Extensions to the Estimation Calculus

Walther’s estimation calculus was designed to prove the termination of functional programs, and can also be used to solve the similar problem of proving the well-foundedness of induction rules. However, there are certain features of the goal formulae which are more common to the problem of induction rule well-foundedness than the problem of termination, and which the calculus cannot handle. We present a sound extension of the calculus that is capable of dealing with these features. The extension develops Walther’s concept of an argument bounded function in two ways: firstly, so that the function may be bounded below by its argument, and secondly, so that a bound may exist between two arguments of a predicate. Our calculus enables automatic proofs of the well-foundedness of a large class of induction rules not captured by the original calculus

Predictors of successful ageing: findings from the longitudinal follow-up of the Lothian Birth Cohort 1921

The progressive ageing of the world's population implies that any age-associated deterioration will become ever more prevalent. Some individuals can be identified as ageing more 'successfully' than their peers; the maintenance of mental abilities in old age is one marker of this. Isolating modifiable determinants of cognitive ageing is therefore a research priority. Factors from the domains of work, social support networks and activity participation were examined in an ageing group retrospectively and contemporaneously. Aged 11, these individuals had taken a test of mental ability (the Moray House Test: MHT) as part of the 1932 Scottish Mental Survey. Some 550 survivors were recruited -79 years old into a longitudinal study of cognitive ageingthe Lothian Birth Cohort 1921-when they again took the MHT, plus a battery of tests (Raven's Progressive Matrices, Verbal Fluency and Logical Memory). A 2nd wave of testing was completed at -83 years old. Over the 4 years of follow-up, significant decline was observed in cognitive ability (composite of the 3 tests) and separately for Raven's and Verbal Fluency, but not for Logical Memory. In regression analyses, higher cognitive ability at age 79 assessed by the MHT (expressed as age-79 IQ) was predicted by less hazardous working conditions, a quieter working environment and receiving more supervisor support; living with a spouse/partner for a fewer number of years in young adulthood and having fewer close friends/relatives in old age; and increased activity in midlife and old age. Each factor explained about 1% to 3% of the variance, independent of age-11 IQ and sex. Less cognitive decline from 79 to 83 years old (on the general ability composite) was associated with increased support from coworkers and walking (versus not) at age 80, each accounting for about 2% of the variance (independent of age-11 IQ and sex). When the analyses were pooled across lifestyle domains and further potential confounders (including education, social class, depression and disease history) were controlled, measures of the hazards encountered at work and lifetime activity participation each accounted for 1% to 3% of the variance in age-79 IQ, whilst walking accounted for about 2% of the variance in later life cognitive change. Inactivity in midlife and a lack of exercise in old age are plausible risk factors for cognitive decline. They are, fortunately, potentially malleable; promoting activity may offer pathways to improved cognitive ageing

Occupational complexity and lifetime cognitive abilities

OBJECTIVE: To examine associations between complexity of main lifetime occupation and cognitive performance in later life. METHODS: Occupational complexity ratings for data, people, and things were collected from the Dictionary of Occupational Titles for 1,066 individuals (men = 534, women = 532) in the Lothian Birth Cohort 1936. IQ data were available from mean age 11 years. Cognitive ability data across the domains of general ability, processing speed, and memory were available at mean age 70 years. RESULTS: General linear model analyses indicated that complexity of work with people and data were associated with better cognitive performance at age 70, after including age 11 IQ, years of education, and social deprivation. CONCLUSIONS: The current findings are supportive of the differential preservation hypotheses that more stimulating environments preserve cognitive ability in later life, although the continued effects into old age are still debated. Studies that have early-life cognitive ability measures are rare, and the current study offers interesting prospects for future research that may further the understanding of successful aging

Leisure activity associated with cognitive ability level, but not cognitive change

Although activity participation is promoted as cognitively-protective, critical questions of causality remain. In a cohort followed every five years from age 75 to 85 years, potential reciprocal associations between level and change in leisure activity participation and level and change in cognitive abilities were examined. Participants in the Glostrup 1914 Cohort, a longitudinal study of ageing, completed standardised cognitive ability tests and reported their leisure activity participation (11 activities defined a leisure activity score) at ages 75, 80 and 85. Higher leisure activity was associated with higher cognitive ability (significant correlations ranged from .15 to .31, p < .05). Between ages 75 and 85, participation in leisure activities and cognitive ability declined significantly. Growth curve models, which provided latent variables for level of and 10-year change in both leisure activity and cognitive ability, confirmed the positive association between levels of leisure activity and cognitive ability (path coefficient = .36, p < .001); however, leisure activity level or change was not associated with cognitive change. Although a positive association between leisure activity and cognitive ability was reported—the likely precedents of this are discussed—there was no evidence that a higher level or maintenance of leisure activity was protective against cognitive decline across a 10-year follow-up