Over the past decade, a large number of deductive object-oriented database languages have been proposed. The earliest of these languages had few object-oriented features, and more and more features have systematically been incorporated in successive languages. However, a language with a clean logical semantics that naturally accounts for all the key object-oriented features, is still missing from the literature. This article takes us another step towards solving this problem. Two features that are currently missing are the encapsulation of rule-based methods in classes, and nonmonotonic structural and behavioral inheritance with overriding, conflict resolution and blocking. This article introduces the syntax of a language with these features. The language is restricted in the sense that we have omitted other object-oriented and deductive features that are now well understood, in order to make our contribution clearer. It then defines a class of databases, called well-defined databases , that have an intuitive meaning and develops a direct logical semantics for this class of databases. The semantics is based on the well-founded semantics from logic programming. The work presented in this article establishes a firm logical foundation for deductive object-oriented databases.