Nominal Logic with Equations Only

Many formal systems, particularly in computer science, may be captured by equations modulated by side conditions asserting the "freshness of names"; these can be reasoned about with Nominal Equational Logic (NEL). Like most logics of this sort NEL employs this notion of freshness as a first class logical connective. However, this can become inconvenient when attempting to translate results from standard equational logic to the nominal setting. This paper presents proof rules for a logic whose only connectives are equations, which we call Nominal Equation-only Logic (NEoL). We prove that NEoL is just as expressive as NEL. We then give a simple description of equality in the empty NEoL-theory, then extend that result to describe freshness in the empty NEL-theory.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Nominal Equational Logic

AbstractThis paper studies the notion of “freshness” that often occurs in the meta-theory of computer science languages involving various kinds of names. Nominal Equational Logic is an extension of ordinary equational logic with assertions about the freshness of names. It is shown to be both sound and complete for the support interpretation of freshness and equality provided by the Gabbay-Pitts nominal sets model of names, binding and α-conversion

Sequent Calculus in the Topos of Trees

Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of trees. We show that the semantics of the propositional fragment of this logic can be given by linear converse-well-founded intuitionistic Kripke frames, so this logic is a marriage of the intuitionistic modal logic KM and the intermediate logic LC. We therefore call this logic $\mathrm{KM}_{\mathrm{lin}}$. We give a sound and cut-free complete sequent calculus for $\mathrm{KM}_{\mathrm{lin}}$ via a strategy that decomposes implication into its static and irreflexive components. Our calculus provides deterministic and terminating backward proof-search, yields decidability of the logic and the coNP-completeness of its validity problem. Our calculus and decision procedure can be restricted to drop linearity and hence capture KM.Comment: Extended version, with full proof details, of a paper accepted to FoSSaCS 2015 (this version edited to fix some minor typos

An international evaluation of cognitive reserve and memory changes in early old age in ten European countries

BACKGROUND: Cognitive reserve was postulated to explain individual differences in susceptibility to ageing, offering apparent protection to those with higher education. We investigated the association between education and change in memory in early old age. METHODS: Immediate and delayed memory scores from over 10,000 individuals aged 65 years and older, from 10 countries of the Survey of Health, Ageing and Retirement in Europe (SHARE), were modeled as a function of time in the study over an 8-year period, fitting independent latent growth models (LGM). Education was used as a marker of cognitive reserve and evaluated in associations with memory performance and rate of change, while accounting for income, general health, smoking, body mass index (BMI), sex and baseline age. RESULTS: In most countries, more educated individuals performed better on both memory tests at baseline, compared to those less educated. However, education was not protective against faster decline, except for in Spain for both immediate and delayed recall (0.007 (SE=0.003) & 0.006 (SE=0.002), and Switzerland for immediate recall 0.006 (SE=0.003). Interestingly, highly educated Italian respondents had slightly faster declines in immediate recall (-0.006 (SE=0.003)). CONCLUSIONS: We found weak evidence of a protective effect of education on memory change in most European samples, although there was a positive association with memory performance at individuals' baseline assessment

Two Asymmetries between Clitic Left and Clitic Right Dislocation in Bulgarian

The paper discusses some subtle points of the syntax of clitic left dislocation and clitic right dislocation in Bulgarian

A scoping review on occupational science research in European contexts

Background A survey showed European occupational scientists cover a broad range in occupational science (OS) research, however, no contemporary overviews of European OS research exists, and current research may provide valuable information for OS and occupational therapy. Aim The aim was to provide an overview of contemporary European OS research. Materials and method A scoping review was performed, including studies conducted in Europe and published in the British Journal of Occupational Therapy (BJOT), the Scandinavian Journal of Occupational Therapy (SJOT) or the Journal of Occupational Science (JOS) between 2015 and 2020. The journals were systematically searched, and quality assessment and thematic analysis were undertaken. Results Findings from 93 articles identified many studies from the Nordic countries. Most studies applied qualitative research methods. Theoretical concepts from OS were used in data generating and discussions. A wide range of demographics, and living conditions were explored. Recent articles took a reflexive stance on the positionality of the researcher/s. Conclusions This review highlights the diversity of OS research, suggesting a solid theoretical knowledge base within European OS research. Significance The results contribute to further development and maturation of the discipline of OS in Europe and internationally

On site 2 : Bruce Armstrong, Paul Boston, Alison Clouston, Susan Norrie

On site 2 : Bruce Armstrong, Paul Boston, Alison Clouston, Susan Norrie Catalogue of exhibition held at the Centre for the Arts Gallery, Oct. 17-31, 1986. Works by Bruce Armstrong, Paul Boston, Alison Clouston, Susan Norri

Educational inequalities in aging-related declines in fluid cognition and the onset of cognitive pathology

AbstractBackgroundEducation has been robustly associated with cognitive reserve and dementia, but not with the rate of cognitive aging, resulting in some confusion about the mechanisms of cognitive aging. This study uses longitudinal data to differentiate between trajectories indicative of healthy versus pathologic cognitive aging.MethodsParticipants included 9401 Health and Retirement Study respondents aged ≥55 years who completed cognitive testing regularly over 17.3 years until most recently in 2012. Individual-specific random change-point modeling was used to identify age of incident pathologic decline; acceleration is interpreted as indicating likely onset of pathologic decline when it is significant and negative.ResultsThese methods detect incident dementia diagnoses with specificity/sensitivity of 89.3%/44.3%, 5.6 years before diagnosis. Each year of education was associated with 0.09 (95% confidence interval [CI], 0.087–0.096; P < .001) standard deviation higher baseline cognition and delayed onset of cognitive pathology (hazard ratio, 0.98; 95% CI, 0.96–0.99; P = .006).ConclusionsLongitudinal random change-point modeling was able to reliably identify incident dementia. Accounting for incident cognitive pathology, we find that education predicts cognitive capability and delayed onset pathologic declines