LING 388: Language and Computers

1. LING 388: Language and Computers Sandiway Fong 10/6 Lecture 13

2. Last Time • Grammars • what is a grammar? • informally • set of “rewrite” rules to parse or “diagram” a sentence • derivation • top-down (from the sentence symbol), bottom-up (from the words) • Definite Clause Grammar (DCG) System • built-in Prolog support for writing grammars • --> is the rewrite symbol • [book], [took] terminals are enclosed in brackets • sentence, vp, npterminals and non-terminal symbols begin with lowercase letters Sentence → NP VP VP → Verb NP Verb → took NP → the man NP → the book sentence --> np, vp. vp --> verb, np. verb --> [took]. np --> [the], [man]. np --> [the], [book].

3. Exercise 1 • example grammar (from last time) • sentence --> np, vp. • vp --> verb, np. • verb --> [took]. • np --> [the], [man]. • np --> [the], [book]. • query format • ?- sentence(S,[]). • S = sentence (as a list) • [] = empty list • i.e. call the start symbol as a predicate and • supply two arguments, a list and an empty list

4. Exercise 1 • Steps: • Put the grammar in a file • Consult it • ?- listing. • (see the underlying Prolog translation of the rules) • Queries ?- sentence([the,man,took,the,book],[]). ?- sentence([the,man|L],[]). ?- sentence(L,[]). ?- sentence([the,X,took,the,Y],[]), \+ X=Y.

5. ?- listing. • Prolog translates DCG rules into ordinary Prolog rules • listing • vp(A, B) :- • verb(A, C), • np(C, B). • np(A, B) :- • det(A, C), • 'C'(C, man, B). • np(A, B) :- • det(A, C), • 'C'(C, book, B). • verb([took|A], A). • det([the|A], A). • det([a|A], A). • sentence(A, B) :- • np(A, C), • vp(C, B). • example • sentence --> np, vp. • vp --> verb, np. • verb --> [took]. • np --> det, [man]. • np --> det, [book]. • det --> [the]. • det --> [a]. variables A,B,C are all going to be lists 'C'(C, man, B) is true when man is the head of C and B is the tail of C i.e. C = [man|B]

6. Exercise 2 • Let’s follow the computation steps Prolog uses to prove it can derive a sentence from the starting non-terminal

7. ?- trace. • listing • vp(A, B) :- • verb(A, C), • np(C, B). • np(A, B) :- • det(A, C), • 'C'(C, man, B). • np(A, B) :- • det(A, C), • 'C'(C, book, B). • verb([took|A], A). • det([the|A], A). • det([a|A], A). • sentence(A, B) :- • np(A, C), • vp(C, B). • derivation • ?- sentence([the,man,took,the,book],[]). • Call: (7) sentence([the, man, took, the, book], []) ? creep • Call: (8) np([the, man, took, the, book], _G353) ? creep • Call: (9) det([the, man, took, the, book], _G353) ? creep • Exit: (9) det([the, man, took, the, book], [man, took, the, book]) ? creep • Call: (9) 'C'([man, took, the, book], man, _G357) ? creep • Exit: (9) 'C'([man, took, the, book], man, [took, the, book]) ? creep • Exit: (8) np([the, man, took, the, book], [took, the, book]) ? creep • Call: (8) vp([took, the, book], []) ? creep • Call: (9) verb([took, the, book], _G353) ? creep • Exit: (9) verb([took, the, book], [the, book]) ? creep • Call: (9) np([the, book], []) ? creep • Call: (10) det([the, book], _G353) ? creep • Exit: (10) det([the, book], [book]) ? creep • Call: (10) 'C'([book], man, []) ? creep • Fail: (10) 'C'([book], man, []) ? creep • Redo: (10) det([the, book], _G353) ? creep • Fail: (10) det([the, book], _G353) ? creep • Redo: (9) np([the, book], []) ? creep • Call: (10) det([the, book], _G353) ? creep • Exit: (10) det([the, book], [book]) ? creep • Call: (10) 'C'([book], book, []) ? creep • Exit: (10) 'C'([book], book, []) ? creep • Exit: (9) np([the, book], []) ? creep • Exit: (8) vp([took, the, book], []) ? creep • Exit: (7) sentence([the, man, took, the, book], []) ? creep • Yes

8. np([the,man,took,the,book],C). vp([took,the,book],[]). vp(C,[]). det([the,man,took,the,book],C’). verb([took,the,book],C”). ‘C’(C’,man,C). np(C”,[]). det([the,man,took,the,book],[man,took,the,book]). verb([took,the,book],[the,book]). ‘C’([man,took,the,book],man,C). ‘C’([man,took,the,book],man,[took,the,book]). np([the,book],[]). det([the,book],C”’). det([the,book],C”’). ‘C’(C”’,man,[]). ‘C’(C”’,book,[]). det([the,book],[book]). ‘C’([book],man,[]). ‘C’([book],book,[]). Grammar Computation ?- sentence([the,man,took,the,book],[]). Underlying Prolog vp(A, B) :- verb(A, C), np(C, B). np(A, B) :- det(A, C), 'C'(C, man, B). np(A, B) :- det(A, C), 'C'(C, book, B). verb([took|A], A). det([the|A], A). det([a|A], A). sentence(A, B) :- np(A, C), vp(C, B). DCG rules vp --> verb, np. np --> det,[man]. np --> det, [book]. verb --> [took]. det --> [the]. det --> [a]. sentence --> np, vp. C=[took,the,book] Animation

9. np([the,man,took,the,book],C). vp(C,[]). det([the,book],[book]). ‘C’([book],book,[]). Grammar Computation Note: the computation tree resembles a parse tree ?- sentence([the,man,took,the,book],[]). verb([took,the,book],C”). np(C”,[]). det([the,man,took,the,book],C’). ‘C’(C’,man,C). verb([took,the,book],[the,book]). det([the,man,took,the,book],[man,took,the,book]). np([the,book],[]). ‘C’([man,took,the,book],man,C). det([the,book],C”’). ‘C’(C”’,book,[]). ‘C’([man,took,the,book],man,[took,the,book]).

10. Grammar Computation Note: the computation tree resembles a parse tree

11. Exercise 3 • Getting Prolog to build a representation of the parse tree [S [NP [Det the] man][VP [V took][NP [Det the] book]]] sentence(np(det(the),man),vp(verb(took),np(det(the),book)))

12. observation ?- trace. computation tree disappears after computation is finished would be nice to keep a parse tree around technique add one argument to each grammar rule to hold part of the parse tree compositionality: combine sub-trees to form larger trees and the complete parse tree Computing Parse Trees

13. Computing Parse Trees • use a recursive Prolog data structure to represent a parse • examples • data structure:verb(took) • functor = verb • argument = took • data structure:det(the) • functor = det • argument = the • data structure:np(det(the),man) • functor = np • 1st argument = det(the) • functor = det • argument = the • 2nd argument = man (1) verb | took (2) det | the (3) np / \ det man | the

14. np([the,man,took,the,book],C). vp(C,[]). det([the,book],[book]). ‘C’([book],book,[]). Computing Parse Trees let’s look at how to create a tree for “the book” ?- sentence([the,man,took,the,book],[]). verb([took,the,book],C”). np(C”,[]). det([the,man,took,the,book],C’). ‘C’(C’,man,C). verb([took,the,book],[the,book]). np --> det, [book]. det([the,man,took,the,book],[man,took,the,book]). np([the,book],[]). ‘C’([man,took,the,book],man,C). det([the,book],C”’). ‘C’(C”’,book,[]). ‘C’([man,took,the,book],man,[took,the,book]).

15. np([the,man,took,the,book],C). vp(C,[]). det(X,[the,book],[book]). ‘C’([book],book,[]). Computing Parse Trees computation tree = parse tree ?- sentence([the,man,took,the,book],[]). X is the extra parameter verb([took,the,book],C”). np(C”,[]). det([the,man,took,the,book],C’). ‘C’(C’,man,C). np --> det, [book]. np(X) --> det(D),[book]. np(np(D,book)) --> det(D),[book]. verb([took,the,book],[the,book]). np --> det, [book]. det([the,man,took,the,book],[man,took,the,book]). det --> [the]. det(X) --> [the]. det(det(the)) --> [the]. np([the,book],[]). ‘C’([man,took,the,book],man,C). np(D,book) det(the) det(X,[the,book],C”’). ‘C’(C”’,book,[]). ‘C’([man,took,the,book],man,[took,the,book]).

16. Computing Parse Trees • original DCG • sentence --> np, vp. • vp --> verb, np. • verb --> [took]. • np --> det, [man]. • np --> det, [book]. • det --> [the]. • revised DCG • sentence(s(NP,VP)) --> np(NP), vp(VP). • vp(vp(V,NP)) --> verb(V), np(NP). • verb(v(took)) --> [took]. • np(np(D,man)) --> det(D), [man]. • np(np(D,book)) --> det(D), [book]. • det(det(the)) --> [the].

17. Computing Parse Trees • revised DCG • sentence(s(NP,VP)) --> np(NP), vp(VP). • vp(vp(V,NP)) --> verb(V), np(NP). • verb(v(took)) --> [took]. • np(np(D,man)) --> det(D), [man]. • np(np(D,book)) --> det(D), [book]. • det(det(the)) --> [the]. • query (with an extra argument) • ?- sentence(P,List,[]). • P = parse tree • List = sentence s(np(det(the),man),vp(v(took),np(det(the),man)))

18. Examples • query • what parse P corresponds to the sentence “the man took the book”? • ?- sentence(P,[the,man,took,the,book],[]). • P = s(np(det(the),man),vp(v(took),np(det(the),book))) ? ; • no • query • what are the possible parses P and word X for the sentence “the man took the X”? • ?- sentence(P,[the,man,took,the,X],[]). • P = s(np(det(the),man),vp(v(took),np(det(the),man))), • X = man ? ; • P = s(np(det(the),man),vp(v(took),np(det(the),book))), • X = book ? ; • no

19. Examples • query • given a parse, what is the corresponding Sentence? • ?- sentence(s(np(det(the),man),vp(v(took),np(det(the),book))),Sentence,[]). • Sentence = [the,man,took,the,book] ? ; • no • query • supply no information, i.e. Parse and Sentence are both variables, • what are the possible sentences and parses? • ?- sentence(Parse,Sentence,[]). • Parse = s(np(det(the),man),vp(v(took),np(det(the),man))), • Sentence = [the,man,took,the,man] ? ; • Parse = s(np(det(the),man),vp(v(took),np(det(the),book))), • Sentence = [the,man,took,the,book] ? ; • Parse = s(np(det(the),book),vp(v(took),np(det(the),man))), • Sentence = [the,book,took,the,man] ? ; • Parse = s(np(det(the),book),vp(v(took),np(det(the),book))), • Sentence = [the,book,took,the,book] ? ; • no

20. Exercise 4 • Idiom chunks • kicked the bucket • has both a literal meaning • and is also a VP (verb phrase) idiom • meaning: • died

21. Exercise 4 • add new rule • “kicked the bucket” is a VP idiom meaning “died” • vp(vp(v(died))) --> [kicked,the,bucket]. • example illustrates the ability to return any parse we like for a given rule • query • what are the possible parses for “the man kicked the bucket”? • ?- sentence(Parse,[the,man,kicked,the,bucket],[]). • Parse = s(np(det(the),man),vp(v(died))) ? ; • no • idiomatic meaning only

22. Exercise 4 • add new rules • for “kicked” and “bucket” as a verb and noun, respectively • verb(v(kicked)) --> [kicked]. • np(np(D,bucket)) --> det(D), [bucket]. • provides the ability to return the literal parse for “kicked the bucket”

23. Exercise 4 • query • what are the possible parses for “the man kicked the bucket”? • ?- sentence(Parse,[the,man,kicked,the,bucket],[]). • Parse = s(np(det(the),man),vp(v(kicked),np(det(the),bucket))) ? ; • Parse = s(np(det(the),man),vp(v(died))) ? ; • no • both idiomatic and literal meanings are now possible • which one comes first? is preferred?