A Cut-Free Sequent System for the Smallest Interpretability Logic

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality . The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + B C implies T + A f(C).The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna's axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88] (see also Hájek and Montagna [HM90] and Hájek and Montagna [HM92]). [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP(cf. de Jongh and Visser [JV91]). The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98].In this paper, we give a cut-free sequent system for IL. To begin with, we give a cut-free system for the sublogic IL4of IL, whose -free fragment is the modal logic K4. A cut-elimination theorem for ILis proved using the system for IK4and a property of Löb's axiom.     

In the worst rather than the best of times: effects of salient intergroup ideology in threatening intergroup interactions

Three studies demonstrated that a salient multicultural ideology increases hostile treatment of threatening outgroup interaction partners. The effect of multiculturalism on hostile behavior was evident regardless of whether threat was operationalized in terms of disagreement with an outgroup partner on important social issues (Studies 1 and 3) or rejection by the partner (Study 2). Moreover, the results clearly point to the learning orientation fostered by multiculturalism--as opposed to other factors such as enhanced other-focus, group-level attributions, or focus on differences--as the critical mediator of its effect on hostile behavior under threat. Thus, it appears that multiculturalism enhances the expression of hostility because it prompts individuals to really engage with and attach meaning and importance to threatening behaviors exhibited by outgroup members. The effects of multiculturalism were distinct from those of anti-racism and color-blindness, which set in motion processes that in many respects are directly opposite to those instantiated by multiculturalism. The findings highlight that the behavioral implications of multiculturalism may be quite different in conflictual interactions than they have previously been demonstrated to be in less threatening exchanges.     

The pitfalls of empathy as a default intergroup interaction strategy: Distinct effects of trying to empathize with a lower status outgroup member who does versus does not express distress

This experiment examined the hypothesis that trying to be empathic during intergroup interaction has positive effects on behavior when an outgroup interaction partner discloses significant hardships and thus expresses a need for support, but negative effects in the absence of a call for help. The results from an ostensible interaction study supported this hypothesis, and revealed that worries regarding negative evaluation partially accounted for the moderating role of partner hardship. Specifically, previous research indicates that trying to be empathic during intergroup interaction prompts individuals to reflect on their own evaluation by their outgroup partner, which for lower-prejudice individuals leads to positive metaperceptions and complacency and for higher-prejudice individuals leads to negative metaperceptions and enhanced effort. In the present study, having the outgroup partner disclose difficulties and distress increased the perceived likelihood of negative evaluation and appeared to trigger stronger efforts to convey positive signals for lower- and higher-prejudice individuals alike.     

Deliberate Self‐Harm in Adolescents Aged 12–18: A Cross‐Sectional Survey of 18,104 Students

Little is known about accurate prevalence and associated factors of deliberate self‐harm (DSH) among adolescents in Asian countries. In this study, the prevalence and associated factors of DSH among adolescents in Japan were examined. Data were derived from a cross‐sectional survey using an anonymous self‐report questionnaire and enrolling 8,620 adolescents aged 12–15 and 9,484 aged 15–18. DSH in the previous 12 months was reported by 3.3% (95% CI, 2.9–3.7) of junior and 4.3% (3.9%–4.7%) of senior high school respondents. The prevalence was more than four times as high among girls as among boys for both age groups. DSH was further strongly associated with having suicidal thoughts, having depression/anxiety symptoms, and having used recreational drugs. These associated factors were similar for both sexes and for both older and younger teenagers. A substantial minority of adolescents present with DSH, even among those aged 12–15. The prevalence of DSH in Japan was in the lower ranges of those reported for Western countries. The identified associated factors were not dissimilar from those reported in the West.