A view of canonical extension

This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties are given. In particular, they are doubly algebraic lattices and their interval topologies agree with their double Scott topologies and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi Symposium on Language, Logic and Computation Bakuriani, Georgia, September 21-25 200

Monotonic Distributive Semilattices

In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; ArgentinaFil: Menchón, María Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

PROFILES OF RECREATIONAL ACTIVITIES OF DAILY LIVING (RADL) IN PATIENTS WITH MENTAL DISORDERS

Background: Activities of daily living, play a key role in the measurement of functional health as defined by the International Classification of Functioning, Disability and Health (ICF) and in prevention and treatment of mental or somatic illnesses. From a clinical context it is important to discriminate between basic “activities of daily living, ADL”, “intentional activities of daily living, IADL”, and “recreational activities of daily living, RADL”. While ADL and IADL have gained much attention in dementia, the elderly, or severe somatic illnesses, there is a lack of research on RADL, which are important in depression, anxiety, or other neurotic disorders. Subjects and methods: 154 unselected inpatients of a department of behavioral and psychosomatic medicine filled in the “Check List of Recreational Activities” to assess the rates and profiles of RADL. Results: Patients reported on average 19.3 (s.d. 7.0) activities (range 4 – 40), i.e. males 21.3 (s.d. 6.5, 9 – 34) and females 18.9 (s.d. 7.1, 4 – 40). Most frequent RADL were passive and unspecific activities like “watching tv” (93.4%). Least frequent were activities which need special skills or preparation like ”horse back riding” (0.7%). Low rates were also found for activities which are in the centre of inpatient occupational therapy like “ceramics” (4.7%) or “silk-painting” (2.6%). There are differences between sexes but not in respect to age (18 to 60), sick leave and unemployment, or diagnostic status. When patients were asked what they would like to do in the future, the same activity profile emerged as when looking at what they had done in the last month Conclusion: The data give a reference profile for recreational activities, help to define what can be considered a normal frequency and spectrum of RADL, and, by this, can guide therapeutic interventions

Can the palatability of healthy, satiety-promoting foods increase with repeated exposure during weight loss?

Repeated exposure to sugary, fatty, and salty foods often enhances their appeal. However, it is unknown if exposure influences learned palatability of foods typically promoted as part of a healthy diet. We tested whether the palatability of pulse containing foods provided during a weight loss intervention which were particularly high in fiber and low in energy density would increase with repeated exposure. At weeks 0, 3, and 6, participants (n = 42; body mass index (BMI) 31.2 ± 4.3 kg/m²) were given a test battery of 28 foods, approximately half which had been provided as part of the intervention, while the remaining half were not foods provided as part of the intervention. In addition, about half of each of the foods (provided as part or not provided as part of the intervention) contained pulses. Participants rated the taste, appearance, odor, and texture pleasantness of each food, and an overall flavor pleasantness score was calculated as the mean of these four scores. Linear mixed model analyses showed an exposure type by week interaction effect for taste, texture and overall flavor pleasantness indicating statistically significant increases in ratings of provided foods in taste and texture from weeks 0 to 3 and 0 to 6, and overall flavor from weeks 0 to 6. Repeated exposure to these foods, whether they contained pulses or not, resulted in a ~4% increase in pleasantness ratings. The long-term clinical relevance of this small increase requires further study.T32 AT000815 - NCCIH NIH HH

Chapter 19: Vulnerability of coastal and estuarine habitats in the Great Barrier Reef to climate change

This chapter attempts to address the vulnerability of the CEM in the Great Barrier Reef region to global climate change. It does not consider individual habitats (eg reefs or seagrasses) but goes beyond the individual species and habitat assessments, to consider impacts on the whole coastal marine community complex, and the ecological processes that support its functioning.This is Chapter 19 of Climate change and the Great Barrier Reef: a vulnerability assessment. The entire book can be found at http://hdl.handle.net/11017/13

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

The Role of Geography in the Information Economy: The Case of Multimedia

In der Diskussion um die Zukunft der Arbeit in der Informationsgesellschaft findet sich sehr häufig die Ansicht vertreten, dass durch die rapide fortschreitende Globalisierung wirtschaftliche Strukturen und Abläufe zunehmend enträumlicht werden und ihre regionale Einbettung immer mehr an Bedeutung verliert. Der Beitrag versucht diese Behauptung zu relativieren. Er tut dies beispielhaft mittels einer Analyse der Multimedia-Industrie. Untersucht wird die räumliche Verteilung der Multimedia-Produzenten sowie die Unternehmens- und Beschäftigungsstrukture

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201