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.     

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.     

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.     

Choice and Logic

There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berrys Paradox, Heterologicality, Russells Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and should be replaced with Hilbert and Bernays conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called logic in recent years must be undertaken, to make it more fit for use.Portions of this paper have previously been published in Logical Studies, vol. 9, http://www.logic.ru/LogStud/09/No9-06.html, and the Australasian Journal of Logic, vol. 2, http://www.philosophy.unimelb.edu.au/ajl/2004/2004_4.pdf.     

V.A. Smirnov’s Results in the Field of Modern Formal Logic

This paper is a survey of V.A. Smirnovs main results in modern logic.     

-autonomous Lattices

-autonomous lattices are the algebraic exponentials and without additive constants. In this paper, we investigate the structure theory of this variety and some of its subvarieties, as well as its relationships with other classes of algebras.     

Set-Theoretic Absoluteness and the Revision Theory of Truth

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.     

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.     

Open live supervision in family therapy

This article reviews changes in models of supervision, resulting from technological developments and reflecting a variety of theoretical approaches. The focus is on open live supervision, conducted in the presence of the family. The supervisor and a therapeutic team join the therapist and the family, creating a complex supra-system that opens up several options for therapeutic intervention. Sessions are videotaped, and therapists use recordings for additional supervision and independent study. Therapists may also show recordings to the family as part of the therapeutic process. The advantages and disadvantages of the model are considered, and examples of some of the therapeutic options are described.This model was developed in the course of the author's work teaching and supervising students at the Counseling Department of the School of Education at the Hebrew University of Jerusalem, and supervising a multi-disciplinary team including physicians, psychologists, and social workers engaged in family therapy at the Municipal Psychological Services for Schools in Jerusalem. A shorter version of this article appeared in Hebrew inSihot 5 1991. Appreciation is expressed to Batya Stein for translating the final version of this article from Hebrew. Reprint requests should be addressed to Katrit Ron, Neve Granot 3-B, Jerusalem 93706, Israel.     

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.     

Having a voice and getting a hearing: An educational perspective on free speech in a plural society

This paper examines Ronald Dworkin's claim that the right to free speech does not include a right to circumstances that encourage citizens to speak nor a right to competent and sympathetic understanding on the part of listeners. Drawing on familiar arguments for the existence of other human rights, the paper challenges Dworkin's claim. Even if, however, the challenge fails and it is not possible to show that there is such a right, that is not the end of the story. It is argued that democratic societies should try to foster conditions in which citizens are encouraged to speak and are listened to sympathetically in the interests of the well-being and flourishing of the polity. The important role education has to play in this is explored.     

Bounded contraction and Gentzen-style formulation of Łukasiewicz logics

In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics.Presented by Jan Zygmunt     

Corporal Punishment

This paper examines the reasons why corporal punishment in the judicial sphere has fallen into moral disfavour in recent decades. Standard objections to the practice, both practical and ethical, are considered and found to be inconclusive. It is argued that corporal punishment is not inevitably more cruel or demeaning than conventionally preferred punitive methods and that consideration should be given to its limited experimental reintroduction.     

Unintelligibility or Defeat: The Issue of Engagement in Philosophical Debates

A recognition of the acutely terministic and agonistic character of philosophizing has led to the perception of a dilemma in philosophical debates: differing positions are capable of being maintained only at the expense of mutual unintelligibility, and a real contact of minds could never be achieved without one side of the controversy abandoning its position and the enabling argumentative tension ceasing to exist. This perception is sustainable, however, only if we continue to accept the assumption that a direct, unmediated confrontation between disputants personifying two sets of rigidly defined terms is the mode of philosophical argumentation. A triadic rather than diadic conception of a typical debate between opposing schools of thought, which differentiates between the opponent and the audience, would address the theoretical misgivings caused by the perceived predicament.     

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.     

Players’ Gender and Male Referees’ Decisions About Aggression in French Soccer: A Preliminary Study

The aim of this study was to examine (a) aggression displayed by players and (b) referees decisions about these behaviors as a function of the gender of the players in French soccer. Twenty-six games (13 for women and 13 for men) were videotaped. Instrumental aggressive acts and referees decisions were then observed. The findings indicated a significant effect of gender on instrumental aggression and referees decisions related to these behaviors. Male players displayed more instrumental aggressive acts than female players did. Nevertheless, relative to the total number of aggressive acts displayed, referees penalized women more than men. Gender stereotypes might be a relevant explanation for these results, as soccer is generally perceived as a masculine-type sport, particularly in France, and aggression as a masculine characteristic.     

Students’ knowledge about the value of discussions for teaching and learning

We are particularly interested in looking at teaching and learning from students perspectives. Focussed interviews and written responses from a number of linked investigations with middle-school and tertiary students highlighted that students perceive discussion to be a valuable teaching -- learning technique. This paper provides text extracts, organised into six key themes, to illustrate students understandings about how discussion helps them to learn. We conclude that, across the whole participant group, knowledge about the various potentials of discussion for learning is wide ranging. However, at the individual level, some students perspectives appear limited. We propose that specific attention to enhancing students pedagogical knowledge about techniques such as discussion should accompany subject matter instruction.