Noise addition is a data distortion technique widely used in data intensive applications. For example, in machine learning tasks it helps to reduce overfitting, whereas in data privacy protection it adds uncertainty to personally identifiable information. Yet, due to its mathematical operating principle, noise addition is a method mainly intended for continuous numerical data. In fact, despite the large amount of nominal data that are being currently compiled and used in data analysis, only a few alternative techniques have been proposed to distort nominal data in a similar way as standard noise addition does for numerical data. Furthermore, all these alternative methods rely on the distribution of the data rather than on the semantics of nominal values, which negatively affects the utility of the distorted outcomes. To tackle this issue, in this paper we present a semantically-grounded alternative to numerical noise suitable for nominal data, which we name semantic noise. By means of semantic noise, and by exploiting structured knowledge sources such as ontologies, we are able to distort nominal data while preserving better their semantics and thus, their analytical utility. To that end, we provide semantically and mathematically coherent versions of the statistical operators required in the noise addition process, which include the difference, the mean, the variance and the covariance. Then, we propose semantic noise addition algorithms that cope with the finite, discrete and non-ordinal nature of nominal data. The proposed algorithms cover both uncorrelated noise addition, which is suited to independent attributes, and correlated noise addition, which can cope with multivariate datasets with dependent attributes. Empirical results show that our proposals offer general and configurable mechanisms to distort nominal data while preserving data semantics better than baseline methods based only on the distribution of the data. (C) 2017 Elsevier B.V. All rights reserved.