Recently, the topic of ontologies has growing attention from the IT community. Various processes of ontology creation, integration, and deployment have been proposed. As a consequence there appeared an urgent need for evaluating the resulting ontologies in a quantitative way. A number of metrics has been defined along with different approaches to measuring the properties of ontologies. In the first part of this paper we review the state of the art in this domain. Special attention is devoted to discussing differences between syntactic measures (referring to various properties of graphs that represent ontologies) and semantic measures (reflecting the properties of the space of ontology models). In the second part we propose an alternative approach to quantification of semantics of an ontology. The original proposal presented here exploits specific methods of representing the space of semantic models used for optimization of reasoning. We argue that this approach enables us to capture different kinds of relations among ontology terms and offers possibilities of devising new useful measures.