We present a formal description of a logical language that is based on a propositional semantic network. Variables in this language are not atomic and have potentially complex structure. We start from the individual components of a semantic network system, atomic nodes and relations that connect nodes, and provide a complete specification for the structure of nodes and a subsumption procedure between nodes. We differ from other work in subsumption in that the representation language is uniform and based on an extended firstorder predicate logic. The language is particularly suitable for addressing some problems associated with natural language processing, namely the representation of complex natural language descriptions and inference associated with description subsumption.