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.     

Knowledge of object manipulation and object function: dissociations in apraxic and nonapraxic subjects

An influential account of selective semantic deficits posits that visual features are heavily weighted in the representations of animals, whereas information about function is central in the representations of tools (e.g., Warrington & Shallice, 1984 ). An alternative account proposes that information about all types of objects-animate and inanimate alike-is represented in a distributed semantic architecture by verbal-propositional, tactile, visual, and proprioceptive-motor nodes, reflecting the degree to which these systems were activated when the knowledge was acquired (e.g., Allport, 1985 ). We studied a group of left hemisphere chronic stroke patients, some of whom were apraxic, with measures of declarative tool and animal knowledge, body part knowledge, and function and manipulation knowledge of artifacts. Apraxic (n=7) and nonapraxic (n=6) subjects demonstrated a double dissociation of performance on tests of tool and animal knowledge, suggesting that the apraxic group was not simply more severely impaired overall. Apraxics were relatively impaired in manipulation knowledge, whereas nonapraxics tended to be relatively impaired in function knowledge. Apraxics were also more impaired with body parts than nonapraxics. The association of gestural praxis, tool knowledge, body part knowledge, and manipulation knowledge suggests a coherent basis for the organization of semantic artifact knowledge in frontoparietal cortical regions specialized for sensorimotor functions, and thus provides support for the distributed architecture account of the semantic system.     

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.     

Visual line bisection in sinistrals and dextrals as a function of hemispace, hand, and scan direction

Visual line bisection was investigated in 26 sinistral and 24 dextral subjects as a function of hemispace, hand and scan direction. An ANOVA revealed significant main effects for hand preference, due to the mean bisection errors of dextral subjects being significantly leftward of those of sinistral subjects; for hand, due to the bisection errors of the left hand being significantly to the left of the right hand; and for scan, due to the bisection errors following a left scan being significantly to the left of a right scan. One significant interaction was found, that between hand and direction of scan, due to a significant difference between left and right hands following a scan from the left but not following a scan from the right. For dextral subjects the leftward bisection errors of the left and right hands following a scan from the left, but not for a scan from the right, differed significantly from the midpoint. For sinistral subjects the leftward bisection errors following a scan from the left and rightward bisection errors following a scan from the right differed significantly from the midpoint for the left hand but not for the right hand. No significant main effect or interactions for hemispace were found. This confirms that both sinistral and dextral subjects display pseudoneglect when using their preferred hand and scanning from the left. However, sinistrals, but not dextrals, will display reversed pseudoneglect when using their preferred hand and adopting a scan direction from the right. These results are discussed in terms of the interaction between three factors, whose influence can jointly and severally produce misbisections, hemispheric specialisation for visuospatial function, hemispheric activation for a manual response, and the allocation of visual attention.