The dissertation of Andreas Stolcke is approved: University of ...

CHAPTER 4. STOCHASTIC CONTEXT-FREE GRAMMARS 100This grammar has a marginally lower posterior probability than the target grammar. The reason why evenfairly wide beam search consistently finds this phrase structure, rather than the traditional one, is subtle, andhas to do with the inherent representational problems for agreement phenomena in CFGs.Because agreement has to be mediated by duplication(or rather, non-merging) of otherwise identicalnonterminal symbols up to the smallest phrase level enclosing the agreeing elements, it is advantageous togroup agreeing, rather than non-agreeing parts of the syntax. This strategy minimizes the number of extranonterminals required. The two fundamental chunking alternatives found in the example (verbs with subject,vs. with object) only regain equal description length once all other generalizations have been found. Thus alocalized search will always prefer the subject-verb grouping.Presumably a actual natural language learner would have access to other cues that favor chunkingverbs with their objects. This can at least be simulated by modifyingthe samples to contain partial bracketings,e.g.,the square (is above the triangle)the triangles (are below circles)It not necessary to add partial bracketing to all samples, since some partially bracketed samples are enoughto make chunking of the remaining ones in the appropriate way the best-scoring decision. The followinggrammar was learned from the same 200-sentence corpus as before, modified so that that 50% of the sampleshad explicit VP bracketing. As expected, this leads to the traditional phrase structure, including the necessarynonterminal duplication to account for agreement.S --> NP_SG VP_SG (101)--> NP_PL VP_PL (99)VP_SG --> VI_SG (27)--> VT_SG NP_SG (19)--> VT_SG NP_PL (18)--> VC_SG PP (37)VP_PL --> VI_PL (37)--> VT_PL NP_SG (17)--> VT_PL NP_PL (16)--> VC_PL PP (29)PP --> P NP_SG (40)--> P NP_PL (26)NP_SG --> DET N_SG (177)NP_PL --> DET N_PL (159)Incidentally, the reason the productionsNP --> NP_SG--> NP_PLare not found is that chunking always replaces all occurrences of a chunk.As a result, the operationschunk(NP_SG) and chunk(NP_PL) would interfere with the productions that handle the agreement, and arerightfully rejected.