Database systems originated as mechanisms for storing and retrieving information. Codd's relational formalism generalized and made far more flexible the forms of data structure and retrieval specification allowed. However, available implementations of relational databases are in terms of hard, static, deterministic relations; whereas in real-world applications data is often imprecise, inherently dynamic and non-deterministic. In recent years there has been a range of developments concerned with representing and using data that can only be represented in these “softer” terms. Some of the work has been explicitly concerned with database systems, but much of it, whilst highly relevant, has been in other application areas. This paper classifies and surveys work on a variety of logical systems in the context of its relevance to database systems. The objective is to show through illustrations what can be incorporated into relational database systems to allow for a wider range of real-world requirements and closer man-computer interation. The current state-of-the-art in natural language interaction with databases is illustrated and discussed. The possibility of paradoxes leading to oscillations in database states is demonstrated. The roles of modal, multi-valued and fuzzy logics in databases are described as discussed.