Full and hat inductive definitions are equivalent in NBG

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA 0, those in second order set theory extending NBG (as well as those in n + 3-th order number theory extending the so-called Bernays−Gödel expansion of full n + 2-order number theory etc.) are. In this article, we establish the equivalence between Δ10\bf-LFP and Δ10\bf-FP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bf-LFP and Δn+20\bf-FP). Our proof also shows the equivalence between ID 1 and ^ID1, both of which are defined in the standard way but with the starting theory PA replaced by ZFC (or full n + 2-th order number theory with global well-ordering).

Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

Wirksamkeit des Programms "Reasoning and Rehabilitation Revised" für inhaftierte Frauen in der Schweiz - eine Erkundungsstudie

Hintergrund Bei dem revidierten Programm „Reasoning and Rehabilitation“ (R&R2) handelt es sich um einen gruppentherapeutischen Ansatz zur Behandlung spezifischer Probleme von Straftätern. Hier werden erstmals Effekte der deutschsprachigen Version für Mädchen und junge Frauen berichtet. Material und Methode Die Effekte des Gruppentrainings wurden bei 11 inhaftierten Frauen durch standardisierte Fragebogen erfasst. Hierbei interessierten Veränderungen sozial-interpersoneller, motivationaler, psychopathologischer und emotionsregulatorischer Merkmale. Zudem wurden die Zufriedenheit mit der Behandlung und der klinische Eindruck erhoben. Ergebnisse Die erfassten proximalen Effektmaße unterstützen überwiegend die Hypothese einer Wirksamkeit des R&R2 bei Frauen. Das Programm erwies sich als veränderungsinduzierend und wurde gut angenommen. Schlussfolgerung Die Ergebnisse dieser isolierten Evaluation des R&R2-Trainings bei Frauen weisen auf positive Veränderungen spezieller Problembereiche hin. Jedoch werden weiterführende Studien zum intra- und extramuralen Verhalten sowie distalen Rückfälligkeitsmaß benötigt.

Improving self-control by practicing logical reasoning

We tested the hypothesis that practicing logical reasoning can improve self-control. In an experimental training study (N = 49 undergraduates), for one week participants engaged in daily mental exercises with or without the requirement to practice logical reasoning. Participants in the logic group showed improvements in self-control, as revealed by anagram performance after a depleting self-control task. The benefits of the intervention were short-lived; participants in the two groups performed similarly just one week after the intervention had ended. We discuss the findings with respect to the strength model of self-control and consider possible benefits of regular cognitive challenges in education.

Exploring the validity and reliability of a questionnaire for evaluating virtual patient design with a special emphasis on fostering clinical reasoning

Background: Virtual patients (VPs) are increasingly used to train clinical reasoning. So far, no validated evaluation instruments for VP design are available. Aims: We examined the validity of an instrument for assessing the perception of VP design by learners. Methods: Three sources of validity evidence were examined: (i) Content was examined based on theory of clinical reasoning and an international VP expert team. (ii) The response process was explored in think-aloud pilot studies with medical students and in content analyses of free text questions accompanying each item of the instrument. (iii) Internal structure was assessed by exploratory factor analysis (EFA) and inter-rater reliability by generalizability analysis. Results: Content analysis was reasonably supported by the theoretical foundation and the VP expert team. The think-aloud studies and analysis of free text comments supported the validity of the instrument. In the EFA, using 2547 student evaluations of a total of 78 VPs, a three-factor model showed a reasonable fit with the data. At least 200 student responses are needed to obtain a reliable evaluation of a VP on all three factors. Conclusion: The instrument has the potential to provide valid information about VP design, provided that many responses per VP are available.

Predicting the onset of psychosis in patients at clinical high risk: practical guide to probabilistic prognostic reasoning

Prediction of psychosis in patients at clinical high risk (CHR) has become a mainstream focus of clinical and research interest worldwide. When using CHR instruments for clinical purposes, the predicted outcome is but only a probability; and, consequently, any therapeutic action following the assessment is based on probabilistic prognostic reasoning. Yet, probabilistic reasoning makes considerable demands on the clinicians. We provide here a scholarly practical guide summarising the key concepts to support clinicians with probabilistic prognostic reasoning in the CHR state. We review risk or cumulative incidence of psychosis in, person-time rate of psychosis, Kaplan-Meier estimates of psychosis risk, measures of prognostic accuracy, sensitivity and specificity in receiver operator characteristic curves, positive and negative predictive values, Bayes’ theorem, likelihood ratios, potentials and limits of real-life applications of prognostic probabilistic reasoning in the CHR state. Understanding basic measures used for prognostic probabilistic reasoning is a prerequisite for successfully implementing the early detection and prevention of psychosis in clinical practice. Future refinement of these measures for CHR patients may actually influence risk management, especially as regards initiating or withholding treatment.

A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

In this article we study subsystems SIDᵥ of the theory ID₁ in which fixed point induction is restricted to properly stratified formulas.

Computer-based summative assessment of clinical reasoning in clerkships: A mixed-method comparison of key feature problems with case-based multiple choice questions

Background: It is yet unclear if there are differences between using electronic key feature problems (KFPs) or electronic case-based multiple choice questions (cbMCQ) for the assessment of clinical decision making. Summary of Work: Fifth year medical students were exposed to clerkships which ended with a summative exam. Assessment of knowledge per exam was done by 6-9 KFPs, 9-20 cbMCQ and 9-28 MC questions. Each KFP consisted of a case vignette and three key features (KF) using “long menu” as question format. We sought students’ perceptions of the KFPs and cbMCQs in focus groups (n of students=39). Furthermore statistical data of 11 exams (n of students=377) concerning the KFPs and (cb)MCQs were compared. Summary of Results: The analysis of the focus groups resulted in four themes reflecting students’ perceptions of KFPs and their comparison with (cb)MCQ: KFPs were perceived as (i) more realistic, (ii) more difficult, (iii) more motivating for the intense study of clinical reasoning than (cb)MCQ and (iv) showed an overall good acceptance when some preconditions are taken into account. The statistical analysis revealed that there was no difference in difficulty; however KFP showed a higher discrimination and reliability (G-coefficient) even when corrected for testing times. Correlation of the different exam parts was intermediate. Conclusions: Students perceived the KFPs as more motivating for the study of clinical reasoning. Statistically KFPs showed a higher discrimination and higher reliability than cbMCQs. Take-home messages: Including KFPs with long menu questions into summative clerkship exams seems to offer positive educational effects.