments, the present research proceeded gradually to investigate the representation of beliefs, the computations people might have in the process of causal belief revision and the mechanism of causal belief revision. By testing the previous models of belief revision in our results, we intend to develop a psychological model of causal belief revision eventually.
To tentatively investigate whether the availability of explanation influences the belief revision, we manipulated the causal structure and the presentation order of the new information and the categorical premises in a classical belief revision task in which participants were asked to choose to revise either the main premise or the categorical premise after detecting an inconsistency. The two independent variables were causal structure and the order of the categorical premise and facts. The former included positive structure (A causes B) and negative structure (A prevents B) while the latter included Modus Ponens order (the categorical premise was presented before the facts, A-not B) and Modus Tollens order (the categorical premise was presented after the facts, not B-A). The dependent variables were the scores of choices on revising the major premise. The results showed that people had a strong tendency to revise the main premise, which was even more obvious in the prevent structure than in the cause one. Inconsistent with what the mental model theory (Hasson,& Johnson-Laird,2003) predicted, the MP and MT orders didn't have an effect on people's belief revsion, and in the meantime, there was no interaction between the two variables. All the results are in favor of explanation hypothesis instead of mental model theory.
To further investigate the decisive role of the availability of explanation in belief revision, we carried out two experiments to directly manipulate the availability of explanations in study two. Participants had to make one of the four choices after detecting an inconsistency:to revise the main premise, to revise the categorical premise, to revise both, to revise none of them. Scores for each choice were recorded. Hypothetical as well as familiar materials were employed in the two experiments. The independent variables were:the availability of the explanations (disablers) for different premises (three levels in experiment 2:explanations for the major premise, explanations for the minor premise and explanations for both; two levels in experiment 3:explanations for the major premise, explanations for the minor premise). Particpants had to give an explanation for the inconsistency after making the choice. The results showed that the manipuplation of the availability of the explanations for a certain premise had a direct effect on the belief revision results regardless of the nature of the materials and the type of the tasks, specifically, increasing the availability of disablers for a premise enhanced the tendence to revise the premise. Furthermore, the consistent response patterns in the hypothetical and familiar materials in the two experiments cast doubt over the entrenchment account.
The previous two studies functionally prove the availability of explanations determine the way people revise their beliefs. In a causal relation, the cause must occur before the effect. So we have to find out the temporal order of the generation of explanation and belief revision response to finally determine the causal relation between explanations and belief revision responses. In study 3, we intended to examine the stage when people give an explanation.
Two experiments were included. In experiment 4, the independent variables were: the strength of the major premises (Those included few disablers were recruited as high-plausible premises; those included many disablers were recruited as low-plausible premises) and the time to give an explanation (to explain before the presentation of the major premise; to explain after the presentation of the inconsistent new information). The dependent variables were:probability judgment of the major premise before and after generating an explanation:p1, p2. The results showed that, asking for explanation before the presentation of the major premise significantly lowered the probability judgment of the high-plausible premises but the same action only slightly brought down the probablity judgment of the low-plausible premises (pi). The inconsistent information given later generally brought down people's confidence of the major premise (p2) regardless of the strength of the major premises and the the time of generating an explanation. However, people lowered the probability more in the high-plausible premises than in the low-plausible premises.The findings in experiment 4 indicated that explanations might be included in the reprentation of the low-plausible premises while for the high-plausible premses, the availability of explanations is so much lower that people have to be forced to generate an explanation. Furthermore, it seems the process of evaluating the explanation is dynamic.
In experiment 5, we used high-plausible premises (mostly daily used rules) with a common cause structure (A causes B; A causes C). People were asked to judge the probability of an effect given the presence of the cause and the presence or absence of another effect (P(C/A,-B) or P(C/A,B)). The independent variables were:consistency of the new information (new information that was consistent with the original propositions; new information that was inconsistent with the original propositions) and relevance of the explanation questions (those questions that asked for an explanation concerning the consistency of the new information were labled as relevant questions, otherwise they were labled as irrelevant questions). The dependent variables were:probability judgment of one effect given the presence of the cause (P(C/A)); probability judgment of the effect given the presence of the cause and the absence (or the presence) of another effect (P(C/A,-B) or P(C/A,B)); Reaction time to read the new information (RT1); Reaction time to judge the probability of P(C/A,-B) or P(C/A, B) (RT2). The reults showed that, people reduced the probability judgment when the new information was negative and increased the probablity judgment when the new information was positive. As for the reaction time, people spent more time reading the negative information than reading the positive information no matter the following explanation question was relevant or not. There was no signifant difference of the time to judge P(C/A,-B) when the new information was inconsistent between the two types of explanatin questions. But it takes longer for people to judge P(C/A,B) when the following question was relevant than when it was irrelevant. The findings in experiment 5 indicated that people would search for an explanation when they are faced with inconsistent information but they won't consider the causal mechanism until they are asked to judge P(C/A,B) when they are faced with positive information.
In study 3, we found out that people either included disablers in the representation of the original beliefs or generated an explanation when they were reading the new information, thus we assume that explanations are usually generated before making a belief revision decision, eventually confirming the causal relation between the availability of explanations and the belief revision responses.
The three stuides above couldn't be accounted by the previous models, we thus proposed the explanation hypothesis on the basis of causal model theory:the representation as well as the causal belief revision process is based on a probabilistic manner instead of an all-or-nothing manner; People hardly reject a premise in the face of some inconsistent information, rather, they choose to doubt a premise. Three computations might be involved in belief revision after inconsistent information arises: people first detect an inconsistency, and then they generate an explanation; finally they reassign the probability of the major premise based on the explanations they have in their mind. The availability of explanation detemines how people revise their beliefs. For the low-plausbility beliefs, explanations might be included in the representation of the major premise while for the high-plausbility beliefs, explanation are generated after they are confronted with inconsisten information.
关于信念调整的机制,哲学和人工智能理论提出了两个基本原则：最小化改变原则和信念牢固性原则。前者强调,在遇到不一致信息时,人们会对原来的信念作出最小化,最保守的调整和修正,从而尽可能多地保留原来的信念(Gardenfors,1988；Harman,1986；James,1907).后者指出,信念在人的知识体系里,其牢固程度有所差异。当必须要放弃或改变一些信念的时候,人们会选择放弃那些最不重要的信息(Gardenfors,1992).以上两个原则的共同问题是,缺少明确的操作化定义,缺少一种合理的测量最小化改变和信念牢固性的手段,最重要的是缺少实证数据的支持。
心理模型理论是目前信念调整领域中第一个完整而系统的心理学理论。它强调,信念是通过心理模型的可能性的方式来表征的,这种表征方式决定了人们信念调整的过程(Johnson.Laird,& Byrne,2002；Johnson-Laird,Girotto,& Legrenzi,2004)。当人从不一致信念推理到一致信念的时候,要经过3个计算过程,每一个过程中,人们分别遵守相应的原则：首先人们会用模型一致性原则来检测不一致信息,然后是遵循不匹配原则作出修正哪一部分信念的决定,最后是产生解释以最终解决信念的冲突(Johnson-Laird,Girotto,& Legrenzi,2004).心理模型理论存在的问题是,它认为信念的表征和信念调整的过程是确定性的,非概率性的。它夸大了理性在信念调整中的作用,它采用二分思想,把人的信念调整看做是个或者否定大前提或者否定小前提的的过程,不符合人们实际的心理过程。此外,该理论还弱化了解释的作用。
解释机制假说是继心理模型理论之后,关于信念调整的第二个心理学解释。它认为,当遇到不一致信息之后,人们会主动建构解释,并将它作为一个新成分,引入原有因果结构,人们正是基于这种新的因果结构进行信念调整的(Walsh,& Sloman,2004,2008; Walsh, Johnson-Laird,2009).解释机制假说目前缺少对信念调整过程或阶段的研究,尤其缺少理论观点的系统构建。
基于以往关于信念调整的研究,本研究通过5个实验,围绕“一个中心两个基本点”——以信念调整的机制为中心,以解释对信念调整的决定性影响和解释建构的阶段为两个基本点,逐步探索因果信念表征的可能形式,因果信念调整的机制及其可能的过程和阶段,从而检验以往关于信念调整的理论,并在此基础上,发展信念调整的心理学理论模型。
为了初步探讨解释是否会对因果信念修正的过程产生作用,研究一在传统的信念调整的任务中操纵了因果结构和新信息的呈现顺序,对比和检验了心理模型理论和解释机制假说。实验一中被试的任务是,在知觉到不一致信息后选择修改大前提或者小前提。实验自变量为：因果结构,包括肯定的因果结构(cause:A发生了导致B发生)和否定的因果结构(prevent:A发生了阻止B发生)；分类前提和事实的呈现顺序,包括肯定前件式(先呈现分类前提再呈现事实,A-not B)和否定后件式(先呈现事实再呈现分类前提not B-A)。实验因变量为被试选择修改大前提的分数。实验一的结果与心理模型理论(Hasson,& Johnson-Laird,2003)预测不一致的是,因果结构和呈现顺序之间的交互作用差异不显著,被试在所有条件下都有修改大前提的强烈倾向,这种倾向在否定的因果结构(prevent)中比在肯定的因果结构中更为明显,肯定前件式和否定后件式这两种呈现顺序对被试修改大前提的倾向没有显著影响。实验结果初步支持基于因果模型理论的解释机制假说,而不支持心理模型理论。
为了进一步确定解释对信念调整过程的决定性影响,研究二直接操纵针对不同前提的反例的解释可获得性高低。本研究中被试的任务是,在检测到不一致信息后,需要选择修改大前提或者类别前提或者两者都修改或者两者都不修改,实验记录被试在每个选项中的分数。实验二和实验三分别采用熟悉和假设性的实验材料,自变量为针对不同前提反例的解释可获得性。在选择任务之后,被试还需要对题项中的冲突信息给出解释,实验者对被试给出的解释进行分类。实验结果发现,无论是熟悉的还是假设性的实验材料中,无论是在选择任务中还是在解释任务中,对前提反例的解释可获得性的操纵可以直接影响被试对原有信念的调整模式,提高针对某类前提的反例的解释可获得性可增强修改某类前提的倾向。此外,熟悉和假设性任务下反应模式的一致性说明了目前的信念牢固性原则对信念调整的解释力比较小。
前两个研究基本上可以从功能上证明,前提反例的解释可获得性决定人们信念调整的结果,要最终确定解释和信念调整反应之间的因果关系,时间上,解释的构建必须发生在信念调整决策之前。因此,研究三的目的是在新的实验范式基础上探索解释构建发生在信念调整中的哪一个阶段。以下两个实验分别研究了不同概率命题的信念调整任务中,人们建构解释可能发生的阶段。
实验四的自变量为：大前提的概率高低(那些包含了很少失效条件的命题为高概率命题,那些包含了很多失效条件的命题为低概率命题)和解释的时间(在大前提出现之前让被试对可能的反例进行解释或者在矛盾信息出现之后让被试对出现的反例进行解释)。实验因变量为：解释产生之前和之后对同一因果信念的概率判断值。实验结果发现,在高概率命题中,大前提之前要求被试对其可能的反例进行解释会降低之后对此前提的概率判断,而在低概率命题中,前提的概率判断因此受到的影响就会小很多。无论是在高概率的信念中还是低概率的信念中,无论是大前提之前给出反例解释还是之后给出解释,只要后面出现关于反例的新信息,被试都会降低针对原来大前提的概率判断。不过,高概率信念条件下的信念调整幅度显著高于低概率信念条件下的信念调整幅度。实验四的结果说明,原有信念概率的高低是影响信念调整的一个重要因素,进一步证实人们的信念表征更可能是概率性的。人们对低概率前提的表征中可能包含了反例的解释,对于高概率的信念,因为其反例的解释可获得性相对比较低,需要附加的任务才可以增加被试提取反例解释的主观努力。另外,人们对解释在信念调整中的作用的评估可能是一个动态过程。
实验五采用单因多果的因果结构(A发生导致B发生；A发生导致C发生),以一般性的规则信念为材料,要求被试在知道原因发生和一个结果发生或者没有发生后判断另一个结果发生的概率大小(P(C/A,B)(一致条件下)或者P(C/A,-B)(不一致条件下))。实验自变量为：新信息的一致性(和原有信念一致的或者不一致的信息)和解释提示问题的相关性(直接询问导致新信息一致性原因的问题为相关问题,否则为不相关问题)。实验因变量为：前后对结果的概率判断,对新信息的阅读时间(RT1)以及第二次判断概率的时间(RT2)。实验结果发现,在概率判断上,当之后出现的新信息是反例时,人们会降低原因所导致的各个结果的概率。当之后出现的新信息是正向例子时,人们会提高原因所导致的各个结果的概率。在反应时上,无论后面解释提示的问题是否是相关问题,人们阅读不一致信息的时间要长于一致信息的时间。在最后判断条件概率P(C/A,-B)或者P(C／A,B)时,不一致条件下,两种问题类型条件下判断反应时没有显著差异。致条件下,问题不相关条件下的判断反应时要长于问题相关条件下的判断反应时。实验五的结果说明,人们会在遇到不一致信息时,马上搜寻解释,而不会在遇到一致信息时,有意去解释原因导致结果的机制。但之后的信念调整任务,比如判断条件概率P(C/A,B)会迫使被试在遇到一致信息后进一步思考因果机制。
研究三发现了人们构建解释发生在信念表征阶段或者阅读矛盾信息时,即人们是在决定如何修改信念之前构建解释的。研究三在时间上确定了解释可获得性和信念调整反应之间的因果关系。
以上三个研究不能很好地支持以往关于信念调整的理论解释,本文因此提出了基于因果模型理论的解释机制假说：人们对因果信念的表征基于的是因果结构,而不是心理模型。对于因果信念,无论是最开始的信念表征还是遇到新信息后的信念调整过程,都更可能是概率性的,而非确定性的。人们很少会直接否定一个前提,而更多地是去修改或者调整前提的概率。从加工阶段上来看,在遇到新信息后,人们先评价不一致信息,然后构建解释,最后根据所产生的解释对原有信念的强度进行重新的调整。从加工机制上来看,解释的性质决定了人们信念调整的模式。对于低强度的信念,人们在表征大前提的时候可能就包含了反例和反例解释。对于高强度的信念,人们是在遇到矛盾信息之后构建解释的。
Belief revision is a process during which a rational agent change the belief state from inconsistency into consistency. Specifically, it is a process in which people first detect an inconsitency between new information and the original belief system, then decide which of the belief set to be revised after finding out a certain part of the belief conflicts with the new information, and eventually to accept the new information so that to adapt to the new enviroment.
Concerning the mechansim of the belief revision, two basic principles had been proposed in philosophy and artificial intelligence:minimal change principle and entrenchment account. The former pointed out, people would make the minimal or the most conservative change of the original belief after detecting an inconsistency so that to maintain as much of the original belief as they can (Gardenfors,1988; Harman, 1986; James,1907).The latter claimed that some beliefs might be more entrenched than others in people's minds and thus more resistant to being abandoned (Gardenfors,1992). Both of the two accounts have been criticized for being lack of a clear operational definition, a proper measurement of the minimal change and entrechment of the belief and above all, they are in shortage of enough supporting data.
Mental model theory has been so far the first psychological account of belief revision, which claimed that, people represent beliefs by constructing sets of mental models in which each model represents a possiblity. Belief revision is built on the representation of the beliefs (Johnson-Laird,& Byrne,2002; Johnson-Laird, Girotto, & Legrenzi,2004). The theory distinguished three main computations, in each of which one principle is supposed to be employed when people reason from inconsistency to consistency:first people must detect an inconsistency within a set of propositions by using the principle of modeling consistency; Second, people use the mismatch principle to decide which of the original belief to be revised. Third, people use the principle of causal knowledge to generate an explantion so that they can eventually resolve the inconsistency (Johnson-Laird, Girotto,& Legrenzi,2004).The problems of the theory lie in threefolds:it adopts an all-or-nothing manner in the representation of the belief as well as in the belief revision process; it overstates the role of rationality in belief revision, and in the meantime, it may underestimate the role of explanation in the process of belief revision.
The explanation hypothesis has been another psychological account of belief revision. It suggested people resolve an inconsistency by explaining its origin. Explanations would be introduced as a new element into the causal structure after an inconsistency arises and people revise their causal beliefs on the basis of the new structure (Walsh,& Sloman,2004,2008; Walsh, Johnson-Laird,2009). The hypothesis fails to investigate the process of the belief revision, neither does it systematically build its theoretical structure on sufficient data.
Based on the previous belief revision studies, this research focused on the mechanism of belief revision by answering two basic questions-how explanations determine belief revision response and when explanations are generated. Consisting of 5 experiments, the present research proceeded gradually to investigate the representation of beliefs, the computations people might have in the process of causal belief revision and the mechanism of causal belief revision. By testing the previous models of belief revision in our results, we intend to develop a psychological model of causal belief revision eventually.
To tentatively investigate whether the availability of explanation influences the belief revision, we manipulated the causal structure and the presentation order of the new information and the categorical premises in a classical belief revision task in which participants were asked to choose to revise either the main premise or the categorical premise after detecting an inconsistency. The two independent variables were causal structure and the order of the categorical premise and facts. The former included positive structure (A causes B) and negative structure (A prevents B) while the latter included Modus Ponens order (the categorical premise was presented before the facts, A-not B) and Modus Tollens order (the categorical premise was presented after the facts, not B-A). The dependent variables were the scores of choices on revising the major premise. The results showed that people had a strong tendency to revise the main premise, which was even more obvious in the prevent structure than in the cause one. Inconsistent with what the mental model theory (Hasson,& Johnson-Laird,2003) predicted, the MP and MT orders didn't have an effect on people's belief revsion, and in the meantime, there was no interaction between the two variables. All the results are in favor of explanation hypothesis instead of mental model theory.
To further investigate the decisive role of the availability of explanation in belief revision, we carried out two experiments to directly manipulate the availability of explanations in study two. Participants had to make one of the four choices after detecting an inconsistency:to revise the main premise, to revise the categorical premise, to revise both, to revise none of them. Scores for each choice were recorded. Hypothetical as well as familiar materials were employed in the two experiments. The independent variables were:the availability of the explanations (disablers) for different premises (three levels in experiment 2:explanations for the major premise, explanations for the minor premise and explanations for both; two levels in experiment 3:explanations for the major premise, explanations for the minor premise). Particpants had to give an explanation for the inconsistency after making the choice. The results showed that the manipuplation of the availability of the explanations for a certain premise had a direct effect on the belief revision results regardless of the nature of the materials and the type of the tasks, specifically, increasing the availability of disablers for a premise enhanced the tendence to revise the premise. Furthermore, the consistent response patterns in the hypothetical and familiar materials in the two experiments cast doubt over the entrenchment account.
The previous two studies functionally prove the availability of explanations determine the way people revise their beliefs. In a causal relation, the cause must occur before the effect. So we have to find out the temporal order of the generation of explanation and belief revision response to finally determine the causal relation between explanations and belief revision responses. In study 3, we intended to examine the stage when people give an explanation.
Two experiments were included. In experiment 4, the independent variables were: the strength of the major premises (Those included few disablers were recruited as high-plausible premises; those included many disablers were recruited as low-plausible premises) and the time to give an explanation (to explain before the presentation of the major premise; to explain after the presentation of the inconsistent new information). The dependent variables were:probability judgment of the major premise before and after generating an explanation:p1, p2. The results showed that, asking for explanation before the presentation of the major premise significantly lowered the probability judgment of the high-plausible premises but the same action only slightly brought down the probablity judgment of the low-plausible premises (pi). The inconsistent information given later generally brought down people's confidence of the major premise (p2) regardless of the strength of the major premises and the the time of generating an explanation. However, people lowered the probability more in the high-plausible premises than in the low-plausible premises.The findings in experiment 4 indicated that explanations might be included in the reprentation of the low-plausible premises while for the high-plausible premses, the availability of explanations is so much lower that people have to be forced to generate an explanation. Furthermore, it seems the process of evaluating the explanation is dynamic.
In experiment 5, we used high-plausible premises (mostly daily used rules) with a common cause structure (A causes B; A causes C). People were asked to judge the probability of an effect given the presence of the cause and the presence or absence of another effect (P(C/A,-B) or P(C/A,B)). The independent variables were:consistency of the new information (new information that was consistent with the original propositions; new information that was inconsistent with the original propositions) and relevance of the explanation questions (those questions that asked for an explanation concerning the consistency of the new information were labled as relevant questions, otherwise they were labled as irrelevant questions). The dependent variables were:probability judgment of one effect given the presence of the cause (P(C/A)); probability judgment of the effect given the presence of the cause and the absence (or the presence) of another effect (P(C/A,-B) or P(C/A,B)); Reaction time to read the new information (RT1); Reaction time to judge the probability of P(C/A,-B) or P(C/A, B) (RT2). The reults showed that, people reduced the probability judgment when the new information was negative and increased the probablity judgment when the new information was positive. As for the reaction time, people spent more time reading the negative information than reading the positive information no matter the following explanation question was relevant or not. There was no signifant difference of the time to judge P(C/A,-B) when the new information was inconsistent between the two types of explanatin questions. But it takes longer for people to judge P(C/A,B) when the following question was relevant than when it was irrelevant. The findings in experiment 5 indicated that people would search for an explanation when they are faced with inconsistent information but they won't consider the causal mechanism until they are asked to judge P(C/A,B) when they are faced with positive information.
In study 3, we found out that people either included disablers in the representation of the original beliefs or generated an explanation when they were reading the new information, thus we assume that explanations are usually generated before making a belief revision decision, eventually confirming the causal relation between the availability of explanations and the belief revision responses.
The three stuides above couldn't be accounted by the previous models, we thus proposed the explanation hypothesis on the basis of causal model theory:the representation as well as the causal belief revision process is based on a probabilistic manner instead of an all-or-nothing manner; People hardly reject a premise in the face of some inconsistent information, rather, they choose to doubt a premise. Three computations might be involved in belief revision after inconsistent information arises: people first detect an inconsistency, and then they generate an explanation; finally they reassign the probability of the major premise based on the explanations they have in their mind. The availability of explanation detemines how people revise their beliefs. For the low-plausbility beliefs, explanations might be included in the representation of the major premise while for the high-plausbility beliefs, explanation are generated after they are confronted with inconsisten information.
引文
Alchourron, C., Gardenfors, P., Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic,50, 510-530.
Alston, W. (1993). The reliability of sense perception. Ithaca:Cornell University Press.
Bechtel, W., Abrahamsen, A. (2005). Explanation:a mechanistic alternative. Stud. Hist. Philos.Sci. C Stud. Hist. Philos. Biol. Biomed. Sci.36,421-41
BonJour, L. (1985). The structure of empirical knowledge. Cambridge:Harvard University Press.
Borgida, A. (1985). Language features for flexible handling of exceptions in information. Sysrems ACM Transactions on Database Systems,10,563-603.
Brewka, G., Dix, J.,& Konolige, K. (1997). Nonmonotonic reasoning:An overview. Stanford, CA:CSLI Publications.
Byrne, R. M. J.,& Walsh C. R. (2005). Resolving Contradictions. To appear in: Johnson-Laird, P.N.& Girotto, V. (Eds.). The shape of reason:essays in honour of Paolo Legrenzi de Kleer, J. (1986). An assumption-based TMS. Artificial Intelligence,28,127-162.
Cummins, D. D. (1995). Naive theories and causal deduction. Memory and Cognition, 23,646-658.
Cummins, D. D., Lubart, T., Alknis, O.,& Rist, R. (1991). Conditional reasoning and causation. Memory and Cognition,19,274-282.
Dalal, M. (1988). Investigations into a theory of knowledge base revision:Preliminary report. Proceedings of the Seventh American Association for Artificial Intelligence, (pp.475479).
Dieussaert, K., Schaeken, W., De Neys, W.,& d'Ydewalle, G. (2000). Initial belief state as predictor of belief revision. Current Psychology of Cognition,19, 277-288.
Doyle, J. (1979). A truth maintenance system. Artificial Intelligence,12,231-272.
Elio, R. (1997). What to believe when inferences are contradicted:The impact of knowledge type and inference rule. Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society (pp.211-216). Mahwah, NJ: Lawrence Erlbaum Associates Inc.
Einhorn, H.J.,& Hogarth, R.M. (1986). Judging probable cause.Psychol. Bull.99, 1-19.
Evans, J.St.B.T.,& Over, D.E., (2004). If. Oxford University Press.
Foo, N.Y.,& Rao, A.S. (1988). Belief revision is a microworld (Tech. Rep. No.325). Sydney:University of Sidney, Basser Department of Computer Science.
Gardenfors, P. (1988). Knowledge in flux. Cambridge, MA:MIT Press.
Gardenfors, P.,& Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, (pp.83-95). Los Altos, Calif.:Morgan Kaufmann.
Gardenfors, P. (1990). The dynamics of belief systems:Foundations vs coherence theories. Revue Internationale de Philosophie,172,24-46.
Gardenfors, P. (1992). Belief revision:An introduction. In P. Gardenfors (Ed.), Belief revision, (pp.1-28). Cambridge:Cambridge University Press.
Gelman, R. (2002). Cognitive development. In Stevens'Handbook of Experimental Psychology, (Eds.), H Pashler, DL Medin, R Gallistel, J Wixted, (pp.396-443). New York:Wiley.3rd ed
Goldvarg, Y.,& Johnson-Laird, P. N. (2001). Naive causality:A mental model theory of causal meaning and reasoning. Cognitive Science,25,565-610.
Harman, G. (1986). Change in view. Cambridge, MA:MIT Press.
Hasson, U.,& Johnson-Laird, P. N. (2003). How reasoning changes your beliefs. Manuscript submitted for publication.
James, W. (1907). Pragmatism-A New Name for Some Old Ways of Thinking. New York:Longmans, Green & Co.
Johnson-Laird, P. N.,& Byrne, R. M. J. (1991). Deduction. Hillsdale, NJ:Erlbaum.
Johnson-Laird, P. N. (1993). Human and machine thinking. Hillsdale, NJ:Erlbaum.
Johnson-Laird, P. N.,& Byrne, R. M. J. (2002). Conditionals:A theory of meaning, pragmatics, and inference. Psychological Review,109,646-678.
Johnson-Laird, P.N.,& Girotto, V., Legrenzi, P. (2004). Reasoning From Inconsistency to Consistency. Psychological Review,111,640-661.
Keil, F. C,& Wilson, R, A. (2000a). Explaining explanation. See Keil & Wilson 2000b, pp.1-18
Keil, F.C.,& Wilson, R. A. (2000). Explanation and Cognition. MIT Press
Keil, F.C. (2006). Explanation and understanding. Annu. Rev. Psychol.57,227-254
Kozhevnikov, M.,& Hegarty, M. (2001). Impetus beliefs as default heuristics: dissociation between explicit and implicit knowledge about motion. Psychon. Bull. Rev.8(3),439-53
Legrenzi, P., Girotto, V.,& Johnson-Laird, P. N. (2003). Models of consistency. Psychological Science,14,131-137.
Legrenzi, P. and Johnson-Laird, P.N. (2005). The evaluation of diagnostic explanations for inconsistencies. Psychologica Belgica,45 (1),19-28.
Levi, I. (1991). The fixation of belief and its undoing:Changing beliefs through inquiry. New York:Cambridge University Press.
Liu, I.-M., Lo, K.-C,& Wu, J.-T. (1996). A probabilistic interpretation of "If-Then". Quarterly Journal of Experimental Psychology,49A,828-844.
Lombrozo, T. (2006). The structure and function of explanations. Trends in Cognitive Sciences,10,464-470.
Moser, P. (1985). Empirical justification. Dordrecht:D. Reidel.
Moser, P. (1989) Knowledge and evidence. Cambridge:Cambridge University Press.
Nebel, B. (1991). Belief revision and default reasoning:Syntax-based approaches. In Proceedings of the Second Conference on Knowledge Representation, (pp. 417-428). San Mateo, Calif.:Morgan Kaufmann.
Pearl, J.(2000). Causality:Models, reasoning and inference. New York:Cambridge University Press.
Politzer, G.,& George, C. (1992). Reasoning under uncertainty and non monotonicity: A pragmatic account. Paper presented at the 25th International Congress of Psychology, Brussels.
Politzer, G.,& Carles, L. (2001). Belief revision and Uncertain Reasoning. Thinking and Reasoning,7,217-234.
Salmon, W. (1984) Scientific Explanation and the Causal Structure of the World. Princeton University Press
Salmon, W. (1989). Four decades of scientific explanation. In Scientific Explanation, ed. P Kitcher,WSalmon, (pp.3-219). Minneapolis:Univ. Minn. Press
Satoh, K. (1988). Nonmonotonic reasoning by minimal belief revision. In Proceedings of the International Conference on Fifth Generation Computer Systems, (pp. 455462). ICOT:Tokyo.
Sloman, S. A. (2005). Causal models:How people think about the world and its alternatives.New York:Oxford University Press.
Sloman, S.A., Barbey A., K,& Hotaling, J. (2009). A Causal Model Theory of the Meanning of Cause, Enable, and Prevent. Cognitive Science,33,21-50.
Spirtes, P., Glymour, C.,& Scheines, R. (1993). Causation, prediction, and search. New York:Springer-Verlag.
Stevenson, R. J.,& Over, D. E. (1995). Deduction from uncertain premises. Quarterly Journal of Experimental Psychology,48A,613-643.
Swain, M. (1979). Justification and the basis of belief. In G. S. Pappas (Ed.), Justification and knowledge:New studies in episremology. Boston:D. Reidel.
Waldmann. M. R. (1996). Knowledge-based causal induction. In D.R. Shanks,K.J. Holyoak,& D.L. Medin (Eds.), The Psychology of Learning and motivation, Vol. 34:Causal Learning, (pp.47-88). San Diego:Academic Press.
Walsh C.R.,& Johnson-Laird, P.N. (2009). A change of mind. Memory & Cognitio, 37(5):624-631.
Walsh, C. R.,& Sloman, S. A. (2004). Revising causal beliefs. In K. Forbus, D. Gentner,& T. Regier (Eds.), Proceedings of the 26th Annual Conference of the Cognitive Science Society, (pp.1423-1427). Mahwah, NJ:Lawrence Erlbaum Associate.
Walsh, C.,& Sloman, S. A. (2008). Updating beliefs with causal models:Violations of screening off. Gluck, M. A., Anderson, J. R,& Kosslyn, S. M. (Eds.). Memory and Mind:A Festschrift for Gordon H. Bower. New Jersey:Lawrence Erlbaum Associates.
Weber, A. (1986). Updating propositional formulas. In Proceedings of the First Conference on Expert Database Systems, (pp.487-500).
Willard, L.,& Yuan, L. (1990). The revised Gardenfors postulates and update semantics, In S. Abiteboul& P.Konellakis (Eds.), Proceedings of the International Conference on Database Theory, (pp.409-421). Volume 470 of Lecture Notes in Computer Science. Berlin:Springer-Verlag.
Woodward, J. (2003). Making Things Happen:A Theory of Causal Explanation. Oxford University Press.
Alston, W. (1993). The reliability of sense perception. Ithaca:Cornell University Press.
Bechtel, W., Abrahamsen, A. (2005). Explanation:a mechanistic alternative. Stud. Hist. Philos.Sci. C Stud. Hist. Philos. Biol. Biomed. Sci.36,421-41
BonJour, L. (1985). The structure of empirical knowledge. Cambridge:Harvard University Press.
Borgida, A. (1985). Language features for flexible handling of exceptions in information. Sysrems ACM Transactions on Database Systems,10,563-603.
Brewka, G., Dix, J.,& Konolige, K. (1997). Nonmonotonic reasoning:An overview. Stanford, CA:CSLI Publications.
Byrne, R. M. J.,& Walsh C. R. (2005). Resolving Contradictions. To appear in: Johnson-Laird, P.N.& Girotto, V. (Eds.). The shape of reason:essays in honour of Paolo Legrenzi de Kleer, J. (1986). An assumption-based TMS. Artificial Intelligence,28,127-162.
Cummins, D. D. (1995). Naive theories and causal deduction. Memory and Cognition, 23,646-658.
Cummins, D. D., Lubart, T., Alknis, O.,& Rist, R. (1991). Conditional reasoning and causation. Memory and Cognition,19,274-282.
Dalal, M. (1988). Investigations into a theory of knowledge base revision:Preliminary report. Proceedings of the Seventh American Association for Artificial Intelligence, (pp.475479).
Dieussaert, K., Schaeken, W., De Neys, W.,& d'Ydewalle, G. (2000). Initial belief state as predictor of belief revision. Current Psychology of Cognition,19, 277-288.
Doyle, J. (1979). A truth maintenance system. Artificial Intelligence,12,231-272.
Elio, R. (1997). What to believe when inferences are contradicted:The impact of knowledge type and inference rule. Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society (pp.211-216). Mahwah, NJ: Lawrence Erlbaum Associates Inc.
Einhorn, H.J.,& Hogarth, R.M. (1986). Judging probable cause.Psychol. Bull.99, 1-19.
Evans, J.St.B.T.,& Over, D.E., (2004). If. Oxford University Press.
Foo, N.Y.,& Rao, A.S. (1988). Belief revision is a microworld (Tech. Rep. No.325). Sydney:University of Sidney, Basser Department of Computer Science.
Gardenfors, P. (1988). Knowledge in flux. Cambridge, MA:MIT Press.
Gardenfors, P.,& Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, (pp.83-95). Los Altos, Calif.:Morgan Kaufmann.
Gardenfors, P. (1990). The dynamics of belief systems:Foundations vs coherence theories. Revue Internationale de Philosophie,172,24-46.
Gardenfors, P. (1992). Belief revision:An introduction. In P. Gardenfors (Ed.), Belief revision, (pp.1-28). Cambridge:Cambridge University Press.
Gelman, R. (2002). Cognitive development. In Stevens'Handbook of Experimental Psychology, (Eds.), H Pashler, DL Medin, R Gallistel, J Wixted, (pp.396-443). New York:Wiley.3rd ed
Goldvarg, Y.,& Johnson-Laird, P. N. (2001). Naive causality:A mental model theory of causal meaning and reasoning. Cognitive Science,25,565-610.
Harman, G. (1986). Change in view. Cambridge, MA:MIT Press.
Hasson, U.,& Johnson-Laird, P. N. (2003). How reasoning changes your beliefs. Manuscript submitted for publication.
James, W. (1907). Pragmatism-A New Name for Some Old Ways of Thinking. New York:Longmans, Green & Co.
Johnson-Laird, P. N.,& Byrne, R. M. J. (1991). Deduction. Hillsdale, NJ:Erlbaum.
Johnson-Laird, P. N. (1993). Human and machine thinking. Hillsdale, NJ:Erlbaum.
Johnson-Laird, P. N.,& Byrne, R. M. J. (2002). Conditionals:A theory of meaning, pragmatics, and inference. Psychological Review,109,646-678.
Johnson-Laird, P.N.,& Girotto, V., Legrenzi, P. (2004). Reasoning From Inconsistency to Consistency. Psychological Review,111,640-661.
Keil, F. C,& Wilson, R, A. (2000a). Explaining explanation. See Keil & Wilson 2000b, pp.1-18
Keil, F.C.,& Wilson, R. A. (2000). Explanation and Cognition. MIT Press
Keil, F.C. (2006). Explanation and understanding. Annu. Rev. Psychol.57,227-254
Kozhevnikov, M.,& Hegarty, M. (2001). Impetus beliefs as default heuristics: dissociation between explicit and implicit knowledge about motion. Psychon. Bull. Rev.8(3),439-53
Legrenzi, P., Girotto, V.,& Johnson-Laird, P. N. (2003). Models of consistency. Psychological Science,14,131-137.
Legrenzi, P. and Johnson-Laird, P.N. (2005). The evaluation of diagnostic explanations for inconsistencies. Psychologica Belgica,45 (1),19-28.
Levi, I. (1991). The fixation of belief and its undoing:Changing beliefs through inquiry. New York:Cambridge University Press.
Liu, I.-M., Lo, K.-C,& Wu, J.-T. (1996). A probabilistic interpretation of "If-Then". Quarterly Journal of Experimental Psychology,49A,828-844.
Lombrozo, T. (2006). The structure and function of explanations. Trends in Cognitive Sciences,10,464-470.
Moser, P. (1985). Empirical justification. Dordrecht:D. Reidel.
Moser, P. (1989) Knowledge and evidence. Cambridge:Cambridge University Press.
Nebel, B. (1991). Belief revision and default reasoning:Syntax-based approaches. In Proceedings of the Second Conference on Knowledge Representation, (pp. 417-428). San Mateo, Calif.:Morgan Kaufmann.
Pearl, J.(2000). Causality:Models, reasoning and inference. New York:Cambridge University Press.
Politzer, G.,& George, C. (1992). Reasoning under uncertainty and non monotonicity: A pragmatic account. Paper presented at the 25th International Congress of Psychology, Brussels.
Politzer, G.,& Carles, L. (2001). Belief revision and Uncertain Reasoning. Thinking and Reasoning,7,217-234.
Salmon, W. (1984) Scientific Explanation and the Causal Structure of the World. Princeton University Press
Salmon, W. (1989). Four decades of scientific explanation. In Scientific Explanation, ed. P Kitcher,WSalmon, (pp.3-219). Minneapolis:Univ. Minn. Press
Satoh, K. (1988). Nonmonotonic reasoning by minimal belief revision. In Proceedings of the International Conference on Fifth Generation Computer Systems, (pp. 455462). ICOT:Tokyo.
Sloman, S. A. (2005). Causal models:How people think about the world and its alternatives.New York:Oxford University Press.
Sloman, S.A., Barbey A., K,& Hotaling, J. (2009). A Causal Model Theory of the Meanning of Cause, Enable, and Prevent. Cognitive Science,33,21-50.
Spirtes, P., Glymour, C.,& Scheines, R. (1993). Causation, prediction, and search. New York:Springer-Verlag.
Stevenson, R. J.,& Over, D. E. (1995). Deduction from uncertain premises. Quarterly Journal of Experimental Psychology,48A,613-643.
Swain, M. (1979). Justification and the basis of belief. In G. S. Pappas (Ed.), Justification and knowledge:New studies in episremology. Boston:D. Reidel.
Waldmann. M. R. (1996). Knowledge-based causal induction. In D.R. Shanks,K.J. Holyoak,& D.L. Medin (Eds.), The Psychology of Learning and motivation, Vol. 34:Causal Learning, (pp.47-88). San Diego:Academic Press.
Walsh C.R.,& Johnson-Laird, P.N. (2009). A change of mind. Memory & Cognitio, 37(5):624-631.
Walsh, C. R.,& Sloman, S. A. (2004). Revising causal beliefs. In K. Forbus, D. Gentner,& T. Regier (Eds.), Proceedings of the 26th Annual Conference of the Cognitive Science Society, (pp.1423-1427). Mahwah, NJ:Lawrence Erlbaum Associate.
Walsh, C.,& Sloman, S. A. (2008). Updating beliefs with causal models:Violations of screening off. Gluck, M. A., Anderson, J. R,& Kosslyn, S. M. (Eds.). Memory and Mind:A Festschrift for Gordon H. Bower. New Jersey:Lawrence Erlbaum Associates.
Weber, A. (1986). Updating propositional formulas. In Proceedings of the First Conference on Expert Database Systems, (pp.487-500).
Willard, L.,& Yuan, L. (1990). The revised Gardenfors postulates and update semantics, In S. Abiteboul& P.Konellakis (Eds.), Proceedings of the International Conference on Database Theory, (pp.409-421). Volume 470 of Lecture Notes in Computer Science. Berlin:Springer-Verlag.
Woodward, J. (2003). Making Things Happen:A Theory of Causal Explanation. Oxford University Press.