INSOMNet is a subysmbolic sentence processing system that produces explicit and graded semantic graph representations. The novel technique of semantic self-organization allows the network to learn typical semantic dependencies between nodes in a graph that helps the INSOMNet process novel sentences. The technique makes it possible to assign case roles flexibly, while retaining the cogntively plausible behavior that characterizes connectionist modeling. INSOMNet has been shown to scale up to to sentences of realistic complexity, including those with dysfluencies in the input and damage in the network. The network also exhibits the crucial cognitive properties of incremental processing, expectations, semantic priming, and nonmonotonoic revision of an interpretation during sentence processing. INSOMNet therefore constitutes a significant step towards building a cogntive parser that works with everyday language that people use.