Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀

The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono's Kripke semantics for the predicate version of FL_ew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order.     

Investigation into Combinatory Systems with Dual Combinators

Combinatory logic is known to be related to substructural logics. Algebraic considerations of the latter, in particular, algebraic considerations of two distinct implications (, ), led to the introduction of dual combinators in Dunn & Meyer 1997. Dual combinators are "mirror images" of the usual combinators and as such do not constitute an interesting subject of investigation by themselves. However, when combined with the usual combinators (e.g., in order to recover associativity in a sequent calculus), the whole system exhibits new features. A dual combinatory system with weak equality typically lacks the Church-Rosser property, and in general it is inconsistent. In many subsystems terms "unexpectedly" turn out to be weakly equivalent. The paper is a preliminary attempt to investigate some of these issues, as well as, briefly compare function application in symmetric -calculus (cf. Barbanera & Berardi 1996) and dual combinatory logic.     

Do Positive Self-Perceptions Have a “Dark Side”? Examination of the Link between Perceptual Bias and Aggression

The hypothesis that positive self-perceptions may have a dark side was investigated in the present study by examining the relationship between positively biased self-perceptions and aggression. Ratings of actual and perceived social acceptance of third-grade (n = 278), fourth-grade (n = 260), and fifth-grade (n = 321) students were compared to form a measure of perceptual bias. Peers provided nominations for overt and relational aggression. Gender differences were found for aggression (males were more overtly and relationally aggressive than females) but not perceptual bias. African-American children held more positive perceptions of their social acceptance and were perceived by peers as more aggressive than Caucasian children. Even after controlling for the effects of gender and ethnicity, more positively biased perceptions were associated with more peer nominations for overt and relational aggression. Contrary to an optimal range of bias hypothesis, even moderately positive self-perceptions were associated with elevated levels of aggression.     

Making a Difference: The Social Ecology of Social Transformation

A multidisciplinary and multilevel framework for social transformation is proposed, encompassing four foundational goals: capacity-building, group empowerment, relational community-building, and culture-challenge. Intervention approaches related to each goal are presented at the setting, geographic community, and societal levels. Four exemplars of social transformation work are then discussed: the Accelerated Schools Project, Meyerhoff Program, ManKind Project, and women's movement. These examples illustrate the synergistic relationship among the four transformational goals, within and across levels of analysis, which is at the heart of the social transformation process. The paper concludes with three challenges to guide our efforts as we enter the new century: (1) to move social transformation to the center of our consciousness as a field; (2) to articulate jointly with allied disciplines, organizations, and citizen groups an encompassing, multidisciplinary, and multilevel framework for social transformation; and (3) to do the above with heart, soul, and humility.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

Relational frame theory,acceptance and commitment therapy,and a functional analytic definition of mindfulness

The present article interprets mindfulness from the point of view of the effects of language and cognition on human action. Relational Frame Theory is described to show how human suffering is created by entanglement with the cognitive networks made possible by language. Mindfulness can be understood as a collection of related processes that function to undermine the dominance of verbal networks, especially involving temporal and evaluative relations. These processes include acceptance, defusion, contact with the present moment, and the transcendent sense of self. Each of these components of mindfulness are targeted in Acceptance and Commitment Therapy, and there is some evidence that they underlie the therapeutic changes induced by this approach. The relation between the present approach to mindfulness and other approaches is discussed.     

Psychoanalysis and empirical research

At the beginning of the nineteenth century, the idea of reason began to lose its universal and absolute value, undermining the view of science as a form of objective knowledge that reveals a fundamental reality. These changes have also had an impact on psychoanalysis, leading to a proliferation of theories and the end of a positivistic approach, epitomized by a 'neutral' analyst who knows the contents of the patient's mind. Hermeneutic philosophy provides a tool with which to explore both theoretical multiplicity and the contribution of the analyst's subjectivity to the analytic process. Furthermore, a hermeneutic approach does not have to be hostile to empirical science, but can be integrated with it in a 'scientific-hermeneutic model' in which historical and biological principles are given equal value.     

Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].