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.     

Confirmation of Scientific Hypotheses as Relations

Summary  In spite of several attempts to explicate the relationship between a scientific hypothesis and evidence, the issue still cries for a satisfactory solution. Logical approaches to confirmation, such as the hypothetico-deductive method and the positive instance account of confirmation, are problematic because of their neglect of the semantic dimension of hypothesis confirmation. Probabilistic accounts of confirmation are no better than logical approaches in this regard. An outstanding probabilistic account of confirmation, the Bayesian approach, for instance, is found to be defective in that it treats evidence as a formal entity and this creates the problem of relevance of evidence to the hypothesis at issue, in addition to the difficulties arising from the subjective interpretation of probabilities. This essay purports to satisfy the need for a successful account of hypothesis confirmation by offering an original formulation based on the notion of instantiation of the relation urged by an hypothesis.     

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.     

Using response times to detect aberrant responses in computerized adaptive testing

A lognormal model for response times is used to check response times for aberrances in examinee behavior on computerized adaptive tests. Both classical procedures and Bayesian posterior predictive checks are presented. For a fixed examinee, responses and response times are independent; checks based on response times offer thus information independent of the results of checks on response patterns. Empirical examples of the use of classical and Bayesian checks for detecting two different types of aberrances in response times are presented. The detection rates for the Bayesian checks outperformed those for the classical checks, but at the cost of higher false-alarm rates. A guideline for the choice between the two types of checks is offered.This study received funding from the Law School Admission Council (LSAC). The opinions and conclusions contained in this paper are those of the authors and do not necessarily reflect the policy and position of LSAC. The authors are most indebted to Wim M. M. Tielen for his computational assistance and to the US Defense Manpower Data Center for the permission to use the ASVAB data set in the empirical examples.     

Bayesian estimation and testing of structural equation models

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, for example, output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters underidentified models, as we illustrate on a simple errors-in-variables model.We thank David Spiegelhalter for suggesting applying the Gibbs sampler to structural equation models to the first author at a 1994 workshop in Wiesbaden. We thank Ulf Böckenholt, Chris Meek, Marijtje van Duijn, Clark Glymour, Ivo Molenaar, Steve Klepper, Thomas Richardson, Teddy Seidenfeld, and Tom Snijders for helpful discussions, mathematical advice, and critiques of earlier drafts of this paper.     

Data versus Spock: lay theories about whether emotion helps or hinders

The android Data from Star Trek admired human emotion whereas Spock viewed emotion as irrational and maladaptive. The theory that emotions fulfil adaptive functions is widely accepted in academic psychology but little is known about laypeople’s theories. The present study assessed the extent to which laypeople share Data’s view of emotion as helpful or Spock’s view of emotion as a hindrance. We also assessed how help and hinder theory endorsement were related to reasoning, emotion regulation, and well-being. Undergraduates (N?=?630) completed a stressful timed reasoning task and questionnaires that assessed their theories of emotion, emotion regulation strategies, happiness, and social support. Overall, participants viewed emotion more as a help than a hindrance. The more they endorsed the view that emotion helps, the better their reasoning scores. Endorsing a help theory also predicted the use of reappraisal which, in turn, predicted greater happiness and social support. In contrast, endorsing the view that emotion hinders was associated with emotion suppression and less social support. Thus, people’s theories about the functionality of emotion may have important implications for their reasoning and emotional well-being.     

On the nature of international sales and sales management research: a social network–analytic perspective

This research uses a combination of text mining, co-word analysis, and social network analysis (SNA) to review 132 international sales and sales management (ISSM) articles published between 1980 and 2017. The study provides a unique view of the past and future of ISSM research and provides three principal contributions. First, from a social network–analytic perspective, it offers a unique examination of the ways ISSM research topics are interconnected, as reflected by keyword network structure. Second, by conducting SNA across two periods (1980–1999 and 2000–2017) and examining the changes in network centrality measures, the study offers initial insights into the evolving nature of the ISSM literature. Third, the study reports keyword network disconnections (i.e., structural holes) to propose a fruitful agenda for future ISSM research. Taken together, this research offers a current perspective of the ISSM research domain's evolving nature.     

The nonlinear effects of conscientiousness on overall job performance and performance dimensions in the Chinese context

The relationship between conscientiousness and job performance has been found to be nonlinear in the West, which challenges conceptually and empirically the traditional assumption of the single linear relationship. In this research, we examined the nonlinear effects of conscientiousness on both overall job performance and performance dimensions (i.e., task performance, adaptive performance and contextual performance) in the Chinese context. The results of our two studies supported some evidence for the nonlinear effect of conscientiousness on overall job performance. In addition, it was found that conscientiousness has different (linear or nonlinear) effects on performance dimensions. These findings suggest that the nonlinear effects of conscientiousness on job performance deserve further investigation, and a distinction should be made with regard to job performance in personnel evaluation. Results are discussed in terms of the significance of considering the nonlinear relationship between conscientiousness and performance criteria.     

Finding MAPs using strongly equivalent high order recurrent symmetric connectionist networks

Belief revision is the problem of finding the most plausible explanation for an observed set of evidences. It has many applications in various scientific domains like natural language understanding, medical diagnosis and computational biology. Bayesian Networks (BN) is an important probabilistic graphical formalism widely used for belief revision tasks. In BN, belief revision can be achieved by finding the maximum a posteriori (MAP) assignment. Finding MAP is an NP-Hard problem. In previous work, we showed how to find the MAP assignment in BN using High Order Recurrent Neural Networks (HORN) through an intermediate representation of Cost-Based Abduction. This method eliminates the need to explicitly construct the energy function in two steps, objective and constraints. This paper builds on that previous work by providing the theoretical foundation and proving that the resultant HORN used to find MAP is strongly equivalent to the original BN it tries to solve.     

The effect of aging on the memory enhancement of the survival judgment task

This study investigated whether or not aging affected the benefit of a survival judgment task. Sixteen young adults and 16 older adults participated in this experiment. In the survival task, participants were requested to judge whether a word was necessary or not in a survival situation. In the self‐referent judgment task, participants were requested to judge how easily the word brings to mind an important personal experience. Participants in each condition were presented 18 concrete nouns at 4‐s intervals. Our results showed that even though the survival judgment task enhanced the memory performance in both the young adults and the older adults, the young adults outperformed the older adults in the survival and self‐referent judgment tasks.