All Normal Extensions of S5-squared Are Finitely Axiomatizable

We prove that every normal extension of the bi-modal system S5² is finitely axiomatizable and that every proper normal extension has NP-complete satisfiability problem.Presented by Heinrich Wansing     

Some Normal Extensions of K4.3

This paper proves the finite model property and the finite axiomatizability of a class of normal modal logics extending K4.3. The frames for these logics are those for K4.3, in each of which every point has a bounded number of irreflexive successors if it is after an infinite ascending chain of (not necessarily distinct) points.     

Generalizations and Extensions of the Probability of Superiority Effect Size Estimator

Researchers are strongly encouraged to accompany the results of statistical tests with appropriate estimates of effect size. For 2-group comparisons, a probability-based effect size estimator (A) has many appealing properties (e.g., it is easy to understand, robust to violations of parametric assumptions, insensitive to outliers). We review generalizations of the A statistic to extend its use to applications with discrete data, with weighted data, with k > 2 groups, and with correlated samples. These generalizations are illustrated through reanalyses of data from published studies on sex differences in the acceptance of hypothetical offers of casual sex and in scores on a measure of economic enlightenment, on age differences in reported levels of Authentic Pride, and in differences between the numbers of promises made and kept in romantic relationships. Drawing from research on the construction of confidence intervals for the A statistic, we recommend a bootstrap method that can be used for each generalization of A. We provide a suite of programs that should make it easy to use the A statistic and accompany it with a confidence interval in a wide variety of research contexts.     

The Challenge-and-Response Model of Normal Anxiety

This article attempts to provide a conceptual framework placing anxiety in a personal growth perspective. The authors first discuss two different theories of anxiety, review some structural models of anxiety, and stress that anxiety should be studied as a certain kind of relation or interaction between the subject and her stimuli. Then a challenge-and-response model of normal anxiety of its cognitive components is established, which sorts anxiety into heteronomous one and autonomic one, and supposes that heteronomous anxiety includes two dimensions: the fall between the level of external challenge and the level of self challenge, and the importance of the external challenge. Some related evidences for the preceding hypothesis are examined, and then compared with related models. Finally, based on the model, a valid coping strategy of anxiety was put forward, from which the mechanism of normal coping style of anxiety in daily life can be well understood.     

Trauma Recovery in the Transgender and Gender Diverse Community: Extensions of the Minority Stress Model for Treatment Planning

Transgender and gender diverse (TGD) populations, including those that do not identify with gender binary constructs (man or woman) are increasingly presenting for treatment of posttrauma sequelae. Providers who offer services for trauma survivors including posttraumatic stress disorder (PTSD) treatment should be knowledgeable about evidence-based care and have some cultural familiarity with TGD experiences. Indeed, the Minority Stress Model suggests that the combination of distal and proximal minority stressors can combine to produce increased mental health symptoms as compared with cisgender peers, though this model has yet to be fully tested. Clients often present with a complicated picture of experiences, which include a variety of minority stressors, microaggressions, discrimination, and traumatic events that can all be related to their identity. However, conceptualizations of trauma treatment in the context of extensive minority stress are lacking. This paper summarizes the existing literature and offers guidance to mental health providers who are well positioned to address stigma, discrimination, violence, and related symptoms that arise from micro-, mezzo- and macro-level spheres of TGD individuals’ experience.     

A Model of Jury Decisions where all Jurors have the same Evidence

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’.     

Loosely Guarded Fragment of First-Order Logic has the Finite Model Property

We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic.     

All for us and us for all: Introducing the 5R Shared Leadership Program

While most leadership programs seek to develop the leadership qualities of the formal team leader, programs that aim to develop the leadership qualities of team members are rare. This article draws on insights from organisational and sport psychology to develop and introduce a new leadership development program — the 5R Shared Leadership Program (5R^S) — that (1) implements a structure of shared leadership (through Shared Leadership Mapping) and (2) further develops participants’ leadership potential (through the 5R’s of Readying, Reflecting, Representing, Realising, and Reporting). More specifically, being a close intertwinement of shared leadership theorising and the social identity approach to leadership, 5R^S helps leaders in the team to create, embody, advance, and embed a collective sense of ‘us’ in their teams. In this article, we aim to shed light on the underpinning theoretical foundation of 5R^S, while also sharing insights about how 5R^S can be delivered in practice. Furthermore, to provide initial insight into the applicability of 5R^S in both organisational and sport contexts, we conducted a longitudinal qualitative comparison study. This involved collecting qualitative data from two initial implementations: with an organisational team (N = 16) and a sport team (N = 16). A critical reflection on these initial implementations of 5R^S leads to recommendations for future efforts to develop shared leadership in organisational and sporting teams. In particular, we highlight the importance of explaining the nature of shared leadership at the start of the program and of having multiple follow-up sessions for participants. In conclusion, by helping leaders in the team to develop and mobilise a sense of ‘us-ness’, 5R^S gives leaders and their teams the tools to create the best possible version of ‘us’.     

A Deep Inference System for the Modal Logic S5

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms. Presented by Heinrich Wansing     

The Finite Model Property for the Implicational Fragment of IPC Without Exchange and Contraction

The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute a Kripke-style relational semantics for it. The results settle a question of Ono and Komori [OK85]. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to differ considerably from the Chinese text series. Both U.S. texts are computation-dominated, presenting various strategies centering on “breaking apart a factor to perform multiplication.” These strategies limit the use of the DP mainly with whole numbers and in a regular direction. The underlying principle of these strategies is seldom made explicit. In contrast, the Chinese text approaches focus on the underlying principle and are well aligned with cognitive research suggestions. Multiple-step word problems with particular structures are used in a systematic and hierarchic manner across grades to help students learn and transfer the DP. The Chinese texts also tend to ask students to “compute in convenient ways” involving various numbers (e.g., whole numbers, decimals, fractions, and percents) and using the DP in both regular and opposite directions. The introduction of repeated variables is a timely application of the DP, which provides an entry to algebra (e.g., expressions and equations with repeated variables). The Chinese approaches (e.g., contextual interferences, spaced practice, and encoding variability) suggest alternative insights into developing U.S. students’ understanding of the DP and readying them for algebra.     

An Exploratory Model of Quality of Life in the U.S. Navy

Previous quality of life (QOL) modeling efforts using data from U.S. Marine Corps personnel have identified specific domains that were related to Reenlistment Intention, with an overall measure of QOL serving as a mediating variable (Kerce, 1995 Kerce, E. W. (1995). Quality of life in the U.S. Marine Corps (Rep. No. NPRDC–TR–95–4). San Diego: Navy Personnel Research and Development Center. [Google Scholar]; White, Baker, & Wolosin, 1999 White, M. A., Baker, H. G., & Wolosin, D. G. (1999). Quality of life in the Marine Corps: A comparison between 1993 and 1998 (Rep. No. NPRDC–TR–99–1). San Diego: Navy Personnel Research and Development Center. [Google Scholar]). This study examined the validity of applying the Kerce life domains model to U.S. Navy personnel. Structural equation modeling analyses failed to replicate the Kerce model of QOL. Exploratory analyses supported a model similar to Hart (1999) Hart, P. M. (1999). Predicting employee life satisfaction: A coherent model of personality, work and nonwork experiences, and domain satisfactions. Journal of Applied Psychology, 4, 564–584.[Crossref] , [Google Scholar] in which (a) life domains are divided into nonwork, or personal, domains and work domains; (b) personal domains are linked to Reenlistment Intention; and (c) work domains are linked with Reenlistment Intention through organizational commitment.     

On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics.     

The Law of Christ All the Way Down

Abstract:  A reading of Paul and Matthew on Christian obedience suggests that the polemic against 'law' is not directed to all forms of religious practice, but instead only to a particular set of religious practices developed by Israel's sages. Law should not therefore be opposed to grace; instead the correct opposition is between the 'law' taught as the proper way of living before God by the majority of rabbis and the law of Christ, taught by Paul, Matthew and others.