In a relational database the information is recorded as rowsin tables. However, in many practical situations theavailable information is incomplete and the values for somecolumns are missing. Yet few existing database managementsystems allow the user to enter null values in the database.This monograph analyses the problems raised by allowing nullvalues in relational databases. The analysis coverssemantical, syntactical, and computational aspects.Algorithms for query evaluation, dependency enforcement andupdates in the presence of null values are also given.The analysis of the computational complexity of thealgorithms suggests that from a practical point of view thedatabase should be stored as Horn tables, which aregeneralizations of ordinary relations, allowing null valuesand Horn clause-like restrictions on these null values. Horntables efficiently support a large class of queries,dependencies and updates.