Spatial metrics of integral and separable dimensions

Two experiments were conducted to investigate the relationship between dimensional integrality and the form of the combination rule or spatial metric used in a similarity judgment task. In Experiment 1, two groups of eight subjects judged the dissimilarity of all pairwise combinations of 12 rectangles differing in height and width (integral dimensions) or 12 circles differing in size and diameter orientation (separable dimensions). The dimensional organization and spatial metric of both sets of dimensions were determined. The results showed that differences in height and width contributed independently to judgments of the overall dissimilarity of rectangles and that these dimensions were combined using a Euclidean metric. In contrast, substantial interactions between circle size and diameter orientation were found. Combinations of these dimensions also appeared to violate the triangle inequality implying that no spatial metric was appropriate. In Experiment 2, parallelogram size and tilt were similarly analyzed. Although some degree of dimensional interaction was observed, it was found that on the average these dimensions were combined using a city-block metric. In a subsequent speeded classification task, orthogonal interference was observed, which suggested that size and tilt are integral dimensions. The implications of both experiments for the supposed association between the Euclidean metric and dimensional integrality are discussed.     

The rapid-smoking technique: Subject characteristics and treatment outcome

There is a lack of consistency in findings regarding subject (S) characteristics and the effects of smoking-control programmes. Research workers appear to assume that abstinence and reduction in smoking rate are merely different points in the same continuum, and therefore seek to correlate S variables with percentage reductions in smoking rate. It is argued that abstinence and reduced smoking are more appropriately viewed as potentially discrete outcomes. Conceptualizing outcome in this manner, a discriminant function analysis was employed to determine whether it is possible to differentiate between Ss who do, or do not, abstain following participation in a treatment programme involving rapid-smoking. It was found that it is possible to discriminate between the two groups of Ss. Advantages deriving from this approach to the investigation of S characteristics and treatment outcome are discussed.     

Deviation from hierarchical structure in recall: Is there an “optimal” structure?

Past research has suggested that proportionally more superordinate than sub-ordinate propositions are recalled from expository texts, following a hierarchical analysis of the text structure. Since free recall has typically followed this hierarchical pattern, several researchers have assumed that the related memory structures are isomorphic to the text structure. However, few of these studies have examined how individual differences and text structure interact to affect free recall. In two experiments, the assumption of hierarchical patterns of children's recall of expository text was tested. In Experiment 1, high- and average-ability fourth graders (9 years old) were asked to read and recall a passage. Experiment 2 was a replication and extension of Experiment 1. In this experiment, fourth and sixth graders (9 and 11 years old) read and recalled a different passage. The combined results of both experiments support the notion that there is probably no one optimal hierarchical structure for storage and retrieval of expository text.     

Relevant Robinson's arithmetic

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.This paper has been greatly influenced by the (largely unpublished) work of E. K. Meyer (cf. [7]) on relevant arithmetic, and I wish to thank him, and also N. D. Belnap, Jr. and D. Cohen for helpful advice. In fairness to Meyer it must be said that he finds my axioms 13 and 13(1) too strong (they are not theorems of his system R# - cf. §4 below). Meyer tells me be finds vindication for his view in my chief theorem of §2. For myself, I find the insights behind Meyer's work on R# to be both stable and fruitful, and if I now had to make a choice, I would follow Meyer in his rejection of my axioms. However, the systems I explore in this paper themselves have a surprising amount of internal consistency of motivation (cf. §5). Let a hundred formal systems bloom.     

A theorem in 3-valued model theory with connections to number theory,type theory,and relevant logic

Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development).     

COVID-19 and Religious Ethics

The editors of the JRE solicited short essays on the COVID-19 pandemic from a group of scholars of religious ethics that reflected on how the field might help them make sense of the complex religious, cultural, ethical, and political implications of the pandemic, and on how the pandemic might shape the future of religious ethics.     

What did mummy say? Dyadic interactions between young "hard to manage" children and their mothers

Thirty preschoolers rated as hard to manage on Goodman's (R. Goodman, 1997) Strengths and Difficulties Questionnaire (SDQ), and a group of matched control children were observed and recorded on audiotape at home, interacting with their mothers (Time 1). At the 18-month follow-up home visits (Time 2), the children and mothers were filmed across 4 observation settings. Mother–child interactions were rated on affect, control, responsiveness and connectedness of communication. At Time 1, mothers of the hard to manage group used more negative control and engaged in fewer connected conversations than did mothers in the control group. At Time 2, mothers of the hard to manage group displayed higher levels of negative control and lower levels of positive control. These results are discussed in terms of the importance of examining connected communication and different observation contexts when examining dyadic mother–child interactions.     

Partiality and Its Dual

This paper explores allowing truth value assignments to be undetermined or "partial" (no truth values) and overdetermined or "inconsistent" (both truth values), thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's (first-degree) relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson's "constructible falsity".     

Model complexity: The fit to random data reconsidered

A recent controversy in the field of depth perception has highlighted an important aspect of model testing concerning a model's complexity, defined as the prior propensity of the model to fit arbitrary data sets. The present article introduces an index of complexity, called the mean minimum distance, defined as the average squared distance between an arbitrary data point and the prediction range of the model. It may also be expressed as a dimensionless quantity called the scaled mean minimum distance. For linear models, theoretical values for the scaled mean minimum distance and the variance of the scaled minimum distance can be readily obtained and compared against empirical estimates obtained from fits to random data. The approach is applied to resolving the question of the relative complexity of the Linear Integration model and the Fuzzy Logic of Perception model, both of which have been the subject of controversy in the field of depth perception. It is concluded that the two models are equally complex. Received: 10 October 1998 / Accepted: 22 December 1998     

Feeling and believing: the influence of emotion on trust

The authors report results from 5 experiments that describe the influence of emotional states on trust. They found that incidental emotions significantly influence trust in unrelated settings. Happiness and gratitude--emotions with positive valence--increase trust, and anger--an emotion with negative valence--decreases trust. Specifically, they found that emotions characterized by other-person control (anger and gratitude) and weak control appraisals (happiness) influence trust significantly more than emotions characterized by personal control (pride and guilt) or situational control (sadness). These findings suggest that emotions are more likely to be misattributed when the appraisals of the emotion are consistent with the judgment task than when the appraisals of the emotion are inconsistent with the judgment task. Emotions do not influence trust when individuals are aware of the source of their emotions or when individuals are very familiar with the trustee.