Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

Reasoning with Factors

The paper proposes an analysis and a formalisation of factor-based reasoning. After examining the relevance of factors in legal reasoning, binary and scalable factors (dimensions) are distinguished and the relations between them are discussed. An account of a fortiori reasoning with both types of factors is developed. This article reports ideas which are discussed and developed in Sartor (2005). We refer to the latter work for the theoretical framework in which our analysis of factors is embedded.     

THOG问题促进效应研究

通过选取经典的THOG问题作为实验材料,探讨了大学生解决具体以及抽象选言推理问题的认知机制,结果发现:(1)具体内容的选言推理问题对抽象内容的选言推理问题有明显的促进效应,表现为先解决逃犯问题后解决THOG问题组的正确率显著高于先解决THOG问题后解决逃犯问题组;(2)提供笼统的解题策略对大学生解决THOG问题几乎没有促进作用。     

Linda问题:"齐当别"抉择模型的解释

大量有关人类归因判断的研究表明,人类经常违反理性概率公理.Tversky和Kahneman(1983)使用Linda问题等特定场景的研究发现,人们系统性地表现出违反理性推断标准,判断合取事件发生概率大于其组成事件发生概率,称之为合取谬误,并用人们使用代表性启发式判断概率来解释该现象产生的原因.然而使用启发式观点对合取谬误现象进行解释过于模糊不清.该文首先介绍了合取谬误现象及其解释模型,然后应用Li(1994,2004)提出的不确定情形下决策理论--"齐当别"抉择模型对Linda问题中合取谬误产生的原因进行了新的解释.     

Reasoning with quantifiers

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity properties of quantified statements--properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning.     

What response times tell of children's behavior on the balance scale task

Analysis of accuracy of responses to balance scale problems gives a global idea of the cognitive processes that underlie problem-solving behavior on this task. We show that response times (RTs) provide additional detailed information about the kind and duration of these processes. We derive predictions about the RTs from Siegler's (1981) model for the balance scale task, including the counterintuitive prediction that young adults are slower than children in solving particular balance scale problems. The predictions were tested in a study in which 191 6- to 22-year-old participants were presented with a computerized balance scale task. RTs were analyzed with regression models. In addition to qualitative differences between items, we also modeled quantitative differences between items in the regression models. Analyses supported the predictions and provided additional knowledge on the rules. Rule II was reformulated as a rule that always involves the encoding, but not always the correct application of the distance cue. RTs provided evidence for the use of a buggy-rule and not an addition-rule. Finally, a relation between rule inconsistency and increased RT was found.     

Distortion of probability and outcome information in risky decisions

Substantial evidence indicates that information is distorted during decision making, but very few studies have assessed the distortion of probability and outcome information in risky decisions. In two studies involving six binary decisions (e.g., banning blood donations from people who have visited England, because of “mad cow disease”), student and nonstudent participants distorted their evaluations of probability and outcome information in the direction of their preferred decision alternative and used these biased evaluations to update their preferences. Participants also evaluated the utilities of possible outcomes more positively when the outcomes could follow only from the preferred alternative and more negatively when they could follow only from the competing alternative. Such circular reasoning is antithetical to the normative consequentialist principles underlying decision analysis. Presenting numerical information as precise values or as ranges of values did not significantly affect information distortion, apparently because the manipulation did not affect perceived ambiguity as intended.     

A causal model theory of the meaning of cause, enable, and prevent

The verbs cause , enable , and prevent express beliefs about the way the world works. We offer a theory of their meaning in terms of the structure of those beliefs expressed using qualitative properties of causal models, a graphical framework for representing causal structure. We propose that these verbs refer to a causal model relevant to a discourse and that "A causes B" expresses the belief that the causal model includes a link from A to B. "A enables/allows B" entails that the model includes a link from A to B, that A represents a category of events necessary for B, and that an alternative cause of B exists. "A prevents B" entails that the model includes a link from A to B and that A reduces the likelihood of B. This theory is able to account for the results of four experiments as well as a variety of existing data on human reasoning.     

不同概率表征的贝叶斯推理试题形式结构的同质性研究

研究从先验概率、概率表征、推理任务等方面探讨了经典贝叶斯推理研究中存在的不足,试图在＂知识和试题双重模型＂框架下,探索现实和标准贝叶斯试题的形式结构的同质性,结果表明：1）自然频次表征比百分比表征的贝叶斯推算题正确率高,这是因为试题的形式结构不同,与概率表征无关;2）贝叶斯判断题与贝叶斯推算题的试题形式结构存在显著差异;3）贝叶斯推算题中,概率词表征与其它两种表征的试题形式结构存在显著差异,其实质是贝叶斯判断。