A Kripke Semantics for the Logic of Gelfand Quantales

Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem for complete lattices. A Rasiowa/Sikorski style semantic tableau system is also presented with the property that if all branches of a tableau are closed, then the formula in question is a theorem of Gelfand Logic. An open branch in a completed tableaux guarantees the existence of an Kripke model in which the formula is not valid; hence it is not a theorem of Gelfand Logic.     

Minimal p-morphic Images, Axiomatizations and Coverings in the Modal Logic K4

We define the concepts of minimal p-morphic image and basic p-morphism for transitive Kripke frames. These concepts are used to determine effectively the least number of variables necessary to axiomatize a tabular extension of K4, and to describe the covers and co-covers of such a logic in the lattice of the extensions of K4.     

The Development of Family Alliance From Pregnancy to Toddlerhood and Child Outcomes at 5 Years

This article presents a longitudinal study of the development of “family alliance” from pregnancy to toddlerhood in a community sample, as well as its links with the emotional and cognitive development of the child at age 5 years. Family alliance is defined as the quality of the interactive coordination between family members. We consider that the alliance constitutes a context for the child to learn emotion regulation and to develop an understanding of inner states. Family interactions (N = 38) were observed at the 5th month of pregnancy and at 3, 9, and 18 months after birth in a standardized situation of observation (Lausanne Trilogue Play). Marital satisfaction and child temperament were assessed through self‐reported questionnaires. Several outcomes of the child at age 5 years were measured: theory of mind performances, predominant emotional themes in pretend play, internalized and externalized symptoms. Results show that (a) three patterns of evolution of family alliance occur: “high stable” (n = 19), “high to low” (n = 10), and “low stable” (n = 9); (b) a high stable alliance is predictive of better outcomes in children at age 5 years, especially regarding theory of mind; (c) the temperament of the child is predictive of child outcomes; and (d) an interaction effect occurs between family alliance and temperament. These results highlight the importance of both family‐level and individual‐level variables for understanding individual differences in the social and cognitive development of children.     

Changing American Congregations: Findings from the Third Wave of the National Congregations Study

The third wave of the National Congregations Study (NCS‐III) was conducted in 2012. The 2012 General Social Survey asked respondents who attend religious services to name their religious congregation, producing a nationally representative cross‐section of congregations from across the religious spectrum. Data about these congregations were collected via a 50‐minute interview with one key informant from 1,331 congregations. Information was gathered about multiple aspects of congregations’ social composition, structure, activities, and programming. Approximately two‐thirds of the NCS‐III questionnaire replicates items from 1998 or 2006–2007 NCS waves. Each congregation was geocoded, and selected data from the 2010 U.S. Census or American Community Survey have been appended. We describe NCS‐III methodology and use the cumulative NCS dataset (containing 4,071 cases) to describe five trends: more ethnic diversity, greater acceptance of gays and lesbians, increasingly informal worship styles, declining size (but not from the perspective of the average attendee), and declining denominational affiliation.     

Personality measured as Murray’s psychological needs and all-cause mortality: 41 years of follow-up of a population-based sample

ObjectiveTo examine the associations between personality traits, measured as Murray’s psychological needs, and mortality over 41 years.MethodWe used a general population sample aged 18–65 (n = 1094) examined in 1970 according to the Cesarec-Marke Personality Schedule (eleven traits) linked to mortality data. Internal associations were examined using factor analysis, and their associations with mortality using Cox proportional hazard regression models.ResultsDuring follow-up, 513 persons died. In men aged 26–45, achievement and affiliation predicted increased mortality: HR = 1.19, 95% CI 1.04–1.36 and HR = 1.16, 95% CI 1.01–1.33 per step on a stanine scale. In men aged 18–25, nurturance was protective: HR = 0.77, 95% CI, 0.64–0.98 per stanine. In women aged 18–25, feelings of guilt increased the risk of mortality, while dominance was protective: HR = 1.38, 95% CI 1.09–1.75, and HR = 0.74, 95% CI 0.55–0.99 per stanine, respectively. In women aged 46–65, exhibition increased the risk of mortality: HR = 1.09, 95% CI, 1.00–1.18 per stanine. There were no significant associations when all age groups were combined.ConclusionsPersonality traits, measured as Murray’s needs, associated with mortality, but the differed according to age at assessment and sex.     

On the logical structure of de Finetti's notion of event

This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti's conception of events and (ii) suggesting that the subjective nature of de Finetti's interpretation of probability emerges in a clearer form against such a logical background. By making explicit the epistemic structure which underlies what we call Choice-based probability we show that whilst all rational degrees of belief must be probabilities, the converse doesn't hold: some probability values don't represent decision-relevant quantifications of uncertainty.     

BIS- and BAS-activation and study outcomes: A mediation study

Building on Gray’s original Reinforcement Sensitivity Theory, we examined how individual differences in students’ activation of the behavioral inhibition (BIS) and the behavioral approach (BAS) systems relate to overcommitment to one’s studies and study engagement, and how these two forms of heavy study investment relate to three academically relevant outcomes. Using data from 565 Dutch university students, structural equation modeling showed that BIS-activation was positively associated with overcommitment to one’s studies, which in turn was positively related to exhaustion and the intention to quit one’s studies. BAS-activation was positively associated with study engagement, which in turn was negatively related to exhaustion and the intention to quit, and positively related to academic performance. Bootstrapping techniques revealed a mediating role of the two forms of heavy study investment. Apparently, BIS- and BAS-activation are associated with heavy study behavior, student well-being, and study outcomes.     

Pure left neglect for Arabic numerals

Arabic numerals are diffused and language-free representations of number magnitude. To be effectively processed, the digits composing Arabic numerals must be spatially arranged along a left-to-right axis. We studied one patient (AK) to show that left neglect, after right hemisphere damage, can selectively impair the computation of the spatial frames underpinning recognition and understanding of Arabic numerals, without impairing the spatial frames for coding alphabetic strings or for coding environmental spatial information. The presence in our brain of these specific and precise spatial frames must be rooted in the paramount importance of Arabic numerals processing in our everyday activities.     

Between the street and the consulting room: The role of therapeutic frame in working with homeless clients

This paper explores the context of psychotherapy with people who are homeless and the kinds of dynamics and challenges that typically arise in this work. The paper specifically considers the process of therapy as it takes place with clients who have been recurrently homeless and who have difficulties with sustaining shelter that has its roots in deficits in early containment. Clinical case material from psychotherapy conducted with two homeless men is presented and the implications of the approach adopted are explored both in relation to policies around the provision of services for homeless people and the more specific issue of psychotherapy intervention.

It is argued that a clear, well-articulated set of expectations has to be developed around this work in order to protect it and to provide it with the greatest opportunity for providing the kind of safety that is required for the development of this work. It is argued that the most important issue here relates to the provision of a consistent therapeutic framework and a care around the development of the specific psychotherapeutic frame within, and in relation to, the other frames present in the person's life.     

论庄存与的《公羊》学

庄存与的《公羊》学虽然受到赵《春秋属辞》的影响 ,但主要限于治学体例 ,而在治学立场上 ,二者其实有根本的歧异。庄存与克服了赵以策书之体说《春秋》的倾向 ,并注重《春秋》例辞背后的立场。这点直接上承汉代《公羊》学。不过 ,庄氏《春秋》学在某些具体的事例解释上与汉代《公羊》学也有差异。庄氏的特点在于对《春秋》变辞的引申与发挥 ,并补充了汉代《公羊》学未曾论述的诸多方面 ,为后人理解《公羊》大义提供了新的线索。