Research Report AI-1989-04
Artificial Intelligence Programs
The University of Georgia
Athens, Georgia 30602
Available by ftp from
aisun1.ai.uga.edu
(128.192.12.9)
Series editor:
Michael Covington
mcovingt@aisun1.ai.uga.edu
PROBLEMS IN APPLYING DISCOURSE REPRESENTATION THEORY
William H. Smith
Piedmont College
Demorest, GA 30535
Artificial Intelligence Programs
The University of Georgia
Athens, Georgia 30602
Introduction
Discourse Representation Theory (DRT) was developed by Hans
Kamp 1981 in order to combine "a definition of truth with a
systematic account of semantic representations (277)". The
semantic representations produced are to provide a bridge between
syntactic parses and model theoretic semantics such that the
representations can be used to determine the truth conditions of
a discourse. This report describes that theory, both the
original, basic form and some extensions that have been suggested
by Kamp and others, and applies it to a "real" discourse in order
to indicate further extensions that will be necessary if DRT is
to be used as a complete theory of semantic representations.
Truth in model theoretic semantics is determined by a
mapping from a representation of the discourse to a model, a
mapping that preserves the properties and relationships of the
discourse. A model consists of two sets: a set of entities (the
universe) and a set of properties of those entities and relations
that hold among them. The discourse representation must likewise
consist of two sets, a set of referenced items and a set of
propositions about those items. A discourse is held to be true
in a model if there is a mapping such that the set of referenced
items maps to a subset of the universe and each property or
relation expressed by the propositions is true of the
corresponding entities in the model.
Kamp addressed the questions of how a discourse places items
in the set of referenced items and of how anaphoric relations can
be expressed in the discourse representation. In particular, he
was concerned with situations in which an item should not be
placed in that set yet should serve as the antecedent for an
anaphoric relationship (the so-called "donkey sentences"). To
that end, he developed the basic version of DRT (1981). Part 1
2
of this report describes that basic theory. Part 2 presents some
extensions to the basic theory. Part 3 describes an attempt to
represent a text in DRT and suggests further extensions that
might be made.
1. Discourse Representation Theory
The central notion of DRT is the Discourse Representation
Structure (DRS). A DRS K is a pair <U, C>, where U is a set of
reference markers (the universe) and C is a set of conditions
(properties, relations, or complex conditions--negation,
disjunction, or implication). The initial DRS, K0, contains none
of the information in the discourse. As the discourse is
processed, the DRS construction algorithm produces a series of K'
as it incorporates material from the discourse into K. For
example
(1) Pedro owns a donkey.
K:<U:{R1, R2},
C:{Pedro(R1),
donkey(R2),
own(R1, R2)}>
Although U and C are described as sets, at least one of
these must be ordered by time of introduction into the discourse
if the construction algorithm is to work properly in assigning
antecedents to anaphoric expressions (cf Goodman 1988).
Antecedent assignment is accomplished by finding an item in U
that agrees with the anaphoric expression (for pronouns, an
entity that agrees in gender and number). Thus, (2) shows an
extension of (1) (:= is an assignment operator, as in Pascal; +
is union of sets):
(2) He beats it.
K: <U,
C := C + {beat(R1, R2)}>
(The basic theory would add R3, R4 to U, and then set them equal
to R1, R2, respectively. A later "clean-up" operation would
eliminate these redundant discourse markers. Here we assume that
3
the clean-up operation has been applied.) A discourse of any
size, however, is likely to include several such entities; most
often, the conflict is resolved by selecting from the candidates
the one that was most recently encountered. In order to make
that selection possible, the set of items must be ordered, and
must in fact be re-ordered every time reference is made to an
entity.
For purposes of exposition, K0 is usually treated as
consisting of empty sets. Such is often not the case in real
discourse, where referring items are often exophoric, their
referents to be found in the nonlinguistic context or in the
shared knowledge of the participants. While DRT allows for such
references, it is not clear how or when the antecedents are to be
entered into K.
Kamp 1985 describes the DRS construction algorithm is "a set
of rules that operate, in a roughly top-down manner, on the nodes
of the parse tree, (2)" converting those nodes into the
conditions of C and, when appropriate, introducing new reference
markers into U. As was noted in the introduction to this report,
the basic version of DRT is directed toward the role of noun-
phrase (NP) nodes in the discourse--their relationship to U.
It would seem, at first glance, that every NP should be
associated with an entity in the model and should therefore have
a corresponding marker in U. (That view is, of course, a great
oversimplification. Most work in DRT has limited itself to
singular concrete NPs, where the oversimplification is not so
drastic.) When the algorithm encounters a NP, it should either
associate it with a marker already present in U (anaphora) or
introduce a new marker, and these were the problems that Kamp
1981 addressed.
The main problem for anaphora is that theories of sentential
syntax do not provide for intersentential anaphora. DRT solves
that problem by creating a unified representation for the
discourse, so that all markers in the discourse are available for
anaphoric relations (with exceptions to be treated shortly).
Conflict resolution is not treated beyond the recency heuristic;
this is not a weakness particular to DRT, for a full treatment of
4
pronominal anaphora must take into consideration grammar,
pragmatics, and knowledge of the real world. Definite noun
phrases perform as do personal pronouns but, since they carry
more content, are less likely to introduce conflict. (Definite
NPs used generically are not considered.)
Proper nouns and indefinite NPs introduce new reference
markers into U. Although this procedure corresponds to the
"first glance" view of natural language, it encounters problems
in sentences that involve negation, disjunction, or conditions:
(3) Pedro does not own a donkey.
(4) Pedro owns a donkey or a cow.
(5) If Pedro owns a donkey he beats it.
One certainly would not want to add a reference marker for
'donkey' in (3); the semantics would require that it map to an
entity in the model, and the sentence explicitly denies its
existence. The same holds for the donkey in (4), since it has
perhaps a 50-50 chance of existing (although it might be useful
to add a marker for the thing that Pedro owns). Sentence (5) is
the so-called "donkey sentence"; it not only introduces a donkey
that may or may not exist, but goes on to make anaphoric
reference to it.
DRT handles sentences of the above types by adding to C one
or more sub-DRSs. Each sub-DRS has its own universe, which is
not visible to the superordinate DRS, and its own condition set,
and the truth value of the sub-DRS is determined by the logical
connective that controls it.
5
(3') K:<U:{R1}
C:{Pedro(R1), ªK',
K':<U:{R2}, C:{own(R1, R2), donkey(R2)}> }>
(4') K:<U:{R1}
C:{Pedro(R1), K' or K'',
K':<U:{R2}, C:{own(R1, R2), donkey(R2)}>
K'':<U:{R3}, C:{own(R1, R3), cow(R3)}> }>
(5') K:<U:{R1}
C:{Pedro(R1), K' -> K'',
K':<U:{R2}, C:{own(R1, R2), donkey(R2)}>
K'':<C:{beat(R1, R2)}> }>
Thus, (3) is true if there is no entity in the model that
satisfies its universe and conditions, (4) is true if there is a
successful mapping from one of its sub-DRSs to the model, and (5)
is true if any mapping that satisfies the antecedent DRS also
satisfies the consequent DRS.
Sentences (4) and (5) introduce an additional problem; each
could be followed by a sentence such as (6):
(6) It is unhappy.
The pair (5-6) is handled by including (6) in the consequent DRS
for (5). The other pair, (4-6), seems to be overlooked by
theorists, but it can be handled, as was suggested above, by
adding to the main DRS a marker for the thing that Pedro owns and
including only the properties -- donkey or cow -- in the sub-
DRSs.
Universal propositions have the same DRS form as
conditionals. The scope of a universally quantified term
relative to an existentially quantified term is indicated by the
U in which the existentially quantified term is placed. Thus,
the usual interpretation of (7) is represented by (7a), while the
interpretation that places 'donkey' outside the scope of 'farmer'
is shown in (7b):
(7) Every farmer owns a donkey.
6
(7a) K:<C:{K' -> K'',
K':<U:{R1}, C:{farmer(R1)}>
K'':<U:{R2}, C:{own(R1, R2), donkey(R2)}> }>
(7b) K:<U:{R2},
C:{donkey(R2), K' -> K'',
K':<U:{R1}, C:{farmer(R1)}>
K'':<C:{own(R1, R2)}> }>
DRT, as described so far, does a very good job of handling a
very small subset of English sentences. Kamp and others have
offered a number of extensions to the basic theory in order to
expand that subset.
2. Extensions to the Basic Theory
The basic theory is confined to a very limited subset of
natural language. In particular, it is limited to singular, non-
generic NPs, to anaphoric reference (i.e. the referent is present
in the discourse), and to sentences whose main verbs do not take
propositions (i.e. DRSs) as arguments. Researchers have offered
extensions to the basic theory that reduce the second and third
of those limitations.
Kamp 1983 and Pinkal 1986 have offered refinements to the
reference-resolving algorithm for definite NPs that extend the
power and accuracy of that algorithm. Kamp distinguishes four
kinds of definite noun phrases (Pinkal: 369):
(8a) Personal and possessive pronouns
( b) Complex demonstratives. (Demonstrative + NP; NP may
include a restrictive relative clause.)
( c) Definite descriptions. ('the' + NP; NP may include a
relative clause.)
( d) Functional definite descriptions. ('the' + NP +
prepositional phrase, the latter limiting the set from
which NP selects.)
Complex demonstratives differ from definite descriptions in that
the latter presuppose a unique referent while the former
presuppose a contrast between two or more possible referents.
Resolution of referential expressions requires the following
7
(Pinkal: 370):
(9a) The DRS K.
( b) A salience ranking of the markers in UK. (Including
recency of reference.)
( c) A selection set of UK whose members are available as
antecedents.
( d) The universe of the real world needed for deictic
reference.
Pinkal argues that definite descriptions are not limited to the
selection set and that there is no motivation for the distinction
between anaphora and exophora (where the referent is not present
in the discourse; it is either physically present--deixis--or
present in shared knowledge).
Guenthner et al. 1986 extend the basic theory by adding two
new types of discourse markers: event markers and time markers.
They include meaning rules in the DRS construction algorithm that
assign each verb and each noun that refers to an action (e.g.
'accident') to an event marker. Each time reference (i.e. time
of day or extent of duration) is assigned to a time marker.
Events are temporally ordered with respect to each other and to
time references: an event may precede or overlap another event or
time, it may be given a time argument expressing its duration,
and it may be a subset of another event. The addition of event
markers makes it possible for predicates to take DRSs as
arguments. Guenthner et al. do not include any examples of such a
use of event markers, but Guenthner 1987 does. In that article
he also makes a notational distinction between events, which
advance the time of the discourse, and situations or static
verbs, which do not.
Spencer-Smith 1987 does not use event markers, but adds a
different type of discourse marker, a proposition marker. This
extension makes it possible to include embedded predicates, such
as infinitival complements and beliefs:
(10) Mary wants to marry a rich man.
8
K:<U:{R1, P1},
C:{Mary(R1), want(R1, P1),
P1:<U:{R2},
C:{rich(R2),
man(R2),
marry(R1, R2)}> }>
The representation of beliefs, which is explored more fully
in Kamp 1985, requires two further additions to DRT: internal and
external anchors. Anchors are used to associate discourse
markers to entities in the world. External anchors are ordered
pairs, <Marker, Entity>, that associate the two as they actually
are, while internal anchors are DRS-like structures that
associate items as the speaker believes they are. The use of
anchors makes it possible to represent propositions that are in
fact contradictory but are not so in the speaker's belief system
because his internal anchors differ from the external anchors:
(11) John believes that Hesperus is pretty and Phosphorus is
not pretty.
External anchors: <R1, John>, <R2, Venus>, <R3, Venus>
Internal anchors:
K:<U:{R2, R3},
C:{evening_star(R2),
morning_star(R3)}>
K:<U:{R1, P1},
C:{John(R1),
believes(R1, P1),
P1:<U:{R2, R3},
C:{pretty(R2),
ªK',
K':<C:{pretty(R3)}> }> }>
These extensions to DRT give it considerable power, but are
far from giving it the power necessary to represent adequately
the full range of meanings available in natural language. In the
next section we attempt to apply DRT to a selection of natural
language in order to discover further extensions that will be
necessary if DRT is to become an adequate theory for the
representation of natural language.
9
3. Application of DRT
The passage to be analyzed here was treated extensively in
Smith 1977 in order to determine the types of information that
must be added to the text in order to obtain a complete
representation of the situation reported by the text. The text
is a narrative passage that has been normed at sixth-grade
readability (ETS 1969). It is particularly interesting because
it forces the reader to treat certain items as if they were in
K0.
In order to represent this passage, it is necessary to
postulate ad hoc extensions to DRT. Although these extensions
work for this passage, they should be regarded as suggestions
only and not as fully developed extensions; some will reveal
their weaknesses as the representation is developed.
The DRS K for the passage will be developed incrementally,
the DRS for each portion being added to the existing DRS. The
clean-up of redundant discourse markers, however, is assumed to
take place before the DRSs are combined. Additional symbols will
be explained as they are introduced. As before, discourse
sentences will be presented in the company of the DRSs that they
add to K; since these sentences, unlike those in previous
examples, have a cumulative effect, they will be denoted with the
prefix N.
In order to treat reference adequately, the items shown
below must be included in DRS K0. These items are, in effect,
imposed on the reader as possible referents. The marker Now
indicates the time of reading.
10
(N0) K:<U0:{R1, R2, Now, R10, R15},
C0:{}>
(N1a) The cave widened out as he went
U := U0 + {E1, E2}
C := C0 + {cave(R1),
E1:widen_out(R1),
E2:go(R2),
E2 o E1,
E2 << Now }
The symbol o indicates that E2 overlaps E1; << indicates
that E2 (and therefore E1) precedes the time of reading.
'widened out' is treated as a unit verb; the 'out' is actually
redundant. Since 'the cave' is definite, its referent must exist
prior to (N1); for this reason R1 is included in U0, and the same
is true of 'he' and R2.
(N1b) and the bottom seemed to drop away little by little
U := U + {R3, E3, P1}
C := C + {bottom(R3),
part-of(R3, R1),
E3:seem(P1),
P1:<U:{E4},
C:{E4:drop_away(R3),
little_by_little(E4)
E4 =< E3}>
E2 o E3}
R3, 'the bottom,' has no apparent antecedent and might have
been included in U0. It seems more likely, however, that it
existed implicitly and that a meaning rule (such as 'Every
physical object has a bottom') resolves the reference. E3 is
true if P1 seems to be true, even if P1 is actually false. Since
E4 is controlled by 'seem,' it is a subset ( =< ) of E3. (I am
not sure that this is what Guenthner et al. mean by subset, since
they offer no examples, but it works here.)
11
(N1c) and then, with no warning, it split in two directions,
U := U + {E5, Set1}
C := C + {ªK1c
K1c:<U:{R4},
C:{warning(R4)}>
E5:split_in(R1, Set1),
E3 << E5,
direction(Set1)}
Since there is no warning, R4 is not visible to the top-
level K. 'directions' introduces what is perhaps the major
weakness in current versions of DRT, a means of representing
plural nouns. The ad hoc solution offered here is to use set
markers, following a suggestion in Guenthner et al. The
proposition direction(Set1) is a notational shorthand for a
complex sub-DRS representing "All members of Set1 are
directions."
12
(N1d) one path leading straight ahead and one off to the
left.
U := U + {E6, R5, R6, E7, R7, R8}
C := C + {path(R5),
E6:lead(R5, R6),
R6 <- Set1,
straight_ahead(R6),
E6 =< E5,
path(R7),
E7:lead(R7, R8),
R8 <- Set1,
to_the_left(R8)
E7 =< E5}
The cohesion of R5 and R7 with R1 is indicated by the fact
that R6 and R8 are members of ( <- ) Set1.
(N2) "If I were an opening to this cave, where would I be?"
he asked himself.
U := U + {E8, P2, R9}
C := C + {E8:ask(R2, R2, P2)
P2:K2a -> K2b,
K2a:<U:{R9}
C:{opening(R9),
part-of(R9, R1),
R2 = R9,
R2 \= R9}>
K2b:<C:{location(R2, ?)}>
E7 << E8 }
(N2) is, on the one hand, almost ridiculous; its only
contribution to the understanding of the passage is the knowledge
that 'he' is lost (Smith 1977), but that knowledge is no more
explicit in the DRS than it is in the sentence itself. On the
other hand, it is a major headache for DRT. (N2) is an embedded
contra-factual conditional whose antecedent is impossible and
whose consequent is a rhetorical question (indicated by the ? as
an argument to location). Its embeddedness, in this case, is
wrong, in the sense that it is not a matter of 'his' belief, but
13
in another situation it might be. The implication itself is
worthless, but another implication might not be. The conclusion
that R9 is not R2 (indicated by \= ) is obvious but might be
useful in another contrafactual. The whole DRS must be added to
K so that the reader can infer, by conversational implicature,
that 'he' does not know the answer to the rhetorical question and
that, since he does not know the answer, he is lost.
(N3) Luke wasn't frightened.
U := U + {Sit1}
C := C + {Luke(R2),
ªSit1,
Sit1:<C:{frightened(R2)}>
Sit1 o E8}
(N3) introduces a situation (more accurately, a non-
situation) whose duration is vague but which at least overlaps
E8.
(N4a) Oh, he knew there were such things in this world as
bottomless caves,
U := U + {Sit2, P3}
C := C + {Sit2:know(R2, P3),
Sit2 o Sit1,
P3:<U:{Sit3, Set2, R10}
C4:{bottomless_caves(Set2),
world(R10),
Sit3:exist_in(Set2, R10),
Sit3 o Sit2}> }
P3 is like an external anchor, in that it is a fact about
the world, but Kamp 1985 does not allow for propositions as
external anchors. It could be treated as an internal anchor, but
it is explicit in the discourse. Both Sit2 and Sit3 are true
throughout the discourse, so they are irrelevant as temporal
markers, but either might have changed during the discourse and
the representation must allow for that possibility.
14
(N4b) where people fell in and were never heard of again,
C4 := C4 + {K4a -> ªK4b,
K4a:<U:{Set3, R11, R12, E9}
C:{people(Set3),
R11 <- Set2,
R12 <- Set3,
fall-in(R12, R11)},
K4b:<U:{R13, E10},
C:{R13 <- Set3,
R13 \= R12,
E10:hear_of(R13, R12),
E9 << E10}> }
This is a continuation of the sub-DRS begun in (N4a); it is
interpreted as a universal: 'No person who falls in such a cave
is ever heard of again.' Since this universal is embedded in a
belief, it does not matter whether such persons exist or not; if
it were not, it would be necessary to replace R11 with a set of
at least two members.
(N4c) but if there had been any such thing around the cottage
he would have heard about it.
U := U + {Set2}
C := C + {K4c -> K4d,
cottage(R15),
K4c:<U:{R14, Sit4},
C:{R14 <- Set2,
Sit4:exist_around(R14, R15),
ªexist_around(R14, R15)}>
K4d:<U:{E11},
C:{E11:hear_about(R2, R14),
E11 << E1}> }
It is not clear whether (N4c) should be treated as a
continuation of the belief initiated in (N4a), as a different
belief, or as a top-level condition. Viewed objectively, it is a
belief (and an illogical one at that), yet it does not seem to be
syntactically embedded in 'know,' or any other verb of belief.
If it is a different belief, or a top-level condition (as it is
treated here), Set2 must be promoted from P3 to the top-level so
15
that it can be visible to other sub-DRSs. R15 must be added to
K0; it is a definite description whose referent cannot be deduced
in the way 'bottom' can be deduced as 'part-of' a cave. As with
K2a, it would seem reasonable to elevate the negation of the
antecedent of a contrafactual to the top-level, but in that case
R14 would not be accessible (it would exist in a subordinate
universe). Since Sit4 is a general proposition, no temporal
relation is assigned; the same is true of Sit5, Sit6, and Sit7
below.
(N5a) This was just a plain, ordinary cave--deeper than most,
but that was all--
U := U + {Sit5, Sit6, Set4}
C := C + {Sit5:plain_cave(R1),
Sit6:ordinary_cave(R1),
just(Sit5),
just(Sit6),
cave(Set4),
ªK5,
K5:<U:{Set5, R16},
C:{Set5 =< Set4,
cardinality(Set5) >
cardinality(Set4)/2,
R16 <- Set5,
R1 <-\- Set5,
deeper_than(R16, R1)}> }
From a logical point of view, most of (N5a) is redundant;
the only useful part is 'deeper than most,' and that belief lacks
credibility. Nevertheless, it poses several problems: handling
the adjective-common noun combination, handling 'just,' and
accounting for 'most' in a manner suitable for logic. The
adjectives 'plain' and 'ordinary' (unlike 'red,' e.g.) have
little meaning until applied to a particular domain-- caves, in
this case. The adverb 'just' means something like 'not other
than' in this case, but how is that meaning determined? It does
not seem to be a syntactic matter, but a DRS is composed from a
16
syntactic parse. K5 is an attempt to handle 'most'; the symbols
< and / have their usual mathematical meanings; <-\- indicates
'not a member of.'
(N5b) and some place there had to be an opening to it.
U := U + {R17, R18, Sit7, P4}
C := C + {place(R17),
opening(R18),
part-of(R18, R1),
Sit7:necessary(P4),
P4:<C:{located(R18, R17)}> }
The truth of (N5b) is doubtful, but given its truth, R17 and R18
must exist at the top-level. It is possible that R18 is
identical to R9, now raised to top-level. Sit7 suggests one way
to handle modal auxiliaries.
(N6) There was, though, one big difference about this cave:
it was Luke's.
U := U + {Sit8, Sit9}
C := C + {Sit8:difference(R1, Set5, Sit9),
Sit9:own(R2, R1),
Sit8 o E1,
Sit9 o Sit8}
The noun 'difference' entails two things that are different
(this cave and other caves) and the thing that distinguishes them
(Sit9). However, only Sit9 is syntactically specified.
17
(N7) He had found it and it was his own secret place.
U := U + {E12, Sit10, R19}
C := C + {E12:find(R2, R1),
E12 << E1,
secret_place(R19),
R19 = R1,
Sit10:own(R2, R19)
E12 << Sit10}
The representation of (N7) is straight-forward; R19 is R1,
but to replace it by R1 in Sit10 is to make Sit10 a copy of Sit9.
This application of DRT has pointed out several needed
extensions to the theory. One of the most obvious is the means
of representing plural NPs, including those with quantifiers that
are less specific than 'all' but more specific than 'some' (e.g.
'most'). Another needed extension is a means of handling terms
that modify conditions: verbs that take verbals as complements
(modals and verbs such as 'seem') and adjectives whose meanings
depend on the particular nouns that they modify. A third
extension is a formalism for specifying arguments that
are not syntactically indicated (such as those for 'difference').
Whether or not the second and third extensions are feasible
without appealing to semantic analysis prior to constructing the
DRS remains to be seen; perhaps the needed machinery is available
in the lexicon.
Conclusion
DRT has been successful in representing a small subset of
natural language, and is being extended to increase the size of
that subset. As we have seen in Part 3 of this report, other
extensions will be necessary before it can handle the full range
of natural language expressions. If those extensions can be
accomplished without appeal to semantics, DRT will prove to be
quite powerful. However, DRT is intended to provide a bridge
between syntactic parses and model theoretic semantics; if
18
semantic analysis is necessary before a DRS can be constructed,
the purpose of DRT has been lost, or at least seriously modified.
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Athens.
Guenthner, F. 1987. Linguistic meaning in discourse
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Guenthner, F., H. Lehman, and W. Schonfeld. 1986. A Theory for
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