Proceedings of the Annual Meeting of the Cognitive Science Society

In this paper, we derive the formalism of harmonic grammar, a connectionist-based theory of linguistic well formedness. Harmonic grammar is a two-level theory, involving a low level connectionist network using a particular kind of distributed representation, and a second, higher level network that uses local representations and which approximately and incompletely describes the aggregate computational behavior of the lower level network. The central hypothesis is that the connectionist well-formedness measure Harmon)^ can be used to model linguistic well-formedness; what is crucial about the relation between the lower and higher level networks is that there is a harmony-preserving mapping between them: they are isoharmonic (at least approximately). In a companion paper (Legendre, Miyata, & Smolensky, 1990; henceforth, "LMSi"), we apply harmonic grammar to a syntactic problem, unaccusativity, and show that the resulting network is capable of a degree of coverage of difficult data that is unparallelled by symbolic approaches of which we are aware: of the 760 sentence types represented in our data, the network correctly predicts the acceptability in all but two cases. In the present paper, we describe the theoretical basis for the two level approach, illustrating the general theory through the derivation from first principles of the unaccusativity network of LMSj.