Semantic web is a vision of the web implementation in which information carries an explicit meaning, so it can be automatically understood, processed, and integrated by machines. Humans are capable of using the web to carry out tasks such as reserving a library book, searching for the lowest price for a smartphone, etc. However, in general machines can not accomplish such tasks without human guidance, as web pages promote presentation, rather than content, so they can be easily interpreted by people but not by machines. Currently, the main languages to represent knowledge in the semantic web are the Resource Description Framework (RDF) and the OWL 2 Ontology Web Language. This book introduces a new family of OWL 2 profiles based on a four level stratified syllogistic fragment of the Set Theory that are characterized by an efficient decision procedure without sacrificing expressiveness together with a Rule Based System naturaly integrated in the language. To demonstrate the expressiveness of these profiles, an application on ancient ceramics cataloguing and classification is provided.