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.     

A formal model for structuring local perceptions of environmental space

The problem of constructing computational models of space that mimic those found in human spatial reasoning is addressed. This paper extends a formal model that addressed point objects in a 2D world to include the presence of line objects and barriers. The problem consists of determining an appropriate global model for the spatial configuration given a sequence of local views or observations. A formal model is proposed based on constraint network theory. The model leads to the identification of stable regions within which perceptual information about the environment changes slowly, and zones of transition within which the perceptual information changes more quickly. A special case of transition zones is a gateway, which may be viewed as a kind of discontinuity or singularity in the model. It is expected that the model obtained will be used to mimic human mental representations of navigable outdoor environments.     

Perseverative responding in a violation-of-expectation task in 6.5-month-old infants

In the present research, 6.5-month-old infants perseverated in a violation-of-expectation task designed to examine their reasoning about width information in containment events. After watching a familiarization event in which a ball was lowered into a wide container, the infants failed to detect the violation in a test event in which the same ball was lowered into a container only half as wide as the ball (narrow-container test event). This negative result (which was replicated in another experiment) was interpreted in terms of a recent problem-solving account of infants' perseverative errors in various means-end tasks (Aguiar, A., & Baillargeon, R. (2000). Perseveration and problem solving in infancy. In H. W. Reese (Ed.), Advances in child development and behavior (Vol. 27, pp. 135-180). San Diego, CA: Academic Press). It was assumed that the infants in the present experiments (1) did not attend to the relative widths of the ball and container in their initial analysis of the narrow-container test event, (2) categorized the event as similar to the familiarization event shown on the preceding trials, and (3) retrieved the expectation they had formed for that event ("the ball will fit into the container"), resulting in a perseverative error. This interpretation was supported by additional experiments in which different modifications were introduced that led to non-perseverative responding, indicating that 6.5-month-old infants could detect the violation in the narrow-container test event. The present findings are important for several reasons. First, they provide the first demonstration of perseverative responding in a violation-of-expectation task. Second, they make clear the breadth and usefulness of the problem-solving account mentioned above. Finally, they add to the evidence for some degree of continuity between infants' and adults' problem-solving abilities.     

An evidential support accumulation model of subjective probability

A model of cue-based probability judgment is developed within the framework of support theory. Cue diagnosticity is evaluated from experience as represented by error-free frequency counts. When presented with a pattern of cues, the diagnostic implications of each cue are assessed independently and then summed to arrive at an assessment of the support for a hypothesis, with greater weight placed on present than on absent cues. The model can also accommodate adjustment of support in light of the baserate or prior probability of a hypothesis. Support for alternatives packed together in a "residual" hypothesis is discounted; fewer cues are consulted in assessing support for alternatives as support for the focal hypothesis increases. Results of fitting this and several alternative models to data from four new multiple-cue probability learning experiments are reported.     

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.     

幼儿反事实推理的错误源分析

本研究选取57名3~5岁幼儿,考察了在两种选择和三种选择的反事实推理任务中儿童的表现以及是否出现现实错误。结果如下:无论在两种还是三种选择的反事实任务中,3岁组儿童的得分显著低于4岁和5岁组儿童,而4岁和5岁组儿童之间不存在显著差异;幼儿在反事实推理中的确会出现现实错误,但除此之外,幼儿在三种选择任务中也会选择现实和正确答案之外的第三个选项。由此可见,年幼儿童可能在抑制现实和建构反事实替代情境方面都存在困难,这尚需我们进一步探究。     

Does change in ethical education influence core moral values? Towards history- and culture-aware morality model with application in automatic moral reasoning

In this study, we focus on ethical education as a means to improve artificial companion’s conceptualization of moral decision-making process in human users. In particular, we focus on automatically determining whether changes in ethical education influenced core moral values in humans throughout the century. We analyze ethics as taught in Japan before WWII and today to verify how much the pre-WWII moral attitudes have in common with those of contemporary Japanese, to what degree what is taught as ethics in school overlaps with the general population’s understanding of ethics, as well as to verify whether a major reform of the guidelines for teaching the school subject of “ethics” at school after 1946 has changed the way common people approach core moral questions (such as those concerning the sacredness of human life). We selected textbooks used in teaching ethics at school from between 1935 and 1937, and those used in junior high schools today (2019) and analyzed what emotional and moral associations such contents generated. The analysis was performed with an automatic moral and emotional reasoning agent and based on the largest available text corpus in Japanese as well as on the resources of a Japanese digital library. As a result, we found out that, despite changes in stereotypical view on Japan’s moral sentiments, especially due to historical events, past and contemporary Japanese share a similar moral evaluation of certain basic moral concepts, although there is a large discrepancy between how they perceive some actions to be beneficial to the society as a whole while at the same time being inconclusive when it comes to assessing the same action’s outcome on the individual performing them and in terms of emotional consequences. Some ethical categories, assessed positively before the war, while being associated with a nationalistic trend in education have also disappeared from the scope of interest of post- war society. The findings of this study support suggestions proposed by others that the development of personal AI systems requires supplementation with moral reasoning. Moreover, the paper builds upon this idea and further suggests that AI systems need to be aware of ethics not as a constant, but as a function with a correction on historical and cultural changes in moral reasoning.