The study on query relaxation which provides approximate answers has received attention. In recent years, some arguments have been made that semantic relationships are useful to present the relationships among data values and calculating the semantic distance between two data values can be used as a quantitative measure to express relative distance. The aim of this article is a hierarchical metricized knowledge abstraction (HiMKA) with an emphasis on combining data abstraction hierarchy and distance measure among data values. We propose the operations and the query relaxation algorithm appropriate to the HiMKA. With various experiments and comparison with other method, we show that the HiMKA is very useful for the quantified approximate query answering and our result is to offer a new methodological framework for query relaxation.