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.     

Encoding Modal Logics in Logical Frameworks

We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert- and Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed -calculus metalanguage of the Logical Frameworks. These formalizations yield readily proof-editors for Modal Logics when implemented in Proof Development Environments, such as Coq or LEGO.     

The application of the satir model of family therapy to the families in Hong Kong: A personal reflection

Practitioners in Hong Kong have shown an increasing interest in various family therapy approaches since the 1980s. This paper offers a critique of the major concepts and techniques of the Satir model applied to families in Hong Kong. Cultural considerations are examined in relation to the family structure and hierarchy, the Chinese self and self-esteem, communication patterns, and family rules. Implications for the application of the Satir model of family therapy in Hong Kong are discussed.     

Lambda Calculus and Intuitionistic Linear Logic

The introduction of Linear Logic extends the Curry-Howard Isomorphism to intensional aspects of the typed functional programming. In particular, every formula of Linear Logic tells whether the term it is a type for, can be either erased/duplicated or not, during a computation. So, Linear Logic can be seen as a model of a computational environment with an explicit control about the management of resources.This paper introduces a typed functional language ! and a categorical model for it.The terms of ! encode a version of natural deduction for Intuitionistic Linear Logic such that linear and non linear assumptions are managed multiplicatively and additively, respectively. Correspondingly, the terms of ! are built out of two disjoint sets of variables. Moreover, the -abstractions of ! bind variables and patterns. The use of two different kinds of variables and the patterns allow a very compact definition of the one-step operational semantics of !, unlike all other extensions of Curry-Howard Isomorphism to Intuitionistic Linear Logic. The language ! is Church-Rosser and enjoys both Strong Normalizability and Subject Reduction.The categorical model induces operational equivalences like, for example, a set of extensional equivalences.The paper presents also an untyped version of ! and a type assignment for it, using formulas of Linear Logic as types. The type assignment inherits from ! all the good computational properties and enjoys also the Principal-Type Property.     

A fallacy of aristotle''s about ends

A distinction between activities and processes plays an important role in Aristotle's argument to establish that the good life is a life of activities, among which metaphysical contemplation is foremost. But, as a result of having failed to distinguish internal from external ends of action, Aristotle makes fallacious inferences from every activity's having an internal end in itself to its possessing features which may be legitimately inferred only from external ends, and from every process's having an internal end that is its terminal point to its having the attainment of that terminal point as an external end. The resulting confusion explains a number of problematic elements in Aristotle's ethical theory.     

Treating the “Wise Baby”

In a previous examination of Ferenczis concept of the Wise Baby (1996), I had noted both its applications and its limitations in the analytic treatment of an unusually intelligent adult. Ferenczis concepts of the origin of intellect in trauma and of the wise baby have often left the indistinct impression of being interrelated phenomena. In this paper, I regard as arguable the notion that very high intelligence is pathological when it is precocious. This return visit to the territory of the wise baby extends Ferenczis ideas about the origin and use of the intellect to include a consideration of what may constitute effective treatment for those who suffer from giftedness.Judith E. Vida, M.D. edits On the Arts for this journal. She is a Founding Member and Faculty of the Institute of Contemporary Psychoanalysis in Los Angeles, CA, a member of both American and International Psychoanalytic Associations, and of the Sándor Ferenczi Society of Budapest. Her private practice is in Pasadena, CA.Address correspondence to Judith E. Vida, 301 S. Fair Oaks Ave., Suite 406A, Pasadena, CA 91105, USA; e-mail: jvida@spence.net     

The Impact of ‘the Dream’ on Women's Experience of the Midlife Transition

Daniel Levinson's claim for the universality of age-linked periods is considered highly controversial considering that his theory evolved from a study consisting of males only. Theories relating to women's development, particularly at midlife, are somewhat scarce and restricted. Using Levinson's theory of adult development as a framework, the present study retrospectively examined the Dream and its impact on women's psychological health and adjustment to the Midlife Transition. Three hundred midlife women completed a questionnaire examining Dream Status, Dream Content, Dream Success, and the psychological health variables, depression, anxiety, self-esteem, and life satisfaction. Dream Success was significantly related to psychological health on dimensions of well-being and composure, and interesting changes were observed in Dream Content across the early and current Dream. Our findings revealed that, despite the overall greater complexity of women's Dreams, Levinson's theory is largely applicable to women's development.     

Semantics for Dual and Symmetric Combinatory Calculi

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical– relational and operational – semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.     

Lordship, Bondage, and the Formation of Homo Religiosus

After a brief exploration of Hegel's writing on the formation of self-consciousness, including the place of religiosity in this formation, the article examines Kojeve's response to a Hegelian homo religiosus, followed by a counter-response to Kojeve's atheism through a peculiar, Jaspersian reading of Erich Fromm's discussion of the x experience. Finally, it will be argued that the desire for mutual recognition, and humanity's yearning for transcendence, are essential experiences in the formation of self-consciousness.     

A narwhal is an animal: partial word knowledge biases adults' decisions

Adults' accuracy on a sentence verification task was measured to assess reliable biases in their responses as a function of their level of knowledge about the target words, as well as adults' ability to reject incorrect ontological category membership for their partially known words. Three levels of word knowledge (known, frontier, and unknown) were assessed in two experiments. Results indicated that participants were conservative decision-makers about sentences using the vocabulary words and that the conservative bias increased in strength as their level of knowledge about the target word increased. When biased guessing was discouraged, results indicated that participants were able to accurately identify both correct and incorrect sentences using targets at all three levels of knowledge, including their partially known words, but were least reliable at rejecting false sentences using unknown targets. Implications for the role of knowing not in adults' vocabulary acquisition are discussed.     

Bringing “The Dead” to Life: Reading James Joyce

The author offers a personal reading of James Joyce's The Dead. She focuses on how the sounds of the language are used to portray the main character's deadness and his beginning to come to life once the barriers to inner self and self-knowledge are broken.     

Measuring Inconsistency

I provide a method of measuring the inconsistency of a set of sentences – from 1-consistency, corresponding to complete consistency, to 0-consistency, corresponding to the explicit presence of a contradiction. Using this notion to analyze the lottery paradox, one can see that the set of sentences capturing the paradox has a high degree of consistency (assuming, of course, a sufficiently large lottery). The measure of consistency, however, is not limited to paradoxes. I also provide results for general sets of sentences.     

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...