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

CHAPTER 4. STOCHASTIC CONTEXT-FREE GRAMMARS 99The problem is demonstrated by the following minimal extension of the baseline grammar toincorporate singular and plural NPs and enforce number agreement between main verb and subject NP.S --> NP_SG VP_SG--> NP_PL VP_PLNP --> NP_SG--> NP_PLNP_SG --> DET N_SGNP_PL --> DET N_PLVP_SG --> VI_SG--> VT_SG NP--> VC_SG PPVP_PL --> VI_PL--> VT_PL NP--> VC_PL PPPP --> P NPDET --> theN_PL --> circles | squares | trianglesN_SG --> circle | square | triangleP --> above | belowVC_SG --> isVC_PL --> areVI_SG --> bounces | rollsVI_PL --> bounce | rollVT_SG --> covers | touchesVT_PL --> cover | touchThe grammar now generates sentences includingthe circle bouncesthe circles bouncethe square is below the trianglesthe squares are below the trianglesThis extensions of the scope of the language comes at a considerable price: the categories N, NP, VP, Vt, Vc,Vi all have to be duplicated to encode the number feature.Subjecting a 200-sentence sample to the merging algorithm exposes an additional, unexpectedproblem. The grammar learned is weakly equivalent to the target grammar; in particular, it contains all of thelexical categories in the target grammar. However, the phrase structure rules found are quite different: theygroup the verbs and prepositions with the subject, rather than the object NPs.S --> NP_SG VI_SG (27)--> NP_PL VI_PL (37)--> X NP_SG (76)--> X NP_PL (60)X --> NP_SG VT_SG (37)--> NP_PL VT_PL (33)--> NP_SG VC_SG P (37)--> NP_PL VC_PL P (29)NP_SG --> DET N_SG (177)NP_PL --> DET N_PL (159)