A Parser for Harmonic Context-Free Grammars

Harmonic Grammar is a connectionist-derived grammar formalism, of which Optimality Theory is a kind of limiting case. Harmonic Grammar is expressive enough to specify the trees that are correct parses on a given contextfree grammar. Here, we show how to construct a connectionist parsing network which finds correct parses given a sentence, of if none exist, signals a rejection. Finally, a brief comparison to other connectionist parsing work is provided. Harmonic grammar is a grammar formalism which uses only soft rules of the following form: If condition X is violated, then the wellformedness (Harmony) of the structure is diminished by CX . [Legendre et al., 1990, 388] A linguistic theory in Harmonic grammar is a set of soft rules and a set of representational possibilities. Applying the soft rules to any representation yields the Harmony value for that representation. A representation with maximal Harmony from some class defined by common substructure — the inputs — is said to be the winning candidate. In Optimality Theory [Prince and Smolensky, 1993] the soft rules are ranked and the CX values are arranged so that no number of violations of lower-ranked soft rules could ever outweigh a violation by a higher ranked one. Harmonic grammar is expressive enough to specify the context-free languages [Smolensky, 1993]. Here Harmony maximization is made to serve as a processing algorithm for a parser. The design for the parser is a way of systematically arranging networks of threshold logic units so that they implement exactly the Harmonic grammar rules for context-free grammars. They maximize the Harmony of representations that share the same terminal entries. The general idea is that these networks do this by de-activating pieces of bad analyses until only correct analyses remain. How Harmonic Grammar specifies context-free languages Harmonic context-free grammar rules (as first presented in [Smolensky, 1993]) are integer occurrence and cooccurrence penalties that are defined on trees. Trees X