Cyclic Inputs. Surface Generation (Part II) Ambiguity-preserving Generation. Ambiguity-preserving Generation. Ambiguity-preserving Generation

Transcription

1 Cyli Inputs The set of strings tht grmmr reltes to yli input struture might e non-ontext-free Surfe Genertion (Prt II) Amiguity-preserving Genertion Amiguity-preserving Genertion Motivtion Motivtion () John sw the mn with the telesope (). with_the_telesope(see(john, mn)). see(john, with_the_telesope(mn)) (3) John sh den Mnn mit dem Fernrohr (4) The duk is redy to et (5). redy(duk, et(someone, duk)). redy(duk, et(duk, something)) (6). Die Ente knn jetzt gegessen werden. Die Ente ist zum Fressen ereit 3 4 Amiguity-preserving Genertion Amiguity-preserving Genertion Motivtion Motivtion (7) John sw her duk with the telesope (8). with_the_telesope(see(john, her_duk)). see(john, with_the_telesope(her_duk)). with_the_telesope(see(john, duk(her))) () John sw the mn with the telesope (3) John sh den Mnn mit dem Fernrohr (0) John sh den Mnn, der ds Fernrohr htte d. see(john, with_the_telesope(duk(her))) (9). John sh ihre Ente mit dem Fernrohr. Mit dem Fernrohr sh John sie sih duken 5 6

2 F-Strutures nd Semnti Representtions Forml Chrteriztion of the Prolem The derivtion reltion for G Δ G { (s,f ) G ssigns to string s the f-struture f } SUBJ TENSE PRED SEM PRED John PRES rrive<subj> REL rrive ARG john f f Deidility prolems Prsing: { f Δ G (s,f ) } for eh terminl string s Genertion: { s Δ G (s,f ) } for eh f-struture f f f f susumes f 7 8 Forml Chrteriztion of the Prolem Amiguity-preserving genertion: { s f..f n ( f f &.. & f n f n & Δ G (s,f ) &.. & Δ G (s,f n )) } for eh set of semnti representtions { f,..,f n } Genertion from Sets of f-strutures For set of f-strutures { f,..,f n } it is in generl not deidle whether { s Δ G (s,f ) &.. & Δ G (s,f n ) } Genertion from semnti representtions: { s f ( f f & Δ G (s,f)) } for eh semnti representtion f n Genertion from sets of f-strutures: { s Δ G (s,f ) &.. & Δ G (s,f n ) } for eh set of f-strutures { f,..,f n } f i f i 9 0 Genertion from Sets of f-strutures Genertion from Sets of f-strutures Given: two ritrry ontext-free grmmrs G (N,T,S,R ) nd G (N,T,S,R ) with N N R R R S S, ( A) S S ( A) Construt: LFG G (N,T,S,R) with N N N { S } nd S N N T T T R R R S S, S S ( A) ( A) S ( A) ( A) s s { s Δ G (s, [A ]) } L(G ) { s Δ G (s, [A ]) } L(G ) S { s Δ G (s, [A ]) & Δ G (s, [A ]) } L(G ) L(G ) iff

3 For semnti representtion f it is in generl not deidle whether { s f ( f f & Δ G (s,f)) } String grmmrs Given: n ritrry CFG grmmr G (N,T,S,R) in CNF (possily with empty produtions) Construt: String(G) (N,T,S,R S ) (PATR) with R S { (r, D r ) r R } 3 4 String grmmrs R S { (r, D r ) r R } String grmmrs R S { (r, D r ) r R } If r A then D r { ( ), ( ) ( ) } If r A ε then D r { ( ) ( ) } A ε A 5 6 String grmmrs R S { (r, D r ) r R } String grmmrs If r A BC then D r { ( ) ( ), ( ) (x ), ( ) (x ) } S A A Dx B C x x B x 3 C x 4 d x 3 x 4 x d 7 8 3

4 The proof Given: two ritrry string grmmrs S x ( SEM), X 0, X 0 x, ( ) # String(G ) (N,T,S,R S ) nd String(G ) (N,T,S,R S ) with N N s L(G ) s L(G ) Construt: G (N,T,S,R) (PATR) with N N N { S } nd S N N T T T R R S R S (S, ( SEM), X 0, X 0 x, ( ) # ) e x one string hs to e prefix of the other 9 0 S ( SEM), S ( SEM), x X 0, X 0 x, ( ) # x X 0, X 0 x, ( ) # s L(G ) s L(G ) s L(G ) s L(G ) x x S ( SEM), S x X 0, X 0 x, ( ) # x s L(G ) s L(G ) s L(G ) s L(G ) G derives [SEM ] iff s s # { s f ([SEM ] f & Δ G (s, f)) } { ww w L(G ) L(G ) } iff L(G ) L(G ) oth strings hve to e identil 3 4 4

5 Summry - The prolem of miguity-preserving genertion is not deidle for the existing unifition-sed grmmr formlisms. + Nturl lnguge grmmrs seem to elong to restrited sulss of grmmrs whose properties ensure the deidility of the prolem. - Whih properties will permit the omputtion of miguity-preserving genertion is fr from eing evident yet. 5 5