We elaborate on the semantics of an enhanced object-oriented semantic network, where multiple instantiation, multiple specialization, and meta-classes are supported for both kinds of objects: entities and properties. By semantics of a semantic network, we mean the information (both explicit and derived) that the semantic network carries. Several data models use semantic networks to organize information. However, many of these models do not have a formalism defining what the semantics of the semantic network is. In our data model, in addition to the Isa relation, we consider a stronger form of specialization for properties, that we call restriction isa, or Risa for short. The Risa relation expresses property value refinement. A distinctive feature of our data model is that it supports the interaction between Isa and Risa relations. The combination of Isa and Risa provides a powerful conceptual modeling mechanism. The user declares objects and relations between objects through a program. Reasoning is done through a number of (built-in) inference rules that allow for derivations both at instance and schema level. Through the inference rules, new objects and new relations between objects are derived. In our data model, inherited properties are considered to be derived objects. In addition to the inference rules, a number of (built-in) system constraints exist for checking the validity of a program.