Classically, risk is characterised by a point value probability indicating the likelihood of occurrence of an adverse effect. However, there are domains where the attainability of objective numerical risk characterisations is increasingly being questioned. This paper reviews the arguments in favour of extending classical techniques of risk assessment to incorporate meaningful qualitative and weak quantitative risk characterisations. A technique in which linguistic uncertainty terms are defined in terms of patterns of argument is then proposed. The technique is demonstrated using a prototype computer-based system for predicting the carcinogenic risk due to novel chemical compounds.