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.     

Der “dritte Weg” der “neo-eurasischen” Zeitschrift “Elementy” -- zurück ins Dritte Reich?

Studies in East European Thought - Articulated in the twenties, the doctrines of the exiled Russian ‘Evrazijstvo’ movement are undergoing a renaissance in Russia today. As the...     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

The Suspended Aesthetic: Slavoj Žižek on Eastern European Film

Slavoj iek's writings on Krzysztof Kies´lowski and Andrej Tarkovskij represent direct challenges to the Central and Eastern European tradition of spiritual art and to dominant aesthetic concepts as such. He refuses to separate the solemn films of Kies´lowski and Tarkovskij from popular culture and stresses their import as ethical statements by their directors. Despite this ethical emphasis, iek makes an important contribution to philosophical aesthetics. He implicitly defines art as a suspension of reality which reveals time in its fragility and potentiality. Defining iek's aesthetics in terms of suspension helps to explain his partiality for Kies´lowski and Tarkovskij and bears comparison to the Russian tradition of philosophical aesthetics, in particular Aleksej Losev and Alexander Bakshy.     

On Alternative Geometries,Arithmetics, and Logics; a Tribute to Łukasiewicz

The paper discusses the similarity between geometry, arithmetic, and logic, specifically with respect to the question of whether applied theories of each may be revised. It argues that they can - even when the revised logic is a paraconsistent one, or the revised arithmetic is an inconsistent one. Indeed, in the case of logic, it argues that logic is not only revisable, but, during its history, it has been revised. The paper also discusses Quine's well known argument against the possibility of logical deviancy.     

Style in Philosophy: Part I

In this article, I attempt to restore the philosophical significance of that nonformalizable, noniterable, "singular' element of natural language that I call "style." I begin by critically addressing the exclusion of such instances of natural language by both semantics-oriented logical analysis and a restricted variation of structuralist linguistics. Despite the obvious advantages – with regard to style – of "pragmatic"approaches to language, such pragmatism merely returns to rule-determination in the guise of "normativity." Although style by definition resists any kind of rule-determination – whether posed in terms of semantics or intersubjective regulations of speech-acts – there can be no consideration of language that ignores the persistence of style in natural language. In terms of cognition, any discursive agent understands more than allowed by either semantics or speech-act theory. I ascribe this element of excessive signification to the role of style. My principal thesis is twofold: (1) a hermeneutic approach (exemplified by Schleiermacher) to literature should reveal the heuristically decisive role played by style in philosophy; and, more radically still, (2) style, in fact, may be crucially determinative of philosophical discourse in general. I suggest that a closer scrutiny of the lesser-known works of Ludwig Wittgenstein, conventionally regarded as having dreamt of a "philosophy without style," may consolidate the restoration of style's philosophical import.     

Reducing reactive aggression in schoolchildren through child,parent, and conjoint parent‐child group interventions: An efficacy study of longitudinal outcomes

This study was the first to evaluate the effectiveness of three different group interventions to reduce children's reactive aggression based on the social information processing (SIP) model. In the first stage of screening, 3,734 children of Grades 4–6 completed the Reactive–Proactive Aggression Questionnaire (RPQ) to assess their reactive and proactive aggression. Respondents with a total score of z ≥ 1 on the RPQ were shortlisted for the second stage of screening by qualitative interview. Interviews with 475 children were conducted to select those who showed reactive aggression featuring a hostile attributional bias. Finally, 126 children (97 males and 29 females) aged 8 to 14 (M = 9.71, SD = 1.23) were selected and randomly assigned to one of the three groups: a child group, a parent group, and a parent–child group. A significant Time × Intervention effect was found for general and reactive aggression. The parent–child group and child group showed a significant drop in general aggression and reactive aggression from posttest to 6‐month follow‐up, after controlling for baseline scores, sex, and age. However, the parent group showed no treatment effect: reactive aggression scores were significantly higher than those in the child group at 6‐month follow‐up. This study has provided strong evidence that children with reactive aggression need direct and specific treatment to reconstruct the steps of the SIP involving the selection and interpretation of cues. The intervention could help to prevent severe violent crimes at the later stage of a reactive aggressor.     

Stepfamilies Doing Family: A Meta‐Ethnography

The present review examines how stepfamily members without a shared history co‐construct a shared family identity and what family processes are relevant in this stepfamily formation. Three databases (Web of Science, PsycInfo, and ProQuest) were systematically searched, resulting in 20 included qualitative studies. The meta‐ethnography approach of Noblit and Hare allowed synthesizing these qualitative studies and constructing a comprehensive framework of stepfamilies doing family. Three interdependent family tasks were identified: (a) honoring the past, (b) marking the present, and (c) investing in the future. Stepfamily members’ experiences of these family tasks are strongly affected by the dominant societal perspectives and characterized by an underlying dialectical tension between wanting to be like a first‐time family and feeling the differences in their family structure at the same time. These findings clearly demonstrate the family work that all stepfamily members undertake and provide a broader context for interpreting stepfamilies’ co‐construction of a new family identity.