..........................................NEXT PREVIOUS INDEX
L03 FS: CFG & Unification: Processing CFG & Unification: Processing o Order of unification not important. Illustrated below by several different evaluation orders. + Example sentence: a child sees toys. + Parse tree for example sentence: S | ------------- | | NP1 VP | | ------ -------- | | | | det n v NP2 | | | | a child sees n | toys * Labels 1 and 2 are put on NP to refer to them umambiguously. - Feature equations may be solved in any order. + Ex.1. Suppose functional equations solved bottom-up on parse tree o Evaluation order 1.1: left-to-right, bottom-up on parse tree - Start evaluation with leaf nodes of NP NP | -------------- | | det n | | a child + Function equations are: - FS(det) = FS from lexical entry for 'a' - FS(n) = FS from entry for 'child' - FS(NP1) = FS(det) U FS(n) + Feature structure (FS) satisfying above equations, are shown attached to nodes below (see lines with dots): NP | -------------- | | det n | | a child . . . . . [CAT n ] . [AGRMNT [NUMBER sg] ] . [ [PERSON 3] ] . [SPEC indef ] [AGRMNT [NUMBER sg] ] [ [PERSON 3] ] + Resulting FS for NP: [ CAT n ] [ SPEC indef ] [ AGRMNT [NUMBER sg] ] [ [PERSON 3] ] o Evaluation order 1.2: Right-to-left, bottom-up on parse tree - Start evaluation with leaf nodes of VP VP | -------- | | v NP | | sees n | toys - FS(VP).AGRMNT = FS(v).AGRMNT. Now, FS for VP is: [TENSE prsnt ] [AGRMNT [NUMBER sg] ] - FS(NP1).AGRMNT = FS(VP).AGRMNT * At this point, the two FSs are checked for compatibility. * Note: In case one FS was not already built, it would get defined by unification (rather than checked). o Another evaluation order 2: Suppose equations are solved from buttom-to-top (for VP subtree) and then top-to-bottom (for subject NP subtree). :-----------<--------------: : S : Functional : | : equation : ------------- : evaluation- : | | : order : NP1 VP : v | | ^ : ------ -------- : : | | | | : : det n v NP2 : : | | | | : <-: a child sees n : | <-- toys - FS(VP).AGRMNT = FS(v).AGRMNT [TENSE prsnt ] [AGRMNT [NUMBER sg] ] - FS(NP1).AGRMNT = FS(VP).AGRMNT * FS for AGRMNT attribute of NP gets defined. * Note: NP1 has not yet been formed. Its lexical entries 'a' and 'child' not yet looked up in lexicon. - FS(NP1) = FS(det) U FS(n) * This results in a check to be performed for attribute AGRMNT in NP1, det and n. (Value for NP1 already defined in previous step.) * As mentioned earlier, '=' is also unification. o Another evaluation order 3: Unification along with derivation of parse tree. + Ex. One possible context free derivation. - S - NP VP - det n VP - a child VP - a child v NP - a child sees NP - a child sees n - a child sees toys - Evaluate feature equations along side - S - NP VP --> FS(NP).AGRMNT = FS(VP).AGRMNT -- Eqn 1 - det n VP --> FS(NP) = FS(det) U FS(n) - a child VP --> FS(NP) = [SPEC indef ] [CAT n ] [AGRMNT [NUM S6] ] [ [PERS 3] ] * Note: FS for VP has the value of AGRMNT. the moment FS for NP is formed. (See Eqn (1))..........................................NEXT PREVIOUS INDEX