On Łukasiewicz's Four-Valued Modal Logic

ukasiewicz's four-valued modal logic is surveyed and analyzed, together with ukasiewicz's motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz's own texts, and related literature.     

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.     

Free Łukasiewicz and Hoop Residuation Algebras

Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops).     

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     

Embedding Logics into Product Logic

We construct a faithful interpretation of ukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable.We prove a completeness theorem for product logic extended by a unary connective of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic.We also prove NP-completeness of the set of propositional formulas satisfiable in product logic (resp. in Gödel's logic).     

Fuzzy Logic and Arithmetical Hierarchy III

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.     

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.     

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...     

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.     

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.     

“The Dead”

Gabriel Conroy, central to James Joyce's novella, The Dead, keys the reader's experience of the evening portrayed. A third-person narration allows for distance, but Gabriel's closely depicted thought processes and actions, and his insistent self-consciousness, shape the story. As such they invite psychoanalytic interpretation and reward it. Gabriel's shocking discovery and reaction to it can be seen to be informed by rendered psychodynamics and a credible internalized past. Joyce and Freud, actual contemporaries, can be seen as contemporaneous in imagination as well.     

Remarks on Gregory's “Actually” Operator

In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing actually operators, Journal of Philosophical Logic 30(1): 57–78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an actually operator with the work of Arthur Prior now known under the name of hybrid logic. This analysis relates the actually axioms to standard hybrid axioms, yields the decidability results in [8], and provides a number of complexity results. Finally, we use a bisimulation argument to show that the hybrid language is strictly more expressive than Gregory's language.     

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.     

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.     

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.     

Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators

The addition of actually operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing actually operators has concentrated entirely upon extensions of KT5 and has employed a particular model-theoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing actually operators, the weakest of which are conservative extensions of K, using a novel generalisation of the standard semantics.     

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.     

Gender Role Stereotyping of Parents in Children’s Picture Books: The Invisible Father

Previous studies reveal the reinforcement of gender stereotypes by picture books children read during the formative years. In these books, boys tend to be portrayed as active leaders, and girls as passive followers. Women and girls are under-represented. Men often exhibit career skills, and women perform traditional tasks in the home. Even when careers are nontraditional, personality characteristics and other qualities and behaviors are often stereotypical. Previous researchers emphasized the narrowly defined roles of women and children in picture books. In this study, we focused on the representation of mothers and fathers, and examined whether men are stereotyped as relatively absent or inept parents. A content analysis of the gender roles exhibited in 200 prominent childrens picture books demonstrated that fathers are largely under-represented, and, when they do appear, they are withdrawn and ineffectual parents. Further research could establish whether seriously deficient models of fatherhood in childrens literature affect the incidence of present, caring fathers in society.