Probabilistic dynamic belief revision

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws.     

Preferential theory revision

Employing a logic program approach, this paper focuses on applying preferential reasoning to theory revision, both by means of preferences among existing theory rules, and by means of preferences on the possible abductive extensions to the theory. And, in particular, how to prefer among plausible abductive explanations justifying observations.     

Weighing the aim of belief

The theory of belief, according to which believing that p essentially involves having as an aim or purpose to believe that p truly, has recently been criticised on the grounds that the putative aim of belief does not interact with the wider aims of believers in the ways we should expect of genuine aims. I argue that this objection to the aim theory fails. When we consider a wider range of deliberative contexts concerning beliefs, it becomes obvious that the aim of belief can interact with and be weighed against the wider aims of agents in the ways required for it to be a genuine aim.     

Memory and epistemic conservatism

Much of the plausibility of epistemic conservatism derives from its prospects of explaining our rationality in holding memory beliefs. In the first two parts of this paper, I argue for the inadequacy of the two standard approaches to the epistemology of memory beliefs, preservationism and evidentialism. In the third, I point out the advantages of the conservative approach and consider how well conservatism survives three of the strongest objections against it. Conservatism does survive, I claim, but only if qualified in certain ways. Appropriately qualified, conservatism is no longer the powerful anti-skeptical tool some have hoped for, but a doctrine closely connected with memory.     

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。     

The virtues of epistemic conservatism

Although several important methodologies implicitly assume the truth of epistemic conservatism, the view that holding a belief confers some measure of justification on the belief, recent criticisms have led some to conclude that epistemic conservatism is an implausible view. That conclusion is mistaken. In this article, I propose a new formulation of epistemic conservatism that is not susceptible to the criticisms leveled at earlier formulations of epistemic conservatism. In addition to withstanding these criticisms, this formulation of epistemic conservatism has several benefits. First, this formulation has the benefits of earlier formulations of epistemic conservatism, that is to say it makes sense of our intuitions about justification in regard to both memory beliefs and beliefs for which we have forgotten our evidence. Second, it provides a good way of responding to the skeptic’s challenge concerning the possibility of possessing knowledge of the external world posed by the Alternative Hypotheses argument. Third, it provides responses to both forms of a new skeptical problem plaguing basic knowledge structure theories, the Problem of Easy Knowledge formulated by Stewart Cohen. I argue that given the many benefits of this formulation of epistemic conservatism and the fact that it is not vulnerable to the criticisms that undermine earlier formulations of epistemic conservatism, this formulation of epistemic conservatism is a plausible view to maintain.     

Understanding the Brandenburger-Keisler Paradox

Adam Brandenburger and H. Jerome Keisler have recently discovered a two person Russell-style paradox. They show that the following configurations of beliefs is impossible: Ann believes that Bob assumes that Ann believes that Bob’s assumption is wrong. In [7] a modal logic interpretation of this paradox is proposed. The idea is to introduce two modal operators intended to represent the agents’ beliefs and assumptions. The goal of this paper is to take this analysis further and study this paradox from the point of view of a modal logician. In particular, we show that the paradox can be seen as a theorem of an appropriate hybrid logic. Special Issue Formal Epistemology II. Edited by Branden Fitelson     

Evidentialism and pragmatic constraints on outright belief

Evidentialism is the view that facts about whether or not an agent is justified in having a particular belief are entirely determined by facts about the agent’s evidence; the agent’s practical needs and interests are irrelevant. I examine an array of arguments against evidentialism (by Jeremy Fantl, Matthew McGrath, David Owens, and others), and demonstrate how their force is affected when we take into account the relation between degrees of belief and outright belief. Once we are sensitive to one of the factors that secure thresholds for outright believing (namely, outright believing that p in a given circumstance requires, at the minimum, that one’s degree of belief that p is high enough for one to be willing to act as if p in the circumstances), we see how pragmatic considerations can be relevant to facts about whether or not an agent is justified in believing that p—but largely as a consequence of the pragmatic constraints on outright believing.

Older children's misunderstanding of uncertain belief after passing the false belief test

A four-location belief task was designed to examine children's understanding of another's uncertain belief after passing a false belief (FB) task. In Experiment 1, after passing the FB task, participants were asked what a puppet would do after he failed to find his toy at the falsely believed location. Most 4-year-olds and half of 6-year-olds children who passed the FB test showed difficulty in handling uncertain belief; answering that the puppet would then look for his toy at the current (moved-to) location. Eight-year-old children and adults all recognized that the puppet would look for the toy everywhere, or at random. In Experiment 2, 4- and 6-year-olds were presented two other search tasks; it was shown that preschoolers could use search strategies to solve a similar search problem when FB was not involved. This new aspect of post-FB understanding can be interpreted in terms of limited understanding of uncertainty in a less-knowledgeable individual and of limited ability to infer the consequences of belief-disconfirmation.     

Preference-based belief revision for rule-based agents

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.     

False belief and language comprehension in Cantonese-speaking children

The current research compared two accounts of the relation between language and false belief in children, namely that (a) language is generally related to false belief because both require secondary representation in a social-interactional context and that (b) specific language structures that explicitly code metarepresentation contribute uniquely to the language-false belief relation. In three studies, attempts were made to correlate Cantonese-speaking children's false belief with their general language comprehension and understanding of certain structures that explicitly express metarepresentational knowledge. Results showed that these structures failed to predict false belief after age, nonverbal intelligence, and general language comprehension were considered. In contrast, general language remained predictive of false belief after controlling for age, nonverbal intelligence, and language structures. The current findings are more consistent with a general language account than a language structure account.     

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.     

Commentary on Ted Ruffman’s “Belief or not belief: …”

I applaud Ruffman for cautioning us against interpreting early sensitivity to others’ beliefs as evidence for an innate theory of mind and for making room for learning. In turn, however, I caution against his claim that all infants need is to understand that people act depending on what they perceive. Instead, infants may keep experiential records (Perner & Roessler, 2010) for other people or records of what they have registered (Apperly & Butterfill, 2009), which makes it less obvious that all required knowledge can be acquired by statistical learning. As a general criticism I remonstrate with current theory of mind research on its lack of concern that we understand people as acting for reasons which goes beyond detecting lawful regularities in behaviour.     

Language and false belief in Korean-speaking and English-speaking children

The link between language and false belief (FB) understanding has been the focus of considerable debate regarding which language component (semantics, general language, or complementation) is necessary for FB development. We examined the relative roles of complementation and receptive vocabulary in FB development in Korean-speaking and English-speaking children. FB understanding, memory for complements involving the verbs think, say and want, and receptive vocabulary were measured at three time points in 59 Korean-speaking children and 72 English-speaking children. A multi-level growth model indicated that the development of receptive vocabulary and separately the development of think understanding uniquely predicted the development of FB understanding. Neither say nor want was associated with FB understanding. The same pattern was found for Korean- and English-speaking children. The results provide evidence for the role of general language in FB understanding and against the unique role of sentential complementation.     

Learning from examples does not prevent order effects in belief revision

A common finding is that information order influences belief revision (e.g., Hogarth & Einhorn, 1992 Hogarth, R. M. and Einhorn, H. J. 1992. Order effects in belief updating: The belief-adjustment model. Cognitive Psychology, 24: 1–55. [Crossref], [Web of Science ®] , [Google Scholar]). We tested personal experience as a possible mitigator. In three experiments participants experienced the probabilistic relationship between pieces of information and object category through a series of trials where they assigned objects (planes) into one of two possible categories (hostile or commercial), given two sequentially presented pieces of probabilistic information (route and ID), and then they had to indicate their belief about the object category before feedback. The results generally confirm the predictions from the Hogarth and Einhorn model. Participants showed a recency effect in their belief revision. Extending previous model evaluations the results indicate that the model predictions also hold for classification decisions, and for pieces of information that vary in their diagnostic values. Personal experience does not appear to prevent order effects in classification decisions based on sequentially presented pieces of information and in belief revision.     

Iterated revision and minimal change of conditional beliefs

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a virtual manner, using uniterated revision.     

Eighteen-month-old infants show false belief understanding in an active helping paradigm

Recently, several studies have claimed that soon after their first birthday infants understand others’ false beliefs. However, some have questioned these findings based on criticisms of the looking-time paradigms used. Here we report a new paradigm to test false belief understanding in infants using a more active behavioral response: helping. Specifically, the task was for infants to help an adult achieve his goal - but to determine that goal infants had to take into account what the adult believed (i.e., whether or not he falsely believed there was a toy inside a box). Results showed that by 18 months of age infants successfully took into account the adult’s belief in the process of attempting to determine his goal. Results for 16-month-olds were in the same direction but less clear. These results represent by far the youngest age of false belief understanding in a task with an active behavioral measure.     

Five-year-old children's difficulty with false belief when the sought entity is a person

A total of 153 children (excluding those who erred on control questions), mainly 5 and 7 years of age, participated in two experiments that involved tests of false belief. In the task, the sought entity was first at Location 1 and then, unknown to the searching protagonist, it moved to Location 2. In Experiment 1, performance was well below ceiling in 5-year-olds when the sought entity was a person, and this contrasted with a task in which the sought entity was a physical object. Performance was especially inaccurate when the sought person moved of his or her own volition rather than when the sought person was requested to move by a third party. Interestingly, 5-year-olds were more likely to nominate Location 1 when asked where the searching protagonist would look first than when asked what he or she would do next. In Experiment 2, however, 5-year-olds also tended to nominate Location 1 following a question that included the word "first" even in a test of true belief--a patently incorrect response. Altogether, the results suggest that 5-year-old children have considerable difficulty with a test of false belief when the sought entity is a person acting under his or her own volition. This suggests that 5-year-olds' handle on states of belief is surprisingly fragile in this kind of task.