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

CHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 117Now consider the sequence of steps necessary to arrive at the traditionalVP phrase structure. First, two chunksare replaced independently: chunk(Vt NP) = VP1 and chunk(Vi NP) = VP2, resulting in the grammarS --> NP VP1S.tr = NP.fS.rel = VP1.gS.lm = VP1.hS --> NP VP2S.tr = NP.fS.rel = VP2.gS.lm = VP2.hVP1 --> Vt NPVP1.g = Vt.gVP1.h = NP.fVP2 --> Vi PPVP2.g = PP.gVP2.h = PP.hA final merging step, merge(VP1, VP2) = VP, gives the familiar result:S --> NP VPS.tr = NP.fS.rel = VP.gS.lm = VP.hVP --> Vt NPVP.g = Vt.gVP.h = NP.fVP --> Vi PPVP.g = PP.gVP.h = PP.hWhile this sequence of steps seems straightforward, it is not the only one possible. The followingalternative sequence uses the same types of operators and yields a grammar that is symmetrical, and thereforeequally preferable on syntactic grounds alone (assuming no other distributional evidence favors one or theother).The alternative sequence of steps starts from the baseline grammar by chunking the ‘wrong’constituents, namely, chunk(NP Vt) = XP1 and chunk(PP Vi) = XP2.S --> XP1 NPS.tr = XP1.hS.rel = XP1.gS.lm = NP.fS --> XP2 NPS.tr = NP.fS.rel = X2.gS.lm = XP2.hXP1 --> NP VtXP2.g = Vt.gXP1.h = NP.fVP2 --> PP ViXP2.g = PP.gXP2.h = PP.hAs before, we can then merge the new two phrase categories, merge(XP1, XP2) = XP. The resulting SCFGproductions have the same number of nonterminals, productions lengths etc. as the original solution, andshould therefore receive the same prior probability, unless a prior is used that explicitly favors certain typesof phrase structures (e.g., right-branching over left-branching). However, the feature equations obtained arequite different, as in this case the specification does not collapse into three equations as before.S --> XP NPS.tr = XP.h [0.5]S.tr = NP.f [0.5]S.rel = XP.gS.lm = NP.f [0.5]S.lm = XP.h [0.5]