Finite axiomatization for some intermediate logics

LetN. be the set of all natural numbers (except zero), and letD _n ^* = {k ∈N ∶k|n} ∪ {0} wherek¦n if and only ifn=k.x f or somex∈N. Then, an ordered setD _n ^* = 〈D _n ^* , ? _n , wherex? _ny iffx¦y for anyx, y∈D _n ^* , can easily be seen to be a pseudo-boolean algebra. In [5], V.A. Jankov has proved that the class of algebras {D _n ^* ∶n∈B}, whereB =,{k ∈N∶ ? \(\mathop \exists \limits_{n \in N} \) (n > 1 ≧n ² k)is finitely axiomatizable. The present paper aims at showing that the class of all algebras {D _n ^* ∶n∈B} is also finitely axiomatizable. First, we prove that an intermediate logic defined as follows: $$LD = Cn(INT \cup \{ p_3 \vee [p_3 \to (p_1 \to p_2 ) \vee (p_2 \to p_1 )]\} )$$ finitely approximatizable. Then, defining, after Kripke, a model as a non-empty ordered setH = 〈K, ?〉, and making use of the set of formulas true in this model, we show that any finite strongly compact pseudo-boolean algebra ? is identical with. the set of formulas true in the Kripke modelH _B = 〈P(?), ?〉 (whereP(?) stands for the family of all prime filters in the algebra ?). Furthermore, the concept of a structure of divisors is defined, and the structure is shown to beH D _n ^* = 〈P (D _n ^* ), ?〉for anyn∈N. Finally, it is proved that for any strongly compact pseudo-boolean algebraU satisfying the axiomp ₃∨ [p ₃→(p₁→p₂)∨(p₂→p₁)] there is a structure of divisorsD _* ⁿ such that it is possible to define a strong homomorphism froomiH D _n ^* ontoH D _U . Exploiting, among others, this property, it turns out to be relatively easy to show that \(LD = \mathop \cap \limits_{n \in N} E(\mathfrak{D}_n^* )\) .     

Construct validation of the Narcissistic Admiration and Rivalry Questionnaire in Spanish-speaking countries: Assessment of the reliability,structural and external validity and cross-cultural equivalence

A recent re-operationalisation of grandiose narcissism has resulted in the distinction of two narcissistic strategies based on the cognitive, affective-motivational and behavioural dynamics: admiration (assertive self-enhancement) and rivalry (antagonistic self-protection). The Narcissistic Admiration and Rivalry Questionnaire (NARQ) was developed to assess this model with two higher-order dimensions. However, cross-validations of the NARQ have not been extensively conducted across diverse population groups and languages. This study aimed to test the internal and external validity (through the relation with envy and self-esteem), reliability and cross-cultural equivalence of the Spanish version of the NARQ. The psychometric properties were evaluated in a Spanish sample (N = 310), and cross-cultural equivalence was tested in participants from Chile (N = 234) and Colombia (N = 256). The results supported the reliability and validity of the Spanish NARQ, as well as the cross-cultural equivalence across Spanish-speaking countries. In addition, we discuss obtained differences across Spanish, Chilean and Colombian sample within two narcissistic strategies.     

Cross-Cultural Sexism and the Effectiveness of Gender (Non)Traditional Advertising: A Comparison of Purchase Intentions in Poland,South Africa,and the United Kingdom

Findings regarding the effectiveness of (non)traditionally gendered advertisements are mixed and largely emanate from the United States. We tested the stereotype content model and ambivalent sexism theory cross-nationally in an advertising context and predicted that paternalistic (vs. envious) female stereotypes will trigger higher purchase intent (PI) irrespective of country (Hypothesis 1), viewers’ benevolent sexism will positively predict PI for paternalistic housewife advertisements (Hypothesis 2a), viewers’ hostile sexism will negatively predict PI for envious businesswoman advertisements (Hypothesis 2b), and these relationships with sexism will be confined to less gender egalitarian countries (i.e., Poland and South Africa) (Hypothesis 3). Statistical analyses of data from 468 Polish, South African, and British university students supported Hypothesis 1 and partially supported Hypotheses 2 and 3. The predicted patterns held for South Africa, but in Poland, viewers’ benevolence positively predicted PI for both advertisement types, with the exception of highly hostile women. British viewers’ hostility positively predicted PI for the housewife advertisement. Our findings support the cross-cultural applicability of the stereotype content model to advertising and suggest that the predictive role of sexism changes depending on its type, advertisement type, country, and gender. We recommend that advertisers should adopt a nuanced approach in predicting the effectiveness of gendered advertisements.     

Validating the coping scale for Chinese athletes using multidimensional Rasch analysis

Objective

The Coping Scale for Chinese Athletes (CSCA) was developed and validated using classic testing theory in 2004 (Chung, Si, Lee, & Liu, 2004). This study aimed to validate CSCA using multidimensional Rasch analysis with the ConQuest software programme.

Method

The sample in this study comprised 367 athletes from mainland China. A Multidimensional Rating Scale model was applied to investigate the validity of the four-dimension scale. Standard fit statistics (Infit and Outfit MNSQ) and Differential item functioning (DIF) were computed to examine the model-data fit. Test reliability and category functioning were also checked.

Results

The item difficulty and the athletes’ trait level of coping were calibrated along the same latent trait scale. Three items were removed from the scale due to misfit with the Rasch model. No DIF across gender was found for the remaining 21 items. Test reliabilities for the four subscales ranged from 0.66 to 0.76. The results also indicated that the original 5-category rating scale structure did not function well.

Conclusion

The multidimensional Rasch analysis supported that the 21-item CSCA measures four latent traits of coping of Chinese athletes as expected. The results also demonstrated advantages of multidimensional Rasch analysis over unidimensional Rasch analysis as well as traditional approach in examining the quality of multidimensional scale in sport settings.     

The bystander-effect: a meta-analytic review on bystander intervention in dangerous and non-dangerous emergencies

Research on bystander intervention has produced a great number of studies showing that the presence of other people in a critical situation reduces the likelihood that an individual will help. As the last systematic review of bystander research was published in 1981 and was not a quantitative meta-analysis in the modern sense, the present meta-analysis updates the knowledge about the bystander effect and its potential moderators. The present work (a) integrates the bystander literature from the 1960s to 2010, (b) provides statistical tests of potential moderators, and (c) presents new theoretical and empirical perspectives on the novel finding of non-negative bystander effects in certain dangerous emergencies as well as situations where bystanders are a source of physical support for the potentially intervening individual. In a fixed effects model, data from over 7,700 participants and 105 independent effect sizes revealed an overall effect size of g = -0.35. The bystander effect was attenuated when situations were perceived as dangerous (compared with non-dangerous), perpetrators were present (compared with non-present), and the costs of intervention were physical (compared with non-physical). This pattern of findings is consistent with the arousal-cost-reward model, which proposes that dangerous emergencies are recognized faster and more clearly as real emergencies, thereby inducing higher levels of arousal and hence more helping. We also identified situations where bystanders provide welcome physical support for the potentially intervening individual and thus reduce the bystander effect, such as when the bystanders were exclusively male, when they were naive rather than passive confederates or only virtually present persons, and when the bystanders were not strangers.