Harmonic Grammars for Formal Languages

Part of Advances in Neural Information Processing Systems 5 (NIPS 1992)

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Paul Smolensky


Basic connectionist principles imply that grammars should take the form of systems of parallel soft constraints defining an optimization problem the solutions to which are the well-formed structures in the language. Such Harmonic Grammars have been successfully applied to a number of problems in the theory of natural languages. Here it is shown that formal languages too can be specified by Harmonic Grammars, rather than by conventional serial re-write rule systems.


In collaboration with Geraldine Legendre, Yoshiro Miyata, and Alan Prince, I have been studying how symbolic computation in human cognition can arise naturally as a higher-level virtual machine realized in appropriately designed lower-level con(cid:173) nectionist networks. The basic computational principles of the approach are these:


a. \Vhell analyzed at the lower level, mental representations are dis(cid:173)

tributed patterns of connectionist activity; when analyzed at a higher level, these same representations constitute symbolic structures. The particular symbolic structure s is characterized as a set of filler/role bindings {f d ri}, using a collection of structural roles {rd each of which may be occupied by a filler fi-a constituent symbolic struc-