In this chapter, we introduce the basics of formal languages and reasoning in a Web context. Denoting information by means of a logical formalism makes it possible to employ established techniques from the field of automated reasoning. However, reasoning in the context of Web-based systems has a distinct set of requirements in terms of
of the information it has to cope with. In turn, this chapter focuses, in a very foundational way, on reasoning on Semantic Web-oriented data. For this purpose, we briefly identify and describe the basic paradigms forming the background for knowledge representation in Web-based Systems. We then examine how these paradigms are reflected in current standards and trends on the Web and what kinds of reasoning they typically facilitate. Based on this, we proceed to focus on concrete reasoning techniques and their particular properties, including optimizations and various other possibilities, e.g., parallelization and approximation, to meet the scalability requirements in Web-based systems.