Stabler - Lx 185/209 2003 3 Extensi<strong>on</strong>s <strong>of</strong> the top-down recognizer 3.1 Unificati<strong>on</strong> grammars (1) How should agreement relati<strong>on</strong>s be captured in a grammar? We actually already have a powerful mechanism available for this: instead <strong>of</strong> “propositi<strong>on</strong>al grammars” we can use “predicate grammars” where the arguments to the predicates can define subcategorizing features <strong>of</strong> each category. We explore this idea here, since it is quite widely used, before c<strong>on</strong>sidering the idea from transformati<strong>on</strong>al grammar that agreement markers are heads <strong>of</strong> their own categories (Pollock 1994, Sportiche 1998, many others). (2) C<strong>on</strong>sider the following grammar: % g2.pl :- op(1200,xfx,:˜). ip :˜ [dp(Per,Num), vp(Per,Num)]. dp(1,s) :˜ [’I’]. dp(2,s) :˜ [you]. dp(3,s) :˜ [it]. dp(3,s) :˜ [she]. dp(3,s) :˜ [he]. dp(3,Num) :˜ [d1(Num)]. d1(Num) :˜ [d0(Num), np(Num)]. d0(_Num) :˜ [the]. d0(p) :˜ [most]. d0(s) :˜ [every]. d0(p) :˜ [few]. np(Num) :˜ [n1(Num)]. n1(Num) :˜ [n0(Num)]. n0(s) :˜ [penguin]. n0(p) :˜ [penguins]. vp(Per,Num) :˜ [v1(Per,Num)]. v1(Per,Num) :˜ [v0(Per,Num)]. v0(1,s) :˜ [sing]. v0(2,s) :˜ [sing]. v0(3,s) :˜ [sings]. v0(3,p) :˜ [sing]. With this grammar g2.pl I produced the following sessi<strong>on</strong>: 1 ?- [td],[g2]. td compiled, 0.00 sec, 1,116 bytes. g2 compiled, 0.01 sec, 2,860 bytes. Yes 2 ?- [every,penguin,sings] ?˜ [ip]. Yes 3 ?- [every,penguins,sing] ?˜ [ip]. No 4 ?- [it,sing] ?˜ [ip]. No 5 ?- [it,sings] ?˜ [ip]. Yes 6 ?- [the,penguin,sings] ?˜ [ip]. Yes 7 ?- [the,penguin,sing] ?˜ [ip]. No 8 ?- [the,penguins,sings] ?˜ [ip]. No 41
Stabler - Lx 185/209 2003 (3) Dalrymple and Kaplan (2000), Bayer and Johns<strong>on</strong> (1995), Ingria (1990), and others have pointed out that agreement seems not always to have the “two way” character <strong>of</strong> unificati<strong>on</strong>. That is, while in English, an ambiguous word can be resolved <strong>on</strong>ly in <strong>on</strong>e way, this is not always true: a. The English fish is ambiguous between singular and plural, and cannot be both: The fish who eats the food gets/*get fat Thefishwhoeatthefood*gets/getfat (This is what we expect if fish has a number feature that gets unified with <strong>on</strong>e particular value.) b. The Polish wh-pr<strong>on</strong>oun kogo is ambiguous between accusative and genitive case, and can be both: Kogo who Janek lubi a Jerzy nienawidzi? Janek likes and Jerzy hates c. (lubi requires acc object and nienawidzi requires gen object.) The German was is ambiguous between accusative and nominative case, and can be both: Ich habe gegessen was übrig war. I have eaten what left was (The German gegessen requires acc object and übrig war needs a nom subject.) Dalrymple and Kaplan (2000) propose that what examples like the last two show is that feature values should not be atoms like sg, pl or nom, acc, gen but (at least in some cases) sets <strong>of</strong> atoms. 3.2 More unificati<strong>on</strong> grammars: case features (4) We can easily extend the grammar g2.pl to require subjects to have nominative case and objects, accusative case, just by adding a case argument to dp: % g3.pl :- op(1200,xfx,:˜). ip :˜ [dp(P,N,nom), i1(P,N)]. i1(P,N) :˜ [i0, vp(P,N)]. i0 :˜ []. dp(1,s,nom) :˜ [’I’]. dp(2,_,_) :˜ [you]. dp(3,s,nom) :˜ [she]. dp(3,s,nom) :˜ [he]. dp(3,s,_) :˜ [it]. dp(3,p,nom) :˜ [they]. dp(1,s,acc) :˜ [’me’]. dp(3,s,acc) :˜ [her]. dp(3,s,acc) :˜ [him]. dp(3,p,acc) :˜ [them]. dp(3,s,_) :˜ [titus]. dp(3,s,_) :˜ [tamora]. dp(3,s,_) :˜ [lavinia]. dp(3,N,_) :˜ [d1(N)]. d1(N) :˜ [d0(N), np(N)]. d0(_) :˜ [the]. d0(p) :˜ [most]. d0(s) :˜ [every]. d0(s) :˜ [some]. d0(p) :˜ [few]. np(N) :˜ [n1(N)]. n1(N) :˜ [n0(N)]. n0(s) :˜ [penguin]. n0(p) :˜ [penguins]. n0(s) :˜ [s<strong>on</strong>g]. n0(p) :˜ [s<strong>on</strong>gs]. vp(P,N) :˜ [v1(P,N)]. v1(P,N) :˜ [v0(intrans,P,N)]. v1(P,N) :˜ [v0(trans,P,N),dp(_,_,acc)]. v0(_,1,_) :˜ [sing]. v0(_,2,_) :˜ [sing]. v0(_,3,s) :˜ [sings]. v0(_,3,p) :˜ [sing]. v0(trans,1,_) :˜ [praise]. v0(trans,2,_) :˜ [praise]. v0(trans,3,s) :˜ [praises]. v0(trans,3,p) :˜ [praise]. v0(intrans,1,_) :˜ [laugh]. v0(intrans,2,_) :˜ [laugh]. v0(intrans,3,s) :˜ [laughs]. v0(intrans,3,p) :˜ [laugh]. (5) The coordinate structure Tamora and Lavinia is plural. We cannot get this kind <strong>of</strong> c<strong>on</strong>structi<strong>on</strong> with rules like the following because they are left recursive, and so problematic for TD: dp(_,p,K) :˜ [dp(_,_,K), coord(dp(_,_,K))]. % nb: left recursi<strong>on</strong> vp(P,N) :˜ [vp(P,N), coord(vp(P,N))]. % nb: left recursi<strong>on</strong> coord(Cat) :˜ [and,Cat]. 42
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