Big data refers to large volumes, complex data sets with various autonomous sources, characterized by continuous growth. Data storage and data collection capabilities are now rapidly expanding in all fields of science and technology due to the rapid development of networks. Evaluating the quality of data is a difficult task in the context of big data, because the speed of semantic data reasoning directly depends on its quality. The appropriate strategies are necessary to evaluate and assess data quality according to the huge amount of data and its rapid generation. Managing a large volume of heterogeneous and distributed data requires defining and continuously updating metadata describing various aspects of data semantics and its quality, such as conformance to metadata schema, provenance, reliability, accuracy and other properties. The article examines the problem of evaluating the quality of big data in the semantic environment. The definition of big data and its semantics is given below and there is a short excursion on a theory of quality assessment. The model and its components which allow to form and specify metrics for quality have already been developed. This model includes such components as: quality characteristics; quality metric; quality system; quality policy. A quality model for big data that defines the main components and requirements for data evaluation has already been proposed. In particular, such evaluation components as: accessibility, relevance, popularity, compliance with the standard, consistency, etc. are highlighted. The problem of inference complexity is demonstrated in the article. Approaches to improving fast semantic inference through materialization and division of the knowledge base into two components, which are expressed by different dialects of descriptive logic, are also considered below. The materialization of big data makes it possible to significantly speed up the processing of requests for information extraction. It is demonstrated how the quality of metadata affects materialization. The proposed model of the knowledge base allows increasing the qualitative indicators of the reasoning speed.