TREE UNIFICATION GRAMMAR 
Frdd Popowich 
School of Computing Science 
Simon Fraser University 
Bumaby, B.C. 
CANADA V5A 186 
ABSTRACT 
Tree Unification Grammar is a declarative unification-bas~:l 
linguistic framework. The basic grammar stmaures of this 
framework are partial descriptions of trees, and the framework 
requires only a single grammar rule to combine these partial 
descriptions. Using this framework, constraints associated with 
various linguistic phenomena (reflexivisation in particular) ~ be 
stated succinctly in the lexicon. 
INTRODUCTION 
There is a mind in uni~ca~on-based grammar formalisms 
towards using a single grammar stmctme to contain the 
phonological, syntactic and semantic information associated with 
a linguistic expression. Adopting'the terminology used by Pollard 
and Sag (1987), this grammar structure is called a sign. Grammar 
rules, guided by the syntactic information contained in signs, are 
used to derive signs associated with complex expressions from 
those of their constituent expressions. The relationship between 
the signs and the complex signs derived from grammar rule 
application can be expressed in derivationai structures. These 
structures both explicitly illustrate relations that are implicit in the 
syntax of the signs and express relations that are present in the 
grammar roles. 
Tree unification grammar (TUG) is a formalism which uses 
function-argument (FA) specif~ationa as its primary grammar 
structures. These specifications resemble partially specified 
derivational stmcmn~ of sign-based formalisms like head-driven 
phrase structure grammar (HPSG) (Pollard and Sag, 1987) and 
unification categorial grammar (UCG) (7_,eevat, Klein and Calder, 
1987). TUG uses FA specifications as lexical entries and 
possesses a single grammar rule which combines these 
specifications to obtain a specification for the complex expression 
being analysed. The use of FA specifications allows 
generafisations that are often captured in grammar rules to be 
captured in the lexicon. 
MOTIVATION 
The development of TUG was a consequence of investigating 
extensions to the UCG framework. As described by Zeevat, 
Kh~,, .-d Calder (1987), UCG is a grammar formalism which 
combines SOme of the notiow~s of categorial grammar with those of 
unification-based formalisms like HPSG and PATR-II (Shicber 
el.at., 1983). 
The nsse.t~h .~tM~,,~d in this lmq~r wu ~ o~ at the Univmlity of EdlnbeJqth 
under the rapport of • BrifiJh C,~-,'~weallh Scholmhlp and at 51hUm FmJ~ 
Uui~ky unde* ms Advmu~ Synmll Imti~e ~ Fellov~hip. Special thar, Jo to 
the Omm: f~ Systmm Scknm md zhe L*bm.atm.y for ~r md 
Rnem~ at Simon Fruer Unlve~izy fro. additkmal ml~pe~ I would I.'%-.. to t/rank Dm~ 
P~ md Om ACL mvi~a for thmt ¢,omm~B ,~4 mIl~ 
Like HPSG, the fundamental construction used in UCG is the 
sign. A UCG sign has auributes for phonology, category, 
semantics and order. Consider the sign for the expression Mary 
walks shown in (I). 
(I) Mary-walks 
smt\[f'm\] 
\[eli \[\[fllmary(fl), \[el\]walk(el,fl)\] 
The phonology attribute of this sign (ie. Mary-walks) represents a 
phonological specification of the linguistic expression associated 
with the sign. For our needs we will use a simple sequence of 
words separated by hyphens. The category structure of a sign is 
very similar to that used by categorial grammar. There are three 
primitive categories, namely sent, np, and noun. Complex 
categories are of the form A / B, where B is a sign and A is a 
category (either primitive or complex). The semantic 
representation uses a language called InL (Zcevat, Klein and 
Calder 1987) which incorporates many of the features of 
discourse ~p, csentation theory (Kamp 1981). An InL formula is 
of the form \[a\]Condition where Condition consists of a predicate 
name followed by its argument list. Each element of the 
argument list is either a variable (ie. discourse marker) or an InL 
formula. The variable a preceding Condition is the index of the 
fonnnla. The order attribute of a sign contains information which 
is used to determine the ordering of the phonology of components 
during rule application. If an argument possesses pre as its order, 
then the phonology of the functor precedes that of the argument in 
that of the msuh. The value post describes the opposite situation. 
There is no restriction on the order of (1) as indicated by the 
appearance of the 'don't care' variable '_' in the order attribute. 
InL variables are assigned sorts. A sort can be thought of as a 
collection of features based on factors like gender and number. 
Unification of variables of incompatible sons will fail, thus 
providing a mechanism by which semantic information can 
restrict possible derivations. There are different sons for events, 
states and objects. Variables of the object sorx may be further 
specified with respect to gender (masculine, feminine, or neuter), 
and number. Unsorted variables will be denoted by the leuer a, 
events by e, states by s, and gendedess objects by x, y, and z. The 
letter m will be used to represent variables corresponding to a 
masculine object, f for feminine, and n for neuter. Unique 
identifiers which will be used to distinguish variables will appear 
as numbers following the variable names (ie. nl, ml, s2). 
Signs may be underspecified and through the application of the 
grammar rules they may become increasingly specified by the 
merging of information. Only two grammar rules are proposed in 
('Zeevat, Klein and Calder, 1987): 
(2) Wt-W2: C: S: - ~ Wt: C4(W2:C2:S2:pre): S: _, 
W2.'C2"S 2:pre 
(3) W2-WI: Ci S: - -d, W2:C2:S2:post , 
Wt: C/(W2:C2:S2:post): S: _ 
228 
They cort~pond to forward (2) end backward O) functional 
application, the two roles in basic categorlal grammar. Capital 
letters am used to denote variables that are associated with 
unspecified values which will be instantiated during a derivation. 
Colons are used to separate the different attributes of the sign 
when the sign is displayed in a horizontal rather than vertical 
manner. Consider the result of applying rule O) to the two signs 
associated with Mary and walks which are shown below. 
(4) Mary: np: mary(fl): _ 
(5) walks 
sent\[fin\] / (..:np\[nom\]:\[x\]S:post) 
\[el\] \[\[x\]S, walk(el,x)\] 
The result of rule application is the sign that was introduced in 
(1). Rule application builds up the semantics of an expression by 
instantiating unspecified components, like S in the lexical entry 
for wa/ks (5), that have been placed into the s~rnantic stmc:ure. 
Associated with every linguistic expression is a derivation tree 
which describes how the sign corresponding to the complete 
expression is derived from grammar rules operating over signs 
associated with lexical entries. The leaves of this binary tree are 
labelled with signs for individual words, the root is labelled by the 
sign for the complete expression, while the other nonterminal 
nodes are associated with intermediate expressions. Each 
nonterminal node is labelled with the result obtained by applying 
a grammar rule to the signs which are referred to by its two 
daughter nodes. The edges to the daughters of a nonterminal 
node are designated functor and argument depending on the role 
that the sign at the daughter node plays during grammar rule 
application. 
As an example, the derivation tree provided in Figure 1 
illustrates how backward functional application (BFA) (3) relates 
the signs for Mary (4) and wa/ks (5) to the sign associated with 
Mary-walks (I). The functor edge of a nontenninal node is 
represented by a line darker than that of the argument edge. Rule 
application combines signs and builds derivation trees as a side 
effect. A more generel form of this operation would be to 
combine trees to yield Uees directly. Partial descriptions of a 
complete derivation tree could be combined to yield an 
increasingly further specified derivation tree. 
The principle advantage of combining partial descriptions lies 
in the ease with which certain dependencieJ between different 
constituents can be described. Consider the general case in UCG 
where a functor is applied to an argument to produce a result~ 
Each of these three constituents possesses its own set of features 
which describes the phonological, syntactic and semantic 
information associated with it (Bouma, Kcenig and Uszkoreit, 
1988). The relationship between these constituents is outlined in 
Figure 2. The information F associated with the funaor can be 
dependent on the information G associated with the argument; the 
dependency relation is shown by the are labelled 0 in. Figure 2. 
Such a dependency c4m be captured in the lexicel entry for the 
functor since the ftmctor contains the information associated with 
the argument in its own category name (as highlighted in bold in 
Figure 2). We have already seen an example of such a 
dependency in Figure I - the senumtic information of the funetor 
is dependent on that of the argumenL While the dependency 
marked by ~ can be captured in the lexicon in UCG, the 
dependency marked by p must be captured by the grammar rule; 
the grammar rule must state how the information F' associated 
with the result is obtained from that of the functor and that of the 
argument. If we adopt the premise that F=F, than p becomes an 
identity relation and there is no need for introducing additional 
grammar rules to capture a more complicated relation p. 
Unfortunately, there are cases where the condition F=F" does not 
apply. For instance, Bomna (1988) argues for the need of a lex 
feature which would distinguish lexical elements from phrases; a 
lexical funotor and its result would have different values for this 
feature (+iex and -lex respectively). Similarly, ff one wanted to 
encode bar level information (Jackendoff, 1977) into the different 
constituents then there would be numerous cases where the bar 
level of a functor and that of its argument would not be the same. 
Most importantly though, we can provide a straightforward 
m~ount of reflexivisation if we are not subject to the requirement 
that F--F' as we shall see shortly. 
BFA Mary-walks sent{~\] 
\[el\] \[\[fl\]m~y(fl)0 \[el\]walk(el&l)\] 
Mary walks 
np\[nom\] sent\[fin\] / (Mary: np\[nom\]: \[fl\]mary(fl): post) 
\[fl\]mmy(fl) \[el\] \[\[fl\]mary(fl), \[el\]walk(el.f l)\] 
post 
Figure 1: Derivation Tree 
resuh 
Figure 2: Dependencies Between Constituents 
By using a partial description of a derivation tree as a lcxical 
antry, dependencies corresponding to O in Figure 2 are captured in 
the lexicon instead of in the grammar rules. For instance, the 
BFA grammar role states that the phonology of the resulting 
coostitmmt consists of the phonology of the argument followed by 
that of the functor. The lexicel entry for walks (5) implicitly 
describes such a relationship through the presence of the post 
feature. This fcamre is interpreted by the grammar role, with the 
relation being explicitly represented in the result. If a partial 
description like the one introduced for wa/ks in Figure 3 is used as 
a lexical entry, this reladon is explicitly represented and the 
presence of a post fcstum is actually not necessary. Furthermore, 
local relationships other than those corresponding to ¢~ and p can 
be captured explicidy in the lexical entry. For instance, the 
features associated with an argmnent can be dependent on those 
of its functor and information associated with the result can be 
directly related to that of the argument. One could even have a 
more long distance dependency, say between an argument and a 
subconstitoent of its funetor, stated dimctiy in the lexical entry. 
Most importantly, the use of FA specifications similar to those 
introduced in Figure 3 allows us to capture the restrictions 
associated with reflexivisation in the lexicon, without requiring 
the introduction of additional grammar rules or principles. 
FUNCTION ARGUMENT SPECIFICATIONS 
Although the grammar rules operate over trees in TUG, signs 
still have a role to play in the organisation of information. The 
signs of TUG differ from those of UCG in several respects. First, 
229 
order information is not an explicit part of the TUG sign. The 
subcategorisation information that is contained in the UCG sign is 
not present in the TUG sign; it is represented in the tree structures 
of the framework instead. On a point of terminology, the second 
attribute of the TUG sign is referred to as the syntax instead of the 
category, since it contains more than just categorial information. 
Finally. the TUG sign will also contain an attribute for binding 
information. For now, however, we will restrict our discussion to 
only the fh'st three attributes of a TUG sign. 
<a> 
\[sl\] _ 
every-W 
\[np,C\] 
\[sl\] impl(\[x\]S) -- 
every o.: W 
\[det\] \[noun,C\] 
\[sl\] impi \[x\]S 
• > man 
\[noun,_\] 
man(ml) 
<~> p: W-walks 
\[u~*,fin) 
LJ P(\[x\]S) (walk(el,x)) 
W walks 
\[np,nom\] {v,fin\] 
{_\] P(\[xIS) walk(el,x) 
wa/k~ 
Figure 3: Lexical Entries 
In TUG, a binary tree called an FA specification is associated 
with every linguistic expression. These specifications resemble 
parl~l descriptions of derivation trees. Each node of this binary 
tree is labelled with a sign. The root node possesses a sign 
corresponding to the complete expression, while the leaves are 
labelled with signs for the component words or morphemes. Each 
nonterm/nal node dominates a functos node aud an argument 
node. The terms functor-sign and argument-sign will be used to 
refer to the signs associated with the functor and argument nodes 
respectively. The left-to-right ordering of functor and argument 
edges is not relevantl To refer to the sign of the root node of s 
tree, the term root.sign will be used. The tees rooted at 
nonterminal nodes of an FA specification will be called subtrees. 
An FA specification contains an auxiliary list which specifies 
subtmes of the FA spe~:ification with which other FA 
specifications must be unified. It is represented as a list of labels 
contained in angle brackets appearing to the left of the FA 
specification as illustrated in the lexical entries introduced in 
Figure 3. Observe that there are two edges leading from the 
functor-sign of the FA specification for every which do not lead to 
any nodes. These hang/rig edges are associated with nodes whose 
terminal or nonterminal status has not yet been established. So an 
FA specification may either state that a constituent has no 
subconstiments (terminal node sign), it may state that it has 
subconstiments (nonterminal node sign), or it may say nothing 
about whether or not a constituent possesses subconstiments 
(node with hanging edges). 
The single grammar rule of TUG is introduced in (6), where H a 
denotes an FA specification with auxiliary list rr 
It describes how the FA specification for a complex linguistic 
expression is obtained from unification of the FA specifications 
associated with component expressions. This rule states that an 
FA specification C (which will be called the auxiliary tree) 
possessing an empty auxiliary Hst \[ \] is unified with the subtree of 
H described by the first element of the auxiliary list of H. \[C/a\] 
denotes the list formed by adding C to the front of the list ~ The 
result of this rule is a more fully i~tanfiated version of the 
primary tree, H. The resnlt's auxiliary list will consist of all but 
the lust element of the auxiliary list of the primary tree. Viewed 
procedurally, this rule states how to construct a new FA 
specification from two pre-existing FA specifications. 
Deelaratively, the rule merely states a relationship between FA 
specifications. To illustrate how FA specifications are 
manipulated by this singJe grammar rule we will trace the 
ooustmction of the FA specification associated with the sentence 
Every man wa/ks, using the lexical entries introduced in Figure 3. 
The lexical entry for every requires an auxiliary tree to be 
unified at the location marked by a. For the moment, let us 
examine the suttee associated with the argument of the lexical 
entry. This subtree describes a functor-argument relation between 
two linguistic expressions. One is a functor noun of unspecified 
case C possessing an index compatible with the 'entity' son, as 
designated by the presence of x, while the other is an argument 
determiner with phonology every. Alternatively, one could view 
the determiner as a ftmctor over the noun as suggested in 
(popowich, 1988). However, treating the noon as the fonctor 
allows a uniform treatment of nouns with possessive determiners 
and those with 'regular' determiners. This is the same treatment 
that has been adopted in HPSG (Pollard and Sag, 1987). We will 
propose that for any subtree the functor-sign and the root-sign 
will generally possess the same syntactic category information, 
except for bar.levi information (Popowich, 1988), in a manner 
t~miniseent of the head fe,'~e convention of GPSG (Gazdar 
et.aL, 1985). Observe that the phonology of the root-sign of this 
subtree is that of the argument-sign followed by that of the 
functor-sign. The argument-sign introduces a semantic index of 
the 'state' sort which will also be the index of the InL formula of 
any constituent which possesses a universally quantified noun 
phrase as its argument. This means that sentences like Every man 
walks will describe a state, even though the word walks describes 
an event. This argument-sign also introduces the semantic 
connective/rap/which is associated with the universal quantifier. 
<> 
\[sH _ 
every-man 
\[np,C\] 
\[sl\] impl(man(ml)) -- 
every man 
\[de~l \[~,Cl 
\[sl\] impl man(m 1) 
Figure 4: Intermediate FA Specification 
When the FA specification for man is treated as a (depth zero) 
auxiliary tree which is unified with a from the lexical entry for 
every, we get a more instantiated FA specification which is 
assoc~ted with every man. This specification, which is 
introduced in Figure 4 is similar to the lexical entry for every 
except that x has been i~stantiated to nti , S to man(m\]), and W to 
230 
man. It also differs from the lexical entry for every in that it does 
not possess any iabelled subtrees with which an auxiliary tree 
could be unified. As an abbreviatory convention, the index 
preceding a predicate which contains the index as its first 
argument will be omitted. So man(ml) is actually an abbreviation 
for \[ml\]man(ml) and walk(el,x) is an abbreviation for 
\[el lwalk(el,x). 
The FA specification for every man can act as an auxiliary tree 
to be unified with \[3 from the lexical entry for w~/~ shown in 
Figure 3. Any potential auxiliary tree must have an argument- 
sign whose syntax is compatible with the 'nominative noun 
phrase' specification. No restrictions are placed on the indices of 
the root and argument signs; these indices will be specified by the 
auxiliary tree. The lexical entry for wal~ states how the 
semantics of the n~ot-sign is formed from that of its functor and 
argument signs. When the FA specification for every man is 
combined with this primary tree, P of the primary tree is unified 
with b~ol of the auxiliary tree, x is instantiated to ml, and S is 
unified with man(ml). C of the auxiliary tree is instantiated m 
nora. The resulting FA specification is shown in Figure 5. 
< > every-man-walks 
\[san~fml 
\[sl\] impl (man(m 1)) (walk(e l,m 1 )) 
every-man walks \[npo~om\] \[v,fin\] 
\[sl\] impl(man(m 1)) walk(el,m 1) 
every man 
(d~l (neun,neml \[sl\] impl man(m 1) 
Figure $: Final FA Specificadon 
The FA specification for the complete sentence describes 
exactly one FA structure. While FA specifications may contain 
variables and partially instantiated attributes, FA structures do 
not. The lexical retries of TUG can be viewed as contributing 
constraints to the FA structure that is associated with a complex 
linguistic expression with the single grammar rule being used to 
combine these constraints. During the analysis of an expression, 
constraints are continually proposed and never rescinded. 
Eventually, these constraints will describe the final FA 
structure(s). Thus we distinguish between information structures 
and the descriptiona of those structures in a manner similar to the 
approach proposed by Kaplan end Bresnan (1982) and discussed 
in detail by Johnson (1987). An FA specification can be 
interpreted as describing a set of FA straetums. Gnmrmar rule 
application thin corresponds to the intersection of the sets 
associated with the component FA specifications. The resulting 
set is associated with a new FA specification. If the resulting set 
contains no FA stmcuues, then there is no FA specification 
associated with the resulting set - grammar rule application fatlsl 
An ungrammatical sentence (ie. one without an FA structure) will 
not be assigned an FA specification. The result of the 
8rammatical analysis of a sentence is the set of FA structures 
described by the final FA specification. Grammatical sentences 
can have one or more FA specifications, each of which will 
describe at least one FA structure. 
We are requiring a wellformed FA specification to describe at 
least one FA structure. In this respect, FA specifications differ 
from the description languages introduced in (Kaspar and Rounds, 
1986) and in (Johnson, 1987). These languages allow 
descriptions for which there may not be associated structures. FA 
specifications are actually higher order descriptions which may be 
defined in terms of these description languages. They are 
intended to (transparently) describe structures associated with 
linguistic expressions; they arc not intended to be a powerful 
language for describing fexmre structures in general. Instead of 
using FA specifications to describe FA structures, we could use 
one of these lower level description languages in conjunction with 
a restriction requiring a wellformed description to describe at least 
one sl.nlcture. 
In TUG, many local dependencies between grammatical 
constituents and some other bounded relationships can be 
stipulated explicitly in lexical entries. This is because FA 
specifications for one lexical entry can directly access information 
contained in the sign associated with a different linguistic 
expression. For instance, we have already seen how the lexical 
ent~ for a quantifier can directly specify semantic information 
(the index) for a sentence in which it is contained. It is possible to 
incorporate the constraints on reflexivisation perspicuously in the 
lexicon without causing unnecessarily complicated lexical entries 
and without requiring the introduction of additional principles or 
grammar rules. 
REFLEXIVE ANTECEDENT INFORMATION 
The TUG treatment of reflexives will be based on the concept 
of reflexive antecedent information, henceforth R-ardecedera 
information. R-antecedent information, which will be distinct 
from the semantic information contained in a sign. will be 
responsible for determining the antecedents of reflexive pronouns. 
The constraints on reflexivisation will determine how the R- 
ante_-'eden__ t information of one sign is related to the information 
contained in other signs of an FA structure. 
Since the signs corresponding to the reflexive and its 
antecedent need not both be present in the FA specification for a 
verb (as illustrated in sentences like John wrote a book about a 
picture of himself), we will introduce a reflexive attribute into the 
TUG sign. This 'binding' attribute will contain the R-antecedent 
information nee_tied for establishing an anaphnric relationship 
between the reflexive and its antecedent. Since we have already 
seen the type of information contained in the first three attributes 
of the sign, let us consider the information contained in the fourth 
attribute. 
The antecedent information is responsible for determining the 
discourse marker that can be the antecedent of the pronoun. 
Based on a proposal for the treatment of personal pronouns 
described in (Johnson and Klein, 1986) we will propose that the 
R-antecedent information explicitly describes the set of potential 
discourse markers available as antecedents for reflexives. This is 
the information that will be contained in the reflexive attribute of 
a sign. The lexical retry for the reflexive will only need to state 
that its antec~ient marker is an element from this store. Unlike 
the Cooper storage mechanism described in (Cooper, 
1983) which has been adopted in various proposals for anaphnra 
(Bach and Panee, 1980, Gazdar et.al., 1985), our reflexive 
attribute contains a set of antecedents, not a set of anaphors. 
The R-antecedent information will be represented as an ordered 
list of discourse markers (sorted variables) corresponding to 
potential antecedents. Lists will be displayed in square brackets 
with the different elements separated by commas. The notation 
\[..J/J will be used to designate x as an arbitrary element from a 
fist with \[x/A\] denoting the list resulting from the addition of an 
dement x to a llst A. The sign associated with a reflexive 
231 
pronoun will resemble the one shown in (7). 
(7) himself 
\[ np, obj \] 
true(m) 
\[...ml_\] 
The discourse marker appearing in the semantic formula 
associated with the reflexive pronoun is an arbitrary element (of 
the masculine sort) of the reflexive attribute of the pronoun. The 
condition true introduced in the semantic attribute is always 
satisfiable for any discourse marker. We will discuss the 
semantics of the reflexive pronoun in more detail shoaly. 
The operation of selecting an arbitrary element from a list of 
arbitrary length is a fairly powerful operation. Nevertheless, it 
seems to be a sufficiently primitive operation to be included in a 
framework. It carmot be expressed in the PATR-rl framework 
(Shieber et.al., 1983) which is often used to implement grammars. 
If functional uncertainty (Kaplan, Maxwell and Zaenm, 
1987) were included as a primitive in PATR-n, then this arbitrary 
element selection operation could be implemented. 
The constraints on reflexivisation, which affect the distribution 
of R-antecedent information and its interaction with other forms 
of information, are incoq~orated directly into the TUG lexical 
entries. One constraint is derived from Keenan's (1974) proposal 
whereby the antecedent for a pronoun is an argument of the 
functor containing the pronoun. This can be incorporated into 
TUG by having the R-antecedent information of a functor consist 
of the R-antecedent information of its parent sign augmented with 
the semantic index I of its argument. To illustrate this 'flow' of 
R-antecedent information, consider an analysis of the simple 
sentence Mary loves herself. 
A series of FA specifications corresponding to different stages 
of an analysis for this sentence are shown in Figure 6. To 
highlight the relevant information, much of the information 
contained in the signs of ti~se FA specifications has nut been 
d/splayed. The first FA specification corresponds to the lexical 
entry for loves. Observe that the R-antecedent information of the 
functor-sign consists of the semantic index of the argument sign; 
the reflexive attribute of the sign associated with the object noun • 
phrase is the same as that of the constituent which contains it 
Also note that the InL formula from the sign associated with the 
verb refc~nces the semantic indices of the signs for the two noun 
phases. The second FA specification from Figure 6 illustrates the 
effect of unifying a sign (actually a depth zero tree) corresponding 
to the noun phrase Mary with the argument-sign of the initial FA 
specification. Note that the semantic index, f/, of Mary is 
introduced into the reflexive attribute of the functor over Mary. It 
also appears as the second argument of the semantic predicate 
love (underlined in the FA specification). Since the lexical entry 
for the verb also embodies the relation requiring the reflexive 
attribute of an argument-sign to contain the same information as 
its parent sign, fl is also introduced into the sign associated with 
the objea noun phrase. This 'flow' of R-antecedent information 
is highlighted by the dark arrows in Figure 6. In the final FA 
specification from this figure, a sign corresponding to the 
reflexive pronoun is unified with the sign of the object noun 
phrase in the FA specification. The reflexive pronoun obtains its 
semantic index from the information contained in its reflexive 
attribute as highlighted by the small arrow. This semantic index 
is used as the final argument in the InL formula associated with 
the verb (which is underlined in the FA specification). 
By incorporating Keenan's (1974) proposed dependency into 
FA specifications in this manner, we obtain a relationship much 
like predication.command (Hellan, 1988) and F.command 
(Chierchia, 1988). Although these 'command' restrictions on 
reflexivisation can account for much of the data concerning the 
distribution of reflexive pronouns, additional restrictions are 
necessary (Popowich, 1988). Just as the syntactic c-command 
relation needs to be used in conjunction with a locality restriction 
(eg. the syntactic 'clause-mate' restriction), the distribution of 
R-antecedent is restric:ed by a semantic locality restriction. Such 
a restriction, which is proposed in Pollard and Sag (1983), 
essentially states that reflexive 'information' cannot pass through 
categories of a generalised prediccuive type. A generalised 
predicative takes an NP denotation as its argument, and returns 
either an NP denotation or a 'proposition.' Adopting the notation 
used in (Dowry, Wall and Peters, 1981), the semantic type of a 
functor that takes expressions of semantic type c~ as arguments to 
produce resulting expressions of type ~ is <a,\[3>. This means that 
the semantic type of a generalised predicative is either 
<NP' ~ > or <NP' ,S" >, where NP" and S' are the semantic 
types associated with noun phrases and sentences respectively. 
Conventional categories that are associated with generalised 
"l'~ ~...4 ~ or r=~i,,iss~im a,~ri~ in (Popo,~i~ t~ u~s the predicatives include possessed nominals (like picture of himself in 
a~o,,'c i~u ~ ot ~ R,~mt/c/,,acz of ~ ,~rsw,=L Sm~ ~ two iaak~ the phrase John's picture of himsel\]) and verb phases. 
L'~ kl~tirad in ra~t c~um, v~ wiU sk~llty o~ dlscu~ion b,/usins tho s~sa~ ~. 
(i) W-Ioves-W' (//) Mary-ioves-W' (iii) Mary-loves-herself 
... 
ii" ii ii" 
W Ioves-W' Mary lovea-W ° Mary loves-herself \[np, 
nora\] ... \[ap, noml ... \[rip, nom\] ... \[i' 
...... tm... 
-- /\ ? 
W' loves / W "/ ~' loves h~rself loves 
\[np,obj\] ... ~ \[np,obj\] ... \[np,obj\] 
\[y\]... Iove(sl,x,y) \[y\]... love(sl.fl,y) Jill... iove(sl,fl,£D ... "'" ... < ... 
Figure 6: Distribution of R-Antecedmt Information 
232 
The presence of • general~ed predicative resulu in the 
blocking of R-antecedent information. Consider a subtree of an 
FA specification (like a in Figure 7) where the functor-sign is a 
n 
Z F.,~d~ 
\[xl \[Yl 
N 
Figure 7: Predicate-Command and Locality Restrictions 
generafisod predicative. The R-antecedent information of the 
generalised predinative is • list consisting of only the semantic 
index of the argument-sign. Tbe R-antecedent informatinn of the 
root-sign does not contribute to that of the functor sign. The signs 
of an FA specification conesponding to genendised predicative 
functors will be marked with • syntactic feature to distinguish 
them from non-goneralised predicatives. Functor-signs will be 
marked with the feature gprd ff they are generalised predicative•. 
Non-generalised predicative functors which take noun phases as 
arguments will be m•rked as ÷prd, and other functors will 
possess the fearer• -prd. Arguments will not be marked with any 
'predicate' features. These fcamres are not actually necess•ry for 
our account of the dism'butiun of reflexive pronouns; our 
restrictions on reflexivisation can be defined in terms of other 
basic features. The use of these features will allow the behsvionr 
of R-antecedent information to be observed more easily, as 
illustrated in Figure 7. 2 Foe predicative functors, the R- 
antecedent information of the funotor-sign is composed of the 
semantic index of the argument-sign and the R-antecedent 
information from the root-sign. Note that the R-antecedent 
information of the sign labelled a is not included in that of the 
generaliscd predicative, but the semantic index of the argument- 
sign of a is included in that of the functor. For nun-predicative 
functors, the R-ante¢~lent information of the root-sign will be the 
same as that of the functor-sign. 
AN EXAMPLE 
Now that we have seen bow R-antecedent information can be 
incorporated into FA specifications, we can exmnine how this 
infonnatiun interacu with other forms of infonnatiun during the 
analysis of a more complex sentence. We shall consider the 
analysis of the smtence Mary Iove~ a picture of herself. After 
introducing various lexical entries, we shall see how they arc 
combined with lexical entries introduced earlier in this paper to 
form more complex FA specifications. 
shmcsd ot u..~p~ them thee di~m~t ~ dlmcdy iutl~ vmlmm 
I~iod ran'ms, tl~y c~m bo mn~d~l in L.-;~t to~c.,~ whlch cm tm us0d in lask:e/ 
ca~ (Sbmbmoud~ 19~.Popowlch, 19~), All otthotazi~/mm~ ~dBmd m 
~ i~l~ cm I~ s~plifizd tlm~lh tl~ m of Imld~. 
In the lexical enu 7 for herself in Figure 8, it is the argument- 
sign that is assoc~ted with the linguistic expression herself. This 
sign contains • restriction \[...f/_\] which specifies that the 
semantic index f associated with herself is • member of the 
reflexive attribute of the sign. This arbitrary element of the 
reflexive store is required to be • variable of the feminine sort. 
The s~tex of this sign states that herself can act only as a noun 
phrase of the objective case. Thus it cannot appear in any 
positions in an FA specification which require the noun phrase to 
possess some other case. like no,~ive. ~e other noun 
phrases, the argument-sign contains the semantic connective and 
which will be used in determining the semantics of the font-sign. 
Unlike lexical entries for proper names and quantified noun 
phrases, the semantics of the argument-sign does not associate 
my restrictive condition on the index it introduces; the condition 
truc is always rafsfiable for any discourse marker. This ties in 
with the view of pronotms being semantically underspecified 
linguistic items. Viewed in terms of DRT (Kamp, 1981), the 
fonnule tru~(.O (which is an abbreviation for \[f\]true(/~) merely 
introduces a discourse marker into the universe but does not 
introduce any condition on that marker. Since the syntax of our 
~antic notation requires a formula to consist of an index- 
condition pair, we need to introduce a condition like true along 
with the discourse marker. 
<> 
\[a\] -- 
herself 
\[np,obj\] 
\[t\] and(u~e~O) ~ __ 
\[...ft_\] 
Figure 8: Lexical Entry for herself 
The Icxical entry for the 'depicfive' preposition of. which is 
used in picmre-nonn constructions, is introduced in Figure 9. Of 
takes an object noun phrase argument to form a constituent which 
modifies a common noun. Additional restrictions would be 
required to ensure that it modifies only depictive nouns like 
picture and portrait. Tim lexical entry requires an auxiliary tree 
corresponding to an object noun phrase to be unified with 0t and 
one for a noun to be unified with \[~. It also introduces a semantic 
formula of(x,y) which requires the entity denoted by x to be of the 
entity denoted by y. Semantic formulae of the form \[aI\[A,B\] are 
sbbreviatiuns for formulae of the form \[a\]and(A)(B). The 
functor-sign of a has been specified as • generalised predicative - 
it takes • noun phrase as an argmnent and results in another noun 
phrase. According to our restrictions on R-antecedent 
information, the R-antecedem information A of the root-sign of a 
is not included in that of the generalised predicative but it is 
included in that of the argument-sign. In this way, the same 
R-antecedent information that is associated with the root-sign of 
0t is also available to the embedded noun phrase (ie. the argument 
of ot) as highlighted in bold in Figure 9. The functor-sign of the 
lexical entry for of possesses the feature +prd since it takes a 
noun phrase as its argument to produce a noun. Since an 
argument sign always inherils its R-antecedent information from 
the root-sign, the same R-antecedent infomaation is associated 
with both the root-sign of the lexical entry and the embedded 
phrase. 
In order to obtain the FA specification for picture of herself 
shown in Fignrc I0, the lexical enU 7 for herself acts as the 
233 
<~> W-of-W' 
\[hoLm\] 
\[x\]\[\[x\]S, \[alP(\[y\]S')(of(x,y))\] A 
~: w 
\[noun,+prd\] 
\[xlS 
\[xlA\] 
c~ of-W" 
{np,of\] 
\[a\] P(\[y\]S')(of(x,y)) 
A 
W' of 
\[np,obj\] \[np,of, gprd\] 
(_\]P(\[y\]$') of(x,y) 
A \[y\] 
Figure 9: Lexical Entry for of 
auxiliary tree which is unified with cz of the lexical enu 7 for of, 
and the lexical entry for picture is unified with \[3. Since 
\[f\]and(tru~O~ ) is an abbreviation for \[j~and(\[f\]tru~O~ ) in Figure 8, 
the unification of this formula with \[_\]P(\[y\]S') from the primary 
tree will result in P becoming instantiated to and, y to~ and 5" to 
true(/). Note that in this example, P is a variable over our (finite) 
set of semantic connectives. The FA specification for herself 
introduces a restriction on the reflexive auribote of the sign 
associated with herself This restriction requiresfto be a member 
of the list A which is still uninstantiated. To represent that the 
restriction \[ ...f/_\] was unified with A, we will introduce A as a 
subscrila on this restriction in the FA specifications that we are 
discussing. This will make it easier to examine the behaviour of 
R-antecedent information. The lexical entry for the noun picture 
introduces a marker of the neuter sort, n/, and includes a 
condition which requires this marker to be a picture pie(M). 
When this lexical entry is combined with the FA specification for 
of herself, x from the primary tree gets instantiated to the variable 
associated with the picture nl. Note that 
\[nl\]and(true(jO)(of(nld~) is equivalent to \[ni\]of(nldO. 
< • picture-of-herself 
\[noun\] 
\[nl\]\[pic(nl), of(nl,f)\] 
A 
of-herself picture 
\[np,of\] \[noun,+prd\] 
\[nl| and(true( f))(o f(n I ,f)) pic(nl) 
A \[nl I A\] 
herself of 
\[np,obj\] \[~,of, gprd\] 
\[t'\]end(true(O) of(nl.O 
\[...fw_\] A \[tl 
Figure I0: FA Specification for a picture-noun 
The FA specification for the determiner a is very similar to the 
one for the universal quantifier introduced in Figure 3. We will 
not discuss it in detail here. Instead we will just note that it is 
constructed so that the reflexive attribute of the mot-sign of the 
FA specification for the phrase a picture of herself will be the 
same as that of the sign associated with the complex noun picture 
of herself. Since the reflexive attribute of the sign associated with 
this complex noun is the same as that of the embedded reflexive 
noun phrase (see Figure I0), this means that the R-antecedent 
information, A, of the complex noun phrase a picture of herself is 
the same as that of the embedded noun phrase associated with the 
reflexive pronoun. So, any antecedents available to the complex 
noun phrase will also be available to the embedded reflexive. 
This will result in the appropriate distribution of R-antecedent 
when the FA specification associated with a picture of herself acts 
as an auxiliary tree to be combined with the primary tree 
corresponding to the lexical entry for love~. 
The lexical entry for the transitive verb loves (Figure 11) 
requires two auxiliary trees corresponding to its ohjea and subject 
noon phrases to be unified with suhtrees a and \[3 respectively. It 
is structured in much the same way as the lexical entry for walks 
discussed earlier. Note that for a, the functor-sign is not a 
generalised predicative and so the R-antecedent information of 
the functor sign is made up of the semantic index y of the 
argument-sign and the R-antecedent information \[x\] of the root- 
sign. \[3 does have a generalised predicative functor-sign, so the 
R-antecedent information A' of the root sign is not included in 
that of the generalised predicative, \[x\]. 
< o., ~• \[3: W-Ioves-W' 
\[sengfin\] 
\[_\] P( \[x\]S)(\[a'\]P'(\[y\]S')(Iove~ s 1,x,y))) 
A" 
W a: loves-W' 
\[rip, nom\] \[v,fin, gprd\] 
\[_\]P(\[xlS) \[a'\]P'(\[ylS ")(love( s l,x,y)) 
A' \[x\] 
W' loves 
\[np,obj\] \[v,fin,+prd\] 
\[1P'(\[y}S') Iove(s l,x,y) \[x\] \[y,x} 
/\ 
Figure II: Lexical Entry forloves 
When the lexical entry for loves takes the FA specification for 
a picture of herself as an auxiliary tree to be unified with a, the 
reflexive attribute A from the auxiliary tree becomes instantiated 
to \[x\]. But recall that there is still an additional restriction placed 
on the A which requires f to be an arbitrary member of A. This 
means that f must be unified with x; the subject of the verb is 
stipulated to be an entity possessing a marker of the feminine sort 
as illustrated in Figure 12. Unification of the auxiliary tree with a 
also results in y being instantiated to the variable associated with 
the picture hi. The semantic formula PIC(nld~ in Figure 12 is an 
abbreviation for the somewhat lengthy formula 
trill \[pie(M), oj~nl J)\]. 
When the FA specification from Figure 12 is combined with 
the auxiliary tree corresponding to the lexical entry for Mary, the 
variable f from the primary tree becomes insmntiated to the 
discourse marker associated with Mary. An attempt to unify an 
FA specification for a 'masculine' noun phrase with \[3 of the 
primary tree would fail since the nominative noun phrase is 
required to possess a semantic index of the feminine son (as 
shown in bold). Thus, for a sentence like John loves a picture of 
herself there would be no FA spedfication and consequently no 
FA structure (unless there were some female entity named John). 
COMPARISON 
The name "Tree Unification Grammar" suggests that TUG 
might be related to other unification-based frameworks as well as 
to other tree-based frameworks. We shall briefly compare TUG 
with some of the beuer known of these related frameworks. A 
234 
< 13 > ~: W-loves-a-picture-of-her self 
\[sent, fin\] 
fl P(\[x\]SX\[sl \]\[PIC(nl,0~ove(sl,fja 1)\]) 
A 
W loves-a-picture-of-herself 
\[np, nora\] \[v,fm,gprd\] 
\[_\]P(\[f\]S) \[s 1 \] \[PIC(nl j),love(s l,f,nl )\] 
A If\] 
a-picture-of-herself loves 
\[np,obj\] \[v,fin,+prd\] 
\[n l\]and(PlC(n l,f)) love(s l,f, nl) if\] {nl,t'\] 
o..t" "'-.o.... 
...:" hcrsclf ""-. 
." \[np,obj\] "'.. ...... \[t\]and(~c~6)"" 
\[fl 
Figure 12: FA Specification for a verb phrase 
more detailed discussion can be found in (Popowich, 1988). 
Uszkoreit (1986) introduces Categorial Unification Grammar 
(CUG) as a class of grammars which combine the features of 
categorial granunars with those of unification granmlars. In 
CUG, directed acyclic graphs (DAGs) are used as the basic 
granunar structures. Granunatical c~t~stituents possess attributes 
for phonology, syntax, and semantics. These constituents are 
essentially the signs of CUG. Two grammar rides, for forward 
and backward funct/onal application, are used to form new 
constituents. CUG is sin~lar to PATR-r\[ in that it could serve as 
a language into which TUGs could be translated. A potential 
disadvantage of CUG is that it might be too unrestricted in the 
type of operations that it allows (van Benthem, 1987). In 
addition, the type of structures allowed in TUG is very restricted 
(binary trees containing only a fixed number of attributes) while 
those allowed in CUG are much less resuicted. The structures 
used by TUG, UCG and other formalisms can be translated into a 
low-level format consisting of CUG DAGs. A major short- 
coming of using CUG or PATR-I/as a linguistic formalism is that 
the dependencies that am necessary for determining anaphoric 
relationships are 'hidden' in the DAG describing the linguistic 
expression; information is distributed in a fiat graph structure with 
no higher order grouping expressed. Although this may be 
beneficial with respect to implementing grammars, it can make it 
difficult to work with the structures. The advantage of the FA 
structure is that it is an explicitly hierarchical ~6v, r.sentation 
structure - a tree with structured .nodes - instead of a graph of 
simple nodes. This hierarchical structure allows many linguistic 
generalisations, particularly those associated with reflexivisation, 
to be stated easily and transparently. 
Tree adjoining grammars (TAGs) (Joshi, Levy and Takahashi, 
1975, Vijay-Shanker and Joshi, 1988) possess trees as basic 
grammar structures, and grammar rules are used to alter the 
structure of these trees. The relationship between TUG and TAG 
is very superficial as will be illustrated after a short description of 
the framework. A TAG contains/n/t/a/trees and auxiliary trees. 
Initial trees are defined as n-ary trees possessing only terminal 
symbols as leaves. The leaves of an auxiliary tree are all terminal 
symbols except for a single nontenninal, the fooL which is of the 
same category as the root of the tree. These two types of trees 
comprise the class of elementary trees. There is a trec adjoining 
operation which is used to form derived trees. AppLication of this 
rule results in the insertion of auxiliary trees into the middle of 
~nitlal trees or other derived trees, subject to speci~c restrictions. 
TAGs are fundamentally different from TUGs since the adjoining 
operation alters the structure of the ume instead of merely further 
instentiating it. Adjoining involves the insertion of trees at 
internal nodes while the TUG operation can be viewed as the 
overlaying of trees to form larger structures. The TAG 
framework has fully specified trees that are modified by other 
fully specified trees in order to obtain more complex fully 
specified trees. In TUG, partially specified trees are combined 
(not modified) in order to ohtain a more fully specified complex 
tree. Feature structure based TAGs (FlAGs) (Vijay-Shanker and 
Joshi, 1988) are more closely related to TUG than traditional 
TAGs. The adjoining operation of FTAG amounts to combining 
a description of the auxiliary tree with that of the tree into which 
it is adjoined. In this way, a more complete description of the 
final tree is gradually constructed. However, in FTAG tree 
descriptions the internal tree structure is not fixed. The 
descriptions are organised so that additional trees may be adjoined 
at specific locations. After all the required adjoining operations 
have been performed, these gaps in the tree structure are closed 
via unification. In TUG tree descriptions (FA specifications) the 
internal tree structure is fixed; the fringe nodes of the FA 
specification are the only ones for which tree structure 
information may not be specified (as designated by the hanging 
edges described exriler). 
The most closely related grammar formalism to TUG is HPSG 
as described in (Pollard and Sag, 1987). The phrasal signs of 
HPSG are almost notational variants of the FA specifications of 
TUG; phrasal signs were not present in the early forms of HPSG 
(Pollard, 1985) from which UCG and TUG evolved. Aside from 
the dighfly different appearance of these different structures, FA 
specifications are slightly more restrictive in that a node may only 
have two descendents instead of the unlimited number allowed in 
HPSG. TUG also differs from HPSG in that it requires only one 
(instead of two) grammar rules. This is a consequence of TUG 
having essentially phrasal-signs as lexical entries. In this way, a 
lexical entry can directly access information other than that 
associated with its sister signs in a derivation tree (or phrasal 
sign). This allows interesting proposals for the treatment of 
reflexives in controlled complements and unbounded dependency 
constructions which am discussed in dc~aJ.l in (Popowich, 1988). 
SUMMARY 
In TUG, the phonological, syntactic, semantic and antecedent 
information describing linguistic expressions is contained in signs 
which are organised into FA structures. These FA structures are 
binary ores which encode the functor-argurnent dependencies 
between the signs corresponding to components of a complex 
expression. Partial specifications of FA structures are associated 
with individual lexical entries and these FA specifications are 
combined by a single grammar role. Dependencies between 
information associated with different linguistic constituents that. 
are traditionally captured by grammar roles are captured explicitly 
in the TUG lexical entries. TUG can in some sense be viewed as 
a 'lexicalised' UCG, where 'lexicelised' is.used in the sense 
discussed in (Schabes, Abeille and Joshi, 1988). 
However, the FA structures described by a TUG analysis of a 
sentence are difficult to obtain as derivation trees in UCG. As 
discussed earlier, the UCG grammar roles require the semantic 
attributes of the root-sign and fonctor-sign of any subtree to be the 
same. Additional grammar rules would be needed by UCG to 
allow the diffenmt relationShil~S between semantic infonmation 
235 
and to allow the three different relations between the R- 
antecedent information of a root-sign and functor-sign. The 
R-antecedent information of a functor-sign can either be the same 
as that of the mot-sign (non-predicative functors), or it can consist 
of the semantic index of its argument in addition to the R- 
antecedent information of the mot-sign (po-.dicative functors), or 
it can contain only the sanantic index of its argument 
(generalised predicative functors). 
The R-antecedent information contained in FA specifications is 
treated on a level equal to the other forms of information; there is 
no need to invoke special mechanisms for passing this 
information. Its distribution is governed by the predication 
command and generalised predicative constraints. The reflexive 
attribute of the sign contains information that m/ght be needed by 
a reflexive pronoun. So if a sign for a reflexive pronoun appears 
in an FA specification, the possible anteee_aen_ ts for the reflexive 
are easily accessible. During ~ unification, if the sign 
associated with a reflexive pronoun contains no variables of the 
appropriate son in its reflexive store, then the use of the pronoun 
is ungrammatical md tree unification fails. Since an FA 
specification is associated with each potential antecedent of a 
reflexive proneen, failure of anaphora resolution can constrain 
possible analyses; if there is no possible antecedent for a 
reflexive, there will not be an FA specification. 
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236 
