What can be learned from failed proofs of non-theorems?

This paper reports an investigation into the link between failed proofs and non-theorems. It seeks to answer the question of whether anything more can be learned from a failed proof attempt than can be discovered from a counter-example. We suggest that the branch of the proof in which failure occurs can be mapped back to the segments of code that are the culprit, helping to locate the error. This process of tracing provides finer grained isolation of the offending code fragments than is possible from the inspection of counter-examples. We also discuss ideas for how such a process could be automated.

Young people with learning disabilities who sexually abuse: understanding, identifying and responding from within generic education and welfare services

This chapter will start by providing an overview of current knowledge about young people with learning disabilities who sexually abuse. Research cited will, unless otherwise indicated, be limited to UK studies since international variations in the definitions of both learning disability and sexual abuse make the use of a wider literature base problematic – particularly that relating to prevalence and incidence. It will then go on to report key findings from a recent study (Fyson et al, 2003; Fyson, 2005) which examined how special schools and statutory child protection and youth offending services in four English local authorities responded to sexually inappropriate or abusive behaviours exhibited by young people with learning disabilities. It will conclude by highlighting areas of current practice which give cause for concern, and suggest some pointers for future best practice.