Syntactic features and synonymy relations: a unified treatment of some proofs of the compactness and interpolation theorems

This paper introduces the notion of syntactic feature to provide a unified treatment of earlier model theoretic proofs of both the compactness and interpolation theorems for a variety of two valued logics including sentential logic, first order logic, and a family of modal sentential logic includingM,B,S ₄ andS ₅. The compactness papers focused on providing a proof of the consequence formulation which exhibited the appropriate finite subset. A unified presentation of these proofs is given by isolating their essential feature and presenting it as an abstract principle about syntactic features. The interpolation papers focused on exhibiting the interpolant. A unified presentation of these proofs is given by isolating their essential feature and presenting it as a second abstract principle about syntactic features. This second principle reduces the problem of exhibiting the interpolant to that of establishing the existence of a family of syntactic features satisfying certain conditions. The existence of such features is established for a variety of logics (including those mentioned above) by purely combinatorial arguments.Presented byMelvin Fitting     

An examination of the cross-ethnic equivalence of measures of negative life events and mental health among Hispanic and Anglo-American children

Recently there has been concern over the need for mental health research within ethnic minority populations, particularly Hispanic populations. Although there has been research focusing upon the similarity of mental health problems among Hispanic and Anglo-American samples, the absence of information regarding the cross-ethnic measurement equivalence of the assessment tools used in these comparisons seriously limits the interpretability of these findings. The two reported studies were designed to (a) examine the cross-ethnic functional and scalar equivalence of several mental health measures by examining the interrelations of these mental health indicators and examining the regression equations using negative life events to predict mental health outcomes; and (b) compare several mental health indicators among Hispanic and Anglo-American 8- to 14-year-old children. Findings suggest considerable cross-ethnic functional and scalar equivalence for the measure of depression, conduct disorders, and negative life events. In addition, findings indicate that the Hispanic children scored higher in depression than did the Anglo-American children, but this difference could be a function of differences in SES. The reader is cautioned that the present samples included only English-speaking and primarily Mexican American children. This study was funded by the National Institute for Mental Health Grant 2-P50-MH39246-06 to support the Preventive Intervention Research Center at Arizona State University. The authors gratefully acknowledge the contributions made by Tim Ayers, Carolyn Berg, Leah Gensheimer, Joanne Gersten, Nancy Groppenbacher, Lisa Jack, Lillian Lengua, Marcia Michaels, Irwin Sandler, and Jerome Short.     

Stress,social support,and problem-solving appraisal/skills: Prediction of suicide severity within a college sample

This study assessed whether stress, social support, and interpersonal problem-solving appraisal/skills were predictive of level of suicidality within a chronic suicidal college sample. Stepwise regression analyses were used to assess whether stress, social support, and problem-solving were independently predictive of severity of suicide ideation. In addition, hierarchical regression analyses were used to test the mediational nature of social support and problem-solving in the stress-suicidality relationship. Problem-solving confidence was found to be a significant predictor of severity of suicide ideation. In addition, both perceived problem-solving skills and social support mediated the relationship between stress and level of suicide ideation. However, only one of the two perceived problem-solving skills interactions was in the expected direction. This study provided support for the importance of problem-solving confidence and the interaction of stress and social support in the prediction of suicide severity. Unlike previous studies, this study did not find problem-solving skills/deficits to mediate the stress-suicidality relationship.This research was supported by NIMH Grant 1-18MH48133.     

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