Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

Canine neurological diseases in a referral hospital population between 1989 and 2000 in Switzerland

OBJECTIVES: To merge clinical information from partly overlapping medical record databases of the Small Animal Teaching Hospital of the Vetsuisse Faculty, University of Berne. To describe the frequencies and localisations of neurological diseases in dogs, as well as their age, gender, breed and geographical distributions. METHODS: In this retrospective study, a new database, with specific variables and a diagnosis key list 'VITAMIN D', was created and defined. A total of 4497 dogs (average of 375 per year) with a well-documented neurological disease were included in the study. A key list for the diagnoses was developed and applied to either the presumptive or the clinical and neurohistopathological diagnosis, with a serial number, a code for localisation and a code for differential diagnoses. RESULTS: Approximately 1159 dogs (26 per cent) had a neurohistopathological diagnosis confirmed, 1431 (32 per cent) had a clinical diagnosis confirmed and 1491 (33 per cent) had a presumptive diagnosis. The most frequent breeds were mixed-breed dogs (577 of 4497, 13 per cent), followed by German shepherd dogs (466 of 4497, 10 per cent). The most common localisations were the forebrain (908 of 4497, 20 per cent) and the spinal cord at the thoracolumbar area (840 of 4497, 19 per cent). Most dogs were diagnosed with degenerative diseases (38 per cent), followed by inflammatory/infectious diseases (14 per cent). The highest number of submissions originated from geographic regions around the referral hospital and from regions with higher human population densities. CLINICAL SIGNIFICANCE: By defining closed-list fields and allocating all data to the corresponding fields, a standardised database that can be used for further studies was generated. The analysis of this study gives examples of the possible uses of a standardised database.

Plant regeneration directs changes in grassland composition after extreme drought: a 13-year study in southern Switzerland

1. The cover of plant species was recorded annually from 1988 to 2000 in nine spatially replicated plots in a species-rich, semi-natural meadow at Negrentino (southern Alps). This period showed large climatic variation and included the centennial maximum and minimum frequency of days with ≥ 10 mm of rain. 2. Changes in species composition were compared between three 4-year intervals characterized by increasingly dry weather (1988–91), a preceding extreme drought (1992–95), and increasingly wet weather (1997–2000). Redundancy analysis and anova with repeated spatial replicates were used to find trends in vegetation data across time. 3. Recruitment capacity, the potential for fast clonal growth and seasonal expansion rate were determined for abundant taxa and tested in general linear models (GLM) as predictors for rates of change in relative cover of species across the climatically defined 4-year intervals. 4. Relative cover of the major growth forms present, graminoids and forbs, changed more in the period following extreme drought than at other times. Recruitment capacity was the only predictor of species’ rates of change. 5. Following perturbation, re-colonization was the primary driver of vegetation dynamics. The dominant grasses, which lacked high recruitment from seed, therefore decreased in relative abundance. This effect persisted until the end of the study and may represent a lasting response to an extreme climatic event.