The paper focuses on discovery of knowledge needed to establish the shared meaning of attributes in a network of distributed autonomous databases. In this paper, we concentrate on the role of equations as definitions of attribute values. We briefly describe various applications of such definitions, including predictions, knowledge verification, intelligent query answering and several others. We present an interface between a distributed autonomous knowledge system, DAKS, and a discovery system 49er. To find knowledge useful in defining attributed missing in one database, the discovery mechanism of 49er can be applied to other databases. DAKS makes requests for definitions and then manages the discovered definitions, verifies their consistency and applies them in its query- answering mechanism. To put a system of equation-based attribute definitions on a firm theoretical foundation, we introduce semantics, which justifies empirical equations in their definitional role. This semantics augments the earlier developed semantics for rules used as attribute definitions.