Cognitive linguists hypothesize that language is the product of general cognitive abilities. Semantic and functional motivations are sought for grammatical patterns, sentence meaning is viewed as the result of constraint satisfaction, and highly regular linguistic patterns are thought to be mediated by the same processes as irregular patterns. In this paper, recent cognitive linguistics arguments emphasizing the schematicity continuum, the non-autonomy of syntax, and the non-compositionality of semantics are presented and their amenability to connectionist modeling described. Some of the conceptual matches between cognitive linguistics and connectionism are then illustrated by a back-propagation model of the diverse meanings of the preposition over. The pattern set consisted of a distribution of form-meaning pairs that was meant to be evocative of English usage in that the regularities implicit in the distribution spanned the spectrum from rules to partial regularities to exceptions. Under pressure to encode these regularities with limited resources, the network used one hidden layer to recode the inputs into a set of abstract properties. The properties discovered by the network correspond closely to semantic features that linguists have proposed when giving an account of the meaning of over.