This document summarizes a lecture on more advanced features of Definite Clause Grammars (DCGs). It discusses how DCGs can handle extra arguments and tests, which allow them to represent languages beyond context-free grammars. Specifically, it shows how DCGs can incorporate subject and object information to represent English grammar more accurately. It also demonstrates how DCGs can generate parse trees by returning structured terms instead of just success/failure.

1. Lecture 8: More DCGs
• Theory
– Examine two important capabilities offered
by DCG notation:
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
• Extra arguments
• Extra tests
– Discuss the status and limitations of DCGs
• Exercises
– Exercises of LPN: 8.1, 8.2
– Practical session

2. Extra arguments
• In the previous lecture we introduced
basic DCG notation
• But DCGs offer more than we have seen
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
so far
– DCGs allow us to specify extra arguments
– These extra arguments can be used for
many purposes

3. Extending the grammar
s --> np, vp.
• This is the simple grammar
from the previous lecture np --> det, n.
vp --> v, np.
• Suppose we also want to
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
deal with sentences
det --> [the].
containing pronouns such
det --> [a].
as
n --> [woman].
she shoots him
n --> [man].
and
he shoots her v --> [shoots].
• What do we need to do?

4. Extending the grammar
s --> np, vp.
• Add rules for pronouns np --> det, n.
• Add a rule saying that noun np --> pro.
phrases can be pronouns vp --> v, np.
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
det --> [the].
• Is this new DCG any good? det --> [a].
n --> [woman].
• What is the problem?
n --> [man].
v --> [shoots].
pro --> [he].
pro --> [she].
pro --> [him].
pro --> [her].

5. Some examples of grammatical
strings accepted by this DCG
s --> np, vp.
np --> det, n.
np --> pro.
?- s([she,shoots,him],[ ]).
vp --> v, np.
yes
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
?- s([a,woman,shoots,him],[ ]).
det --> [the].
yes
det --> [a].
n --> [woman].
n --> [man].
v --> [shoots].
pro --> [he].
pro --> [she].
pro --> [him].
pro --> [her].

6. Some examples of ungrammatical
strings accepted by this DCG
s --> np, vp.
np --> det, n.
np --> pro.
?- s([a,woman,shoots,he],[ ]).
vp --> v, np.
yes
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
?- s([her,shoots,a,man],[ ]).
det --> [the].
yes
det --> [a].
s([her,shoots,she],[ ]).
n --> [woman].
yes
n --> [man].
v --> [shoots].
pro --> [he].
pro --> [she].
pro --> [him].
pro --> [her].

7. What is going wrong?
• The DCG ignores some basic facts
about English
– she and he are subject pronouns and
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
cannot be used in object position
– her and him are object pronouns and
cannot be used in subject position
• It is obvious what we need to do:
extend the DCG with information about
subject and object
• How do we do this?

8. A naïve way…
s --> np_subject, vp.
np_subject --> det, n. np_object --> det, n.
np_subject --> pro_subject. np_object --> pro_object.
vp --> v, np_object.
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
det --> [the].
det --> [a].
n --> [woman].
n --> [man].
v --> [shoots].
pro_subject --> [he].
pro_subject --> [she].
pro_object --> [him].
pro_object --> [her].

9. Nice way using extra arguments
s --> np(subject), vp.
np(_) --> det, n.
np(X) --> pro(X).
vp --> v, np(object).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
det --> [the].
det --> [a].
n --> [woman].
n --> [man].
v --> [shoots].
pro(subject) --> [he].
pro(subject) --> [she].
pro(object) --> [him].
pro(object) --> [her].

10. This works…
s --> np(subject), vp.
np(_) --> det, n.
np(X) --> pro(X). ?- s([she,shoots,him],[ ]).
vp --> v, np(object). yes
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v. ?- s([she,shoots,he],[ ]).
det --> [the]. no
det --> [a]. ?-
n --> [woman].
n --> [man].
v --> [shoots].
pro(subject) --> [he].
pro(subject) --> [she].
pro(object) --> [him].
pro(object) --> [her].

11. What is really going on?
• Recall that the rule:
s --> np,vp.
is really syntactic sugar for:
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
s(A,B):- np(A,C), vp(C,B).

12. What is really going on?
• Recall that the rule:
s --> np,vp.
is really syntactic sugar for:
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
s(A,B):- np(A,C), vp(C,B).
• The rule
s --> np(subject),vp.
translates into:
s(A,B):- np(subject,A,C), vp(C,B).

13. Listing noun phrases
s --> np(subject), vp. ?- np(Type, NP, [ ]).
np(_) --> det, n. Type =_
np(X) --> pro(X). NP = [the,woman];
vp --> v, np(object).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v. Type =_
det --> [the]. NP = [the,man];
det --> [a].
n --> [woman]. Type =_
n --> [man]. NP = [a,woman];
v --> [shoots].
pro(subject) --> [he]. Type =_
pro(subject) --> [she]. NP = [a,man];
pro(object) --> [him].
pro(object) --> [her]. Type =subject
NP = [he]

14. Building parse trees
• The programs we have discussed so
far have been able to recognise
grammatical structure of sentences
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
• But we would also like to have a
program that gives us an analysis of
their structure
• In particular we would like to see the
trees the grammar assigns to
sentences

15. Parse tree example
s
vp
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
np np
det n v det n
the woman shoots a man

16. Parse tree in Prolog
s(np(det(the),n(woman)),
s
vp(v(shoots),np(det(a),n(man)))))
vp
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
np np
det n v det n
the woman shoots a man

17. DCG that builds parse tree
s --> np(subject), vp.
np(_) --> det, n.
np(X) --> pro(X).
vp --> v, np(object).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v.
det --> [the].
det --> [a].
n --> [woman].
n --> [man].
v --> [shoots].
pro(subject) --> [he].
pro(subject) --> [she].
pro(object) --> [him].
pro(object) --> [her].

18. DCG that builds parse tree
s --> np(subject), vp. s(s(NP,VP)) --> np(subject,NP), vp(VP).
np(_) --> det, n. np(_,np(Det,N)) --> det(Det), n(N).
np(X) --> pro(X). np(X,np(Pro)) --> pro(X,Pro).
vp --> v, np(object). vp(vp(V,NP)) --> v(V), np(object,NP).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v. vp(vp(V)) --> v(V)).
det --> [the]. det(det(the)) --> [the].
det --> [a]. det(det(a)) --> [a].
n --> [woman]. n(n(woman)) --> [woman].
n --> [man]. n(n(man)) --> [man].
v --> [shoots]. v(v(shoots)) --> [shoots].
pro(subject) --> [he]. pro(subject,pro(he)) --> [he].
pro(subject) --> [she]. pro(subject,pro(she)) --> [she].
pro(object) --> [him]. pro(object,pro(him)) --> [him].
pro(object) --> [her]. pro(object,pro(her)) --> [her].

19. Generating parse trees
s(s(NP,VP)) --> np(subject,NP), vp(VP).
np(_,np(Det,N)) --> det(Det), n(N).
np(X,np(Pro)) --> pro(X,Pro).
vp(vp(V,NP)) --> v(V), np(object,NP).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp(vp(V)) --> v(V)).
det(det(the)) --> [the].
det(det(a)) --> [a].
?- s(T,[he,shoots],[]).
n(n(woman)) --> [woman].
T = s(np(pro(he)),vp(v(shoots)))
n(n(man)) --> [man].
yes
v(v(shoots)) --> [shoots].
pro(subject,pro(he)) --> [he].
pro(subject,pro(she)) --> [she].
pro(object,pro(him)) --> [him].
pro(object,pro(her)) --> [her].

20. Generating parse trees
s(s(NP,VP)) --> np(subject,NP), vp(VP).
np(_,np(Det,N)) --> det(Det), n(N).
?- s(Tree,S,[]).
np(X,np(Pro)) --> pro(X,Pro).
vp(vp(V,NP)) --> v(V), np(object,NP).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp(vp(V)) --> v(V)).
det(det(the)) --> [the].
det(det(a)) --> [a].
n(n(woman)) --> [woman].
n(n(man)) --> [man].
v(v(shoots)) --> [shoots].
pro(subject,pro(he)) --> [he].
pro(subject,pro(she)) --> [she].
pro(object,pro(him)) --> [him].
pro(object,pro(her)) --> [her].

21. Beyond context free languages
• In the previous lecture we presented
DCGs as a useful tool for working with
context free grammars
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
• However, DCGs can deal with a lot
more than just context free grammars
• The extra arguments gives us the tools
for coping with any computable
language
• We will illustrate this by looking at the
formal language anbncn{ε}

22. An example
• The language anbncn{ε} consists of
strings such as abc, aabbcc,
aaabbbccc, aaaabbbbcccc, and so on
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
• This language is not context free – it is
impossible to write a context free
grammar that produces exactly these
strings
• But it is very easy to write a DCG that
does this

23. DCG for anbncn{ε}
s(Count) --> as(Count), bc(Count), cs(Count).
as(0) --> [].
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
as(succ(Count)) --> [a], as(Count).
bs(0) --> [].
bs(succ(Count)) --> [b], bs(Count).
cs(0) --> [].
cs(succ(Count)) --> [c], cs(Count).

24. © Patrick Blackburn, Johan Bos & Kristina Striegnitz
• LPN 8.1
Exercises

25. Extra goals
• Any DCG rule is really syntactic
structure for ordinary Prolog rule
• So it is not really surprising we can also
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
call any Prolog predicate from the right-
hand side of a DCG rule
• This is done by using curly brackets { }

26. Example: DCG for anbncn{ε}
s(Count) --> as(Count), bc(Count), cs(Count).
as(0) --> [].
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
as(NewCnt) --> [a], as(Cnt), {NewCnt is Cnt + 1}.
bs(0) --> [].
bs(NewCnt) --> [b], bs(Cnt), {NewCnt is Cnt + 1}.
cs(0) --> [].
cs(NewCnt) --> [c], cs(Cnt), {NewCnt is Cnt + 1}.

27. Separating rules and lexicon
• One classic application of the extra
goals of DCGs in computational
linguistics is separating the grammar
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
rules from the lexicon
• What does this mean?
– Eliminate all mention of individual words in
the DCG
– Record all information about individual
words in a separate lexicon

28. The basic grammar
s --> np, vp.
np --> det, n.
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v, np.
vp --> v.
det --> [the].
det --> [a].
n --> [woman].
n --> [man].
v --> [shoots].

29. The modular grammar
s --> np, vp.
s --> np, vp.
np --> det, n. lex(the, det).
np --> det, n.
lex(a, det).
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
vp --> v, np. lex(woman, n).
vp --> v, np.
vp --> v. lex(man, n).
vp --> v.
 lex(shoots, v).
+
det --> [the].
det --> [Word], {lex(Word,det)}.
det --> [a].
n --> [Word], {lex(Word,n)}.
n --> [woman].
n --> [man].
v --> [Word], {lex(Word,v)}.
v --> [shoots].

30. Concluding Remarks
• DCGs are a simple tool for encoding context
free grammars
• But in fact DCGs are a full-fledged
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
programming language and can be used for
many different purposes
• For linguistic purposes, DCG have
drawbacks
– Left-recursive rules
– DCGs are interpreted top-down
• DCGs are no longer state-of-the-art, but they
remain a useful tool

31. Next lecture
• A closer look at terms
– Introduce the identity predicate
– Take a closer look at term structure
© Patrick Blackburn, Johan Bos & Kristina Striegnitz
– Introduce pre-defined Prolog predicates
that test whether a given term is of a
certain type
– Show how to define new operators in
Prolog