CSA2050: DCG I1 CSA2050 Introduction to Computational Linguistics Lecture 8 Definite Clause Grammars

CSA2050: DCG I2 Rationale Logic CFG + Sentence Prolog Program Sentence Structure

CSA2050: DCG I3 Logic Rules and Grammar Rules Basic Question: what is the connection between logic rules and grammar rules?  x  y male(x) & parent(x,y) → father(x,y ) S → NP VP They are both concerned with the definition of predicates.

CSA2050: DCG I4 Logic Rules and Grammar Rules Logic: arbitrary n-ary predicates, eg raining; clever(x); father(x,y); between(x,y,z) Grammar Rules: predicates over text segments, eg np(x); vp(y); s(z).

CSA2050: DCG I5 Text Segments A text segment is a sequence of consecutive words. A text segment can be identified by two pointers, if we assign names to the spaces between words. 0 the 1 cat 2 sat 3 on 4 the 5 mat 6 (0,6) is the whole sentence (0,2) is the first noun phrase

CSA2050: DCG I6 From Grammar Rules to Logic The general statement made by the CF rule S → NP, VP can be summarised using predicates over segments with the following logic statement NP(p1,p) & VP(p,p2) => S(p1,p2)

CSA2050: DCG I7 From Grammar Rules to Logic 0 the 1 cat 2 sat 3 on 4 the 5 mat 6 NP VP S

CSA2050: DCG I8 From Logic to Prolog Each logic statement of the form NP(p1,p) & VP(p,p2) => S(p1,p2) Corresponds to the "definite clause" s(P1,P2) :- np(P1,P), vp(P,P2).

CSA2050: DCG I9 Converting a Grammar S → NP, VP NP → N NP → Det N VP → V NP s(P1,P2) :- np(P1,P), vp(P,P2). np(P1,P2) :- n(P1,P2). np(P1,P2) :- det(P1,P), n(P,P2). vp(P1,P2) :- v(P1,P), np(P, P2)

CSA2050: DCG I10 Lexical Categories and Rules Lexical categories are those which are not defined in the grammar itself (eg. N and V in our grammar) Instead, they are defined by the words that they rewrite V → run, sleep, talk etc Lexical categories always derive exactly one input token.

CSA2050: DCG I11 Lexical Rules A rule defining lexical category C must express the following information: there is a C between positions p1 and p2 if some word of syntactic category C spans those positions There are many different ways to translate such a rule into a Prolog clause. Each way needs to make reference to how the input sentence is represented.

CSA2050: DCG I12 Defining Lexical Categories Each category is defined in terms of the words it can rewrite d(P1,P2) :- input(P1,P2,[the]). n(P1,P2) :- input(P1,P2,[cat]). n(P1,P2) :- input(P1,P2,['John']). v(P1,P2) :- input(P1,P2,[ate]). How is the input sentence represented?

CSA2050: DCG I13 Representing the Input Define the predicate input(P1,P2,L) such that P1 and P2 are positions and L is a list containing the words spanning those positions Checkpoint: show how to represent the input sentence "John ate the cat"

CSA2050: DCG I14 John ate the cat input(0,1,['John']). input(1,2,[ate]). input(2,3,[the]). input(3,4,[cat]). Checkpoints Why is John in quotes? Why use a list of one element rather than an atom? Is this the only way to do it?

CSA2050: DCG I15 Complete Program 1. Grammar s(P1,P2) :- np(P1,P), vp(P,P2). np(P1,P2) :- n(P1,P2). np(P1,P2) :- d(P1,P), n(P,P2). vp(P1,P2) :- v(P1,P2). vp(P1,P2) :- v(P1,P), np(P, P2) 2. Lexicon d(P1,P2) :- input(P1,P2,[the]). n(P1,P2) :- input(P1,P2,[cat]). n(P1,P2) :- input(P1,P2,['John']). v(P1,P2) :- input(P1,P2,[ate]). 3. Input input(0,1,['John']). input(1,2,[ate]). input(2,3,[the]). input(3,4,[cat]). 4. Query ?- s(0,4).

CSA2050: DCG I16 Trace of query?- vp(1,4) 1 1 Call: vp(1,4) ? 2 2 Call: v(1,4) ? 3 3 Call: input(1,4,[ate]) ? 3 3 Fail: input(1,4,[ate]) ? 2 2 Fail: v(1,4) ? 2 2 Call: v(1,_349) ? 3 3 Call: input(1,_349,[ate]) ? 3 3 Exit: input(1,2,[ate]) ? 2 2 Exit: v(1,2) ? 4 2 Call: np(2,4) ? 5 3 Call: n(2,4) ? 6 4 Call: input(2,4,[cat]) ? 6 4 Fail: input(2,4,[cat]) ? 6 4 Call: input(2,4,[John]) ? 6 4 Fail: input(2,4,[John]) ? 5 3 Fail: n(2,4) ? 5 3 Call: d(2,_1338) ? 6 4 Call: input(2,_1338,[the]) ? 6 4 Exit: input(2,3,[the]) ? 5 3 Exit: d(2,3) ? 7 3 Call: n(3,4) ? 8 4 Call: input(3,4,[cat]) ? 8 4 Exit: input(3,4,[cat]) ? 7 3 Exit: n(3,4) ? 4 2 Exit: np(2,4) ? 1 1 Exit: vp(1,4) ?

CSA2050: DCG I17 Representing the Sentence Using Difference Lists We can represent the input as a pair of pointers The first pointer points to the entire list The second pointer points to a suffix of the list. The represented list is the difference between the two lists. input(['John',ate,the,cat],['John',ate,the,cat]). input(['John',ate,the,cat],[ate,the,cat]). input(['John',ate,the,cat],[the,cat]). input(['John',ate,the,cat],[]). input([X|Y],Y,X).

CSA2050: DCG I18 DCG Notation The conversion of CF rules into Prolog is so simple that it can be done automatically. Clauses in DCG notation: s --> np, vp. np --> d, n. n --> [cat]. are automatically translated when read in to s(P1,P2) --> np(P1,P),vp(P,P2). np(P1,P2) --> d(P1,P), n(P,P2). n([dog|L],L).

CSA2050: DCG I19 DCG Notation Every DCG rule takes the form nonterminal --> expansion where expansion is any of A nonterminal symbol np A list of non-terminal symbols [each,other] A null constitutent [ ] A plain Prolog goal enclosed in braces {write('Found')} A series of any of these expansions joined by commas.

CSA2050: DCG I20 Complete DCG 1. Grammar s --> np, vp. np --> n. np --> d, n. vp --> v. vp --> v, np 2. Lexicon d --> [the]. n --> [cat]. n --> ['John']. v --> ['ate']. 3. Input 4. Query ?- s(['john', ate, the, cat], []).

CSA2050: DCG I21 Checkpoints What is your system's translation of s --> np, vp. n --> [cat].