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

CHAPTER 4. STOCHASTIC CONTEXT-FREE GRAMMARS 98After processing 100 random samples of this grammar (which now generates an unbounded numberof sentences), the following phrase structure rules are found.S --> NP VC PP (22)--> NP VI (10)--> NP VT NP (29)--> PP COMMA NP VI (19)--> PP VC NP (20)PP --> P NP (112)NP --> DET N (241)--> NP PP (51)The induced rule structure differs in two aspects from the target. Firstly, no VP phrase structure in inferred.This is not surprising since each of the VP realizations appears only in a single rule, i.e., there is nogeneralization or greater succinctness to be gained from positing a VP constituent. Secondly, the embeddingof PP in NP is realized in two, rather than one recursion: one left-recursive through the NP rule, and onetail-recursive through the PP rule. This redundancy also leads to a slightly suboptimal score compared to thetarget grammar. Still, the grammar found is clearly weakly equivalent to the target.AgreementAnother pervasive phenomenon in natural languages is agreement, whereby two lexical itemsor constituents are forced to share one of more (abstract) features such as number, gender, case marking,etc. For our purposes we can construe the phonologically motivated alternation of English determiners (‘a’and ‘the’ versus ‘an’ and ‘thee’) as a case of NP-internal agreement. A minimal extension of the baselinegrammar to this end is the following (only nonterminals that differ from the baseline are shown):NP --> Det1 N1--> Det2 N2Det1 --> a--> theDet2 --> an--> theeN1 --> circle--> square--> triangleN2 --> arc--> octagonAfter merging 40 random samples, these productions were in fact generalized correctly, while theremainder of the grammar was identical to the one learned before from the baseline corpus.It should be noted that context-free grammars are not particularly suited to the description ofagreement phenomena, especially if the agreeing constituents are separated by material not affected by theagreement. A CFG description in this case has to replicate syntactic categories up to the smallest enclosingconstituent level. 1414 The standard solution to this problem is to factor agreement into a separate description, usually using a feature-based formalism.