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.     

On Modal μ-Calculus and Non-Well-Founded Set Theory

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal -calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.     

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.     

Young children's sensitivity to probabilistic phonotactics in the developing lexicon

A series of three experiments examined children's sensitivity to probabilistic phonotactic structure as reflected in the relative frequencies with which speech sounds occur and co-occur in American English. Children, ages 212 and 312 years, participated in a nonword repetition task that examined their sensitivity to the frequency of individual phonetic segments and to the frequency of combinations of segments. After partialling out ease of articulation and lexical variables, both groups of children repeated higher phonotactic frequency nonwords more accurately than they did low phonotactic frequency nonwords, suggesting sensitivity to phoneme frequency. In addition, sensitivity to individual phonetic segments increased with age. Finally, older children, but not younger children, were sensitive to the frequency of larger (diphone) units. These results suggest not only that young children are sensitive to fine-grained acoustic-phonetic information in the developing lexicon but also that sensitivity to all aspects of the sound structure increases over development. Implications for the acoustic nature of both developing and mature lexical representations are discussed.     

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).     

The "what" and "where" of object representations in infancy

Four-month-olds' memory for surface feature and location information was tested following brief occlusions. When the target objects were images of female faces or monochromatic asterisks infants showed increased looking times following a change in identity or color but not following a change in location or combinations of feature and location information. When the target objects were images of manipulable toys, the infants showed increased looking times following a change in location but not identity or the binding of location and identity information. This evidence is consistent with the idea that young infants are unable to maintain the information processed separately in both the dorsal and ventral visual streams during occlusions. Our results suggest that it is the target's affordance for action that determines whether the dorsal or ventral information is selectively maintained during occlusion.     

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.     

The Role of Creativity in Marriage and Family Therapy Practice: A National Online Study

The purpose of this study, using an online methodology, was to investigate therapists' perceptions of the role of creativity in couples' and family therapy. Along with completing a quantitative measure assessing creativity in their work, participants responded to four open-ended questions which addressed the meaning of creativity, characteristics of a creative family therapist, some creative interventions they have used with couples and families, and barriers to their own creativity as a family therapist. A total of 142 marriage and family therapists in 36 states in the United States participated. The findings shed light on the unique importance of creativity in couples and family treatment.