Type-inheritance Combinatory Categorial Grammar
John Beavers
CSLI, Stanford University
Stanford, CA, 94305
jbeavers@csli.stanford.edu
Abstract
In this paper I outline Type-inheritance Combi-
natory Categorial Grammar (TCCG), an imple-
mented feature structure based CCG fragment
of English. TCCG combines the fully lexical
nature of CCG with the type-inheritance hierar-
chies and complex feature structures of Head-
driven Phrase Structure Grammars (HPSG).
The result is a CCG/HPSG hybrid that com-
bines linguistic generalizations previously only
statable in one theory or the other, even extend-
ing the set of statable generalizations to those
not easily captured by either theory.
1 Introduction
Type-inheritance Combinatory Categorial Gram-
mar (TCCG) is a type-inheritance, unification-based
CCG of the English fragment in Sag and Wa-
sow (1999), implemented in the LKB (Copestake,
2002), a grammar development platform for pro-
ducing efficient grammars for deep parsing. Typ-
ically, work in CCG (Steedman, 1996, 2000, in-
ter alia) has focused on theoretical issues such as
constituency and a principled syntax/semantics in-
terface, with less work spent on the organization
of grammatical information (see Baldridge 2002).
Work in HPSG (Pollard and Sag, 1994; Ginzburg
and Sag, 2000, inter alia) has instead focused on
well-grounded structuring of grammatical informa-
tion, most specifically in terms of type-inheritance
hierarchies, although often at the cost of coverage
and elegance (see Penn and Hoetmer 2003). How-
ever, the respective foci of work in these frame-
works are largely orthogonal, suggesting a great po-
tential in combining them, as recent work by Villav-
icencio (2001) and Baldridge (2002) has demon-
strated. Following directly on this work, I adopt the
type hierarchies of HPSG wholesale into TCCG, ex-
ploring directly the theoretical advantages this hy-
brid approach yields, with direct comparison to pre-
vious CCG and HPSG work. A full description
of TCCG is beyond the scope of this paper (see
Beavers 2002); I sketch below just a few of its ad-
vantages. In a0 2 I discuss background information
about encoding TCCG in the LKB, including how
TCCG deals with the so-called “spurious ambigu-
ity” problem of CCG. In a0 3 I compare the rele-
vant features of HPSG and CCG and discuss pre-
vious work that has combined them. In a0 4 I discuss
the advantages type hierarchies bring to CCG, us-
ing the structure of the lexicon as well as the struc-
ture of lexical mapping rules as case studies. In a0 5
I discuss the advantages of CCG’s highly lexical-
ist nature over common HPSG analyses and how
these are encoded in TCCG. In a0 6 I discuss one
domain (modification) where TCCG shows poten-
tial to simplify common analyses in both HPSG and
CCG grammars due to its hybrid nature.
2 Implementation Details
I assume for this paper a rudimentary understand-
ing of CCG. TCCG encodes as usual a small set
of simplex syntactic categories (S, N, NP, PP, and
CONJ) from which complex categories are built via
slash operators. For example, eat is assigned cate-
gory (Sa1 NP)a2 NP, i.e. eat is a function from an NP
to its right to a function from an NP to its left to S.
The basic rule-set is outlined in (1):1
(1) (a) Forward Functional Application (a3 ) :
Xa4 Y Y a5 X
(b) Backward Functional Application (a6 ) :
Y Xa7 Y a5 X
(c) Forward Functional Composition (a3 Ba8 ) :
Xa4 Y Ya4 Za9 ...a4 Z
a8
a5 Xa4 Za9 ...a4 Z
a8
(for na10 2)
(d) Backward Functional Composition (a6 B) :
Ya7 Z Xa7 Y a5 Xa7 Z
(e) Forward Type Raising (a3 T) :
NP
a8a12a11a14a13
a5 Sa4 (Sa7 NP
a8a12a11a14a13
)
(f) Backward Type Raising (a6 T) :
X a5 Ta7 (Ta4 X)
(g) Backward Crossed Substitution (a6 Sa15 ) :
Ya4 Z (Xa7 Y)a4 Z a5 Xa4 Z (where X=Sa7 $)
(h) Coordination (a16 ) :
X CONJ X a5 X
1The $-notation indicates meta-categories: $ stands for any
list of categories (e.g. X$ could be Xa7 Y, Xa4 Y, (Xa7 Y)a4 Z, etc.),
a7 $ for a list of backward-slashed categories, and a4 $ for a list of
forward-slashed categories. Subscripts indicate category iden-
tity, e.g. $a9 refers to the same list in all its uses in one category.
Note that a0 B is generalized to allow for com-
position of a1 -ary functions (but currently only for
a1a3a2a5a4 ), and a0 T is restricted to nominative subject
NPs (the only place in English where it is impor-
tant). Turning to encoding, I assume a sign-based
packaging of syntactic and semantic information:2
(2) (a) a6a7
a7
a7
a7
a7
a7
a7
a7
a7
a7
a7
a7
a7
a7a8
sign
ORTH *diff-list-of-strings*
NF nf
SS
a6a7
a7
a7
a7
a7
a7a8
synsem
ROOT
a6
a8 root-struct
RCAT basic-category
FEATS features
a9a10
CAT category
SEM sem-struct
a9a12a11
a11
a11
a11
a11
a11
a10
DTRS list-of-signs
a9a12a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a10
(b) Feature Description
ORTH Orthography
NF Normal form feature
SS Syntactic/Semantic info
ROOT Root category info
RCAT Simple root category
FEATS Morphosyntactic features
CAT Category information
SEM Semantic information
DTRS Phrasal daughters
Following Baldridge (2002), the root category is
the final result of a category after all applications
(e.g. S for a transitive verb (Sa1 NP)a2 NP) and defines
the morphosyntactic features of a category. Ignor-
ing the details of the category type hierarchy, sim-
plex categories are atomic types and complex cat-
egories are feature structures with a simplex result
and a list of arguments as illustrated in (3).
(3) (a) Argument: (b) Complex Category:
a6
a8
argument
ARG synsem
SLASH slash-struct
a9a10
a6
a8 complex-category
RESULT category
ACTIVE lista13 argsa14
a9a10
(c) Example Argument: (d) (((Sa15 NP)a16 NP)a16 NP):
a6
a8
argument
ARG a17 CAT np
SLASH back-slash
a9a10
a6
a8 complex-category
RESULT s
ACTIVEa18 a15 NP,a16 NP,a16 NPa19
a9a10
(Abbreviated as a15 NP)
Finally, I briefly discuss how TCCG deals with
the so-called “spurious ambiguity” of CCG. The
combinatory power of CCG allows for a potentially
exponential number of parses for a given reading
of a single string.3 A considerable amount of work
2In this paper I ignore the semantics of TCCG. It is worth
noting that I do not adopt the a20 -calculus semantics typical of
CCG but opt instead for the Minimal Recursion Semantics
(MRS) (Copestake et al., 1999) native to the LKB.
3However, the so-called “spurious” parses are in fact mo-
tivated by intonational and information structural phrases, as
argued by Steedman (2000), although TCCG does not imple-
ment any prosody information.
has focused on spurious ambiguity and its effects on
efficiency (see Karttunen 1986; see Vijay-Shankar
and Weir 1990 for proof of a polynominal-time
parsing algorithm and Clark and Curran 2004b for
statistical models of CCG parsing), however most of
these solutions are parser based. Rather than mak-
ing proprietary modifications to the LKB’s parser, I
instead adopt Eisner’s (1996) CCG normal form to
eliminate spurious ambiguity. Eisner demonstrates
that the parse forest assigned to a given string can be
partitioned into semantic equivalence classes such
that there is only one “canonical” (normal form)
structure per equivalence class, where the normal
form prefers application over B and right-branching
a0 B over left-branching a0 B (and vice versa for
a21 B).4 These preferences are statable as constraints
on what may serve as the primary functors of differ-
ent combinators. I implement this by assigning one
of the values in (4) to the feature NF:
(4) nf
tr
bc-tr
ot
bc-ot-tr fc-ot-tr
fc
fc-tr fc-ot
bc
bc-ot
An NF value fc marks a sign as being the out-
put of a0 B, bc as the output of a21 B, ot as a lexi-
cal item or the output of application, and tr as the
output of T. The subtypes are disjunctive, so that
fc-ot-tr is either a lexeme or the output of a0 B, ap-
plication, or T. Each combinator constrains the NF
features of its output and daughters to be of specific
value. For example, to prefer right-branching a0 B
over left-branching a0 B, a0 B is constrained as in (5).
(5) (Xa2 Y)a22a24a23a26a25a28a27a30a29a31a25a32a29a34a33 Ya2 Z a35 Xa2 Za36a37a23
This constraint says that the output of a0 B is
marked fc and its left daughter is bc-ot-tr, i.e. must
be a lexical item or the output of a21 B, application, T,
but not another a0 B (marked fc), thus ruling out left-
branching a0 B over right-branching a0 B. Other com-
binators in (1) are constrained similarly. The cumu-
lative effect results in only one “canonical” parse
for each reading of a given string. For more dis-
cussion of the efficiency of this approach see Eisner
(1996) and Clark and Curran (2004a). For purposes
of TCCG, however, eliminating spurious ambiguity
facilitates exploration of TCCG’s hybrid nature by
making direct comparisons possible between types
of grammatical encoding in TCCG and more stan-
dard HPSG/CCG approaches, which I turn to next.
4Eisner’s constraints on
a6 Sa15 only apply to CCGs with a6 B
a8for
a38 a3a40a39 and are thus ignored. I do augment Eisner’s system
by restricting T to only occur when needed for B.
3 A Comparison of CCG and HPSG
In this section I briefly review some major dif-
ferences between CCG and HPSG. Both theories
share roots in the same strand of lexicalist syntax,
wherein grammatical information is lexically en-
coded and combination is category driven. While
the two theories differ considerably in several fun-
damental ways, there are two key differences rele-
vant to this discussion. The first is how categories
are constructed. In CCG the restricted set of sim-
plex categories, the means by which complex cat-
egories are built, and the generality of the com-
binators collectively yield a principled system that
conforms strongly to the lexicalist assumption that
all combinatory information is encoded categorially.
HPSG, however, allows a wide range of simplex cat-
egories and no restrictions on types of rules, allow-
ing uneven divisions of combinatory information
between categories and constructions. In principle
a CCG style category/combinatory system is possi-
ble in HPSG (as TCCG demonstrates), but in prac-
tice large scale HPSGs tend to represent information
heterogeneously, making certain cross-cutting gen-
eralizations difficult to state, largely a result of the
directions HPSG has taken as a research program.
The second relevant difference between these the-
ories is how categories are structured relative to one
another. Traditionally, CCG offers no grammatical
tools to statically relate categories. Instead, these re-
lationships are left implicit even when linguistically
relevant, only statable meta-theoretically. HPSG
has from its inception employed multiple inheri-
tance type hierarchies (e.g. as in (4)), where some
of the grammatical information for a particular sign
is inherited from its immediate supertype, which it-
self inherits grammatical information from which
its supertype, and all types share inherited informa-
tion with their sisters. The result is a richly struc-
tured set of relationships between linguistic units
that reduces redundancy and can be exploited to
state grammatical and typological generalizations.
As noted in a0 1, the respective advantages of these
theories are compatible, and much previous work
has exploited this fact. Use of unification (a core
operation in HPSG) in CG dates at least as far
back as Karttunen (1986, 1989), Uszkoreit (1986),
and Zeevat (1988). Work on incorporating inheri-
tance hierarchies into CCG is relatively more recent.
Most notably Villavicencio (2001) implements a hy-
brid CCG/HPSG grammar in the LKB for purposes
of exploring a principles and parameters acquisi-
tion model, defining parameters in terms of un-
derspecified type hierarchies that the learner makes
more precise during the learning process.5 Moving
5Note that TCCG employs a different type of CG than
beyond acquisition, Baldridge (2002) argues more
generally for a type-hierarchy approach to the struc-
ture of a CCG lexicon so as to reduce redundancy
and capture broader typological generalizations, al-
though he does not explicitly flesh out this pro-
posal.6 With TCCG I build directly on this pre-
vious work by applying Villavicenio’s type inheri-
tance techniques to the issues raised by Baldridge,
addressing head on the advantages of a hybrid ap-
proach and comparing it to prior HPSG and CCG
analyses. In the following sections I outline several
case studies of this approach.7
4 Advantages of TCCG over CCG
I turn first to the use of type hierarchies and lexi-
cal mapping rules in TCCG and the elimination of
redundancy this brings to CCG. Using as my case
study the hierarchy of verbal signs, in CCG the fol-
lowing categories are assigned to various verb types
(note that in TCCG CPs are categorially finite NPs):
(6) (a) Intransitive (sleep): Sa1 NP
(b) Intransitive PP complement (speak (to)):
(Sa1 NP)a2 PP
(c) Intransitive CP complement (think):
(Sa1 NP)a2 NPa36a1a0a3a2
(d) Intransitive PP-CP complement (say
(to)): ((Sa1 NP)a2 NPa36a1a0a3a2 )a2 PP
(e) Intransitive CP-subject (suck): Sa1 NPa36a4a0a5a2
(f) Transitive verbs (see): (Sa1 NP)a2 NP
(g) Transitive PP complement (donate):
((Sa1 NP)a2 PP)a2 NP
(h) Transitive CP complement (tell):
((Sa1 NP)a2 NPa36a1a0a3a2 )a2 NP
(i) Ditransitive (give): ((Sa1 NP)a2 NP)a2 NP
(j) Subject control (want/appear):
(Sa1 NP)a2 (Sa1 NP)
(k) Object control (persuade/ask):
((Sa1 NP)a2 (Sa1 NP))a2 NP
(l) Auxiliary (will): (Sa1 NP)a2 (Sa1 NP)
Villavicencio’s implementation, which has generalized weak
permutation and product categories but no type-raising.
6See also Erkan (2003) for a recent attempt to describe mor-
phosyntactic features in CCG via type hierarchies.
7Before proceeding I should note that TCCG is based pri-
marily on Sag and Wasow (1999). This source was chosen for
two reasons: (a) TCCG is primarily a proof-of-concept and thus
a relatively constrained textbook grammar is ideally suited to
exploring the issues addressed here and (b) a parallel HPSG im-
plementation already exists that could provide for direct com-
parisons (although this is a matter of future work). However,
development of TCCG has been informed by a wider range of
work in CCG and HPSG and the conclusions I draw are appli-
cable to both theories at large.
Of course, several linguistically relevant relation-
ships hold across these types, as shown in (7).
(7) (a) All verbs share morphosyntactic features.
(b) All verbs have a leftward subject.
(c) All verbs obey obliqueness hierarchies
(NPs are closest to verbs, obliques
further, modulo syntactic operations like
heavy-NP shift).
(d) All complements are rightward.
(e) Barring morphosyntax, auxiliary and
control verbs share a category.
While these generalizations are of course deriv-
able meta-theoretically (from the categories in (6),
there is no explicit mechanism in CCG for stating
static relationships (there are mechanisms for de-
riving categories, which I discuss below). TCCG,
however, captures (7) via a lexical type hierarchy,
the subtype for transitive verbs given in (8).8
(8) s-lxm
verb-lxm
tv-lxm
cptv-lxm dtv-lxm ptv-lxm stv-lxm orc-lxm
orv-lxm ocv-lxm
rcv-lxm
...
...
...
Each sign in TCCG is assigned a type in such a
hierarchy, where relevant generalizations in super-
types are inherited by subtypes. For example, the
constraint that all verbs are rooted in S is stated on
s-lxm, while the constraint that they all have left-
ward subjects is stated on verb-lxm:
(9) verb-lxm := a0 SS
a17 CAT a17 ACTIVEa18 a15 NP, ...a19a2a1
Further specializations add additional informa-
tion, for example tv-lxm adds information that there
is at least one additional item in the valence of the
verb ((Sa1 NP)a2 X$). This type hierarchy has sev-
eral advantages. First, it significantly reduces re-
dundancy, since each constraint relevant for mul-
tiple categories is (ideally) stated only once. Sec-
ond, these types provide a locus for cross-linguistic
typological generalizations, an advantage that goes
beyond parsimony. For example, the slash-marking
8I use the following type abbreviations: s-lxm=lexeme
rooted in S, n-lxm=lexeme rooted in N, verb-lxm=verb,
tv=transitive verb, rcv=control verb, cptv=CP complement tran-
sitive verb, dtv=ditransitive verb, ptv=PP complement transi-
tive verb, stv=strictly transitive verb, orc=object control verb,
orv=object raising verb, ocv=object equi verb.
constraint on verb-lxm in (9) defines English as an
SV language. For a language like Irish this type
could encode a general VS constraint (e.g. verb-lxm
:= Sa2 NP$). Thus the type hierarchy provides an ex-
plicit means for encoding broad typological param-
eters not directly statable in CCG (see Bender et al.
2002 for further discussion and Villavicencio 2001
on acquisition of word order parameters).
However, even (6) is not exhaustive of all pos-
sible verbal categories, since each verb carries not
just its “basic” category but also a cluster of other
categories corresponding to various lexical opera-
tions. For example, give is associated with several
categories, including but not limited to:
(10) (a) Double object: ((Sa1 NP)a2 NP)a2 NP
(b) NP-PP complement: ((Sa1 NP)a2 PPa29 a27 )a2 NP
(c) Passivized double object, no agent:
(Sa1 NP)a2 NP
(d) Passivized double object with agent:
((Sa1 NP)a2 PPa22a4a3 )a2 NP
(e) Passivized NP-PP complement, no agent:
(Sa1 NP)a2 PPa29 a27
(f) Passivized NP-PP complement with
agent: ((Sa1 NP)a2 PPa22a4a3 )a2 PPa29 a27
Many standard CCG approaches encode these
categories redundantly, although frequently these
relationships are described via meta-rules (for in-
stance as proposed by Carpenter 1992 and assumed
implicitly in Steedman 2000). For instance, the
meta-rule for dative shift could be stated as (11):
(11) ((Sa7 NPa5 )a4 NPa6 )a4 NPa7 a5 ((Sa7 NPa5 )a4 PPa8
a11a10a9
a7 )a4 NPa6
This meta-rule simply says that any double-object
verb will also have a dative-shifted category as well.
The meta-rule approach is of course similar to the
lexical mapping rules common in much HPSG lit-
erature (cf. Flickinger 1987, inter alia), and in fact
the rule in (11) is implemented as in (12).
(12) dative-shift :=
a6a7
a7
a7
a7
a7
a7
a7
a7
a7
a7
a7
a7a8
SS a17 CAT
a6a7
a7
a7a8
RESULT a9
ACTIVE a11 a12 a15 NP, a16 PP
a6
a8 AGR
a13
FORM f to
SEM a14
a9a10
, a15 a16 NPa16
a9a12a11
a11
a11
a10
DTRS a11
a6a7
a7a8
SS a17 CAT
a6a7a8 RESULT
a9
ACTIVE a11 a12 , a15 , a16 NPa17 SEM a14AGR
a13 a18
a16
a9a11
a10
a9a11
a11
a10
a16
a9a12a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a11
a10
However, the difference between meta-rules and
lexical rules is that the latter are first-class grammat-
ical entities and can themselves can be organized
hierarchically in a way that eliminates redundancy
and captures several linguistic generalizations. An
illustrative example is the encoding of predicative
XPs (Kim is happy/on time/the person who came).
TCCG adopts the Pollard and Sag (1994) analy-
sis that predicative (ad)nominals have the category
(Sa1 NP) and thus are compatible with the selectional
restrictions of be ((Sa1 NP)a2 (Sa1 NP)). A simple so-
lution for generating predicative XPs is to derive
(Sa1 NP)$a0 categories from NP$a0 (Det/lexical NPs)
and Na1 N$a0 (for Adjs/Ps) via the lexical rules in (13).
(13) (a) Predicative NPs: NPa5 $a9 a5 (Sa7 NPa5 )$a9
(b) Predicative adnominals: Na5a3a2 Na5 $a9 a5 (Sa7 NPa5 )$a9
These two rules clearly share a number of simi-
larities that positing the two rules independently do
not capture. In TCCG, however, the type hierarchy
captures the larger similarities, where the rules for
predicative NPs and predicative modifiers share a
supertype that captures common information:
(14) predicative
predicative-np predicative-mod
The type predicative encodes the general
Nom$ a35 (Sa4a37a33a6a5a8a7a10a9 a1 NP)$ (Sa4a37a33a6a5a11a7a10a9 a1 NP)$ form of the
rules; predicative-np and predicative-mod merely
further specify the daughter category as in (13).
Again, while many CCG approaches employ meta-
rules, the type hierarchy of TCCG allows further
generalizations even among such meta-rules. In
sum, the use of type hierarchies and lexical rules re-
sults in a grammar where each lexical item has (ide-
ally) one category, with shared information stated
once. Additional categories are derived via mapping
rules, themselves organized hierarchically, thus cap-
turing a variety of cross-cutting generalizations.
5 Advantages of TCCG over HPSG
TCCG of course adopts wholesale the type-
inheritance, unification based approach of HPSG,
adding nothing new to the underlying framework.
Nonetheless, by adopting a CCG style syntax
TCCG makes possible more direct comparisons of
the coverage and heavily lexical nature of standard
CCG analyses to common HPSG approaches. Ex-
panding the coverage over Sag and Wasow (1999),
TCCG implements CCG analyses of a wide range
of unbounded dependency phenomena (e.g. pied-
piping, relative clauses, p-gaps, *that-t effects; see
Sag 1997, Ginzburg and Sag 2000 for well worked
out HPSG analyses). More generally, TCCG imple-
ments CCG analyses of non-constituent coordina-
tion (e.g. right node raising and argument cluster co-
ordination), largely unanalyzed in HPSG (although
see Yatabe 2002, Chrysmann 2003, Beavers and Sag
to appear). These are all well-known advantage of
CCG and I will not discuss them at length.
In this section, however, I focus on how the fully
lexical nature of TCCG simplifies the analysis of
bare nominals, which in Ginzburg and Sag (2000)
are analyzed constructionally: a plural/mass ¯N is
pumped to an NP with appropriate semantics (al-
though see Beavers 2003 for an alternative HPSG
proposal without pumping). The motivation for a
phrasal pumping rule is to ensure (a) that modifiers
may modify the ¯N before the category is changed to
NP and (b) that the added existential/generic quanti-
fier outscopes all constituents of the ¯N. For instance,
to build the NP happy dogs from Cleveland in HPSG
lexically would generate a lexical NP dogs incom-
patible with the constraints on modifiers like happy
(which have ¯N MOD values) and further would pre-
vent the added quantifier to outscope the modifiers.
However, a phrasal approach misses the broader
generalization that these constructions are lexically
triggered (by particular noun classes/inflection) and
again heterogeneously spreads out language partic-
ular grammatical information between the lexicon
and phrasal rules. At least in terms of parsimony a
lexical rule approach would be preferred as it local-
izes the operation to one component of the grammar.
CCG allows for such a fully lexical analysis of bare
plurals. The relevant categories are shown in (15):
(15) (a) Nouns: N$
(b) Attributive adjectives: Na2 N$
(c) Attributive prepositions: Na1 Na2 NP
(d) Relativizers: (((Na1 N)a2 $a0 )a2 (Sa2 $a0 a2 NP))$a12
(d) Determiners: NPa2 N
N, Adj, Rel, and P are all of form N$, with
only Det rooted in NP. Adopting Carpenter’s (1992)
meta-rule analysis of bare NPs to TCCG, I analyze
bare nominals via a simple HPSG-style lexical rule
of the form in N$a0 a35 NP$a0 such that (ad)nominal
can be pumped to a function rooted in NP (adding
the appropriate quantificational semantics), essen-
tially making them determiners. Thus when build-
ing a bare NP the pumped category is necessarily
the final functor, ensuring no category mismatches
and the correct semantics, as shown in (16).9
(16) (a) NP
dogs
(b) NP (a13 )
NPa16 N
happy
N
dogs
(c) NP (a14 )
N
dogs
NPa15 N
from Cleveland
9I represent derivations as trees rather than the usual CCG
notation to be consistent with the LKB’s tree-based output.
Note that the normal form described in a15 2 rules out (16e).
(d) NP (a13 )
NPa16 N
happy
N (a14 )
N
dogs
Na15 N
from Cleveland
(e) NP (a14 )
N (a13 )
Na16 N
happy
N
dogs
NPa15 N
from Cleveland
A variety of other phenomena have been imple-
mented lexically in TCCG without the use of ad-
ditional syntactic rules above and beyond the ones
assumed above in a0 2, reducing the number of differ-
ent kinds of syntactic and constructional rules com-
mon in HPSG analyses. Thus, TCCG validates and
makes more accessible the possibilities of fully lexi-
cal CCG-style analyses in HPSG without modifying
the underlying framework.
6 Advantages over both HPSG and CCG
One advantage over both HPSG and CCG comes in
the treatment of modifiers. In most HPSG literature
modifiers form a heterogeneous class: due to the un-
constrained possibilities of category formation, the
HEAD category and the synsem in MOD are not in-
herently related and thus do not necessarily allow
for any further generalizations. In CCG, however,
modifiers all have the general form Xa1 X$, where
X is typically a basic category (Adjs are of cate-
gory Na2 N$, Ps are Na1 N$, Advs are Sa1 S$ (ignoring
VP-Advs)). Yet this generalization is not codifiable
in CCG terms and each modifier must redundantly
encode the same form. In TCCG, however, I posit
a type xp-mod-lxm that characterizes these general-
izations over modifiers of basic categories:
(17) Xa1 X$, X a simplex category:
xp-mod-lxm :=
a6a7
a7
a7
a7
a7a8 SS
a6a7
a7
a7
a7a8
ROOT a17 FEATS a9
CAT
a6a7
a7a8
RESULT a12
ACTIVE a11
a0
ARG a17 ROOT a17 FEATS
a9
CAT a12 a18a2a1 , ...a16
a9a12a11
a11
a10
a9a11
a11
a11
a11
a10
a9a12a11
a11
a11
a11
a11
a10
Here the category and morphosyntactic features
of the first argument are shared with the result, with
the rest of the arguments left underspecified, captur-
ing the general nature of modifiers in TCCG.10 The
advantage to the type hierarchy here is that most of
the relevant information about each kind of modi-
fier is now only stated once. Subtypes of this type
10This is a simplification of the approach actually imple-
mented in TCCG, which enriches the slash values of all cat-
egories with modalities indicating the “semantic” headedness
of the category, following Baldridge (2002) and Kruijff (2001),
providing further generalizations over modifiers, but the details
are irrelevant for this discussion.
need only add relevant additional information, for
instance the supertype of all adjectives, adj-lxm, in-
herits from both xp-mod-lxm (meaning it’s a modi-
fier) and nom-lxm (meaning it’s rooted in N), adding
only the constraint that slash in Xa1 X$ be forward:
(18) Adjectives are Na2 N$:
adj-lxm :=
a17 SS a17 CAT a17 ACTIVE a3 a16a5a4a7a6 , ...a8
a18
Transitive and intransitive subtypes of adj-lxm
further specialize the $, and similar structuring of
information occurs for all other modifier types.
Thus the commonalities and differences of a wide
variety of modifiers are captured in terms of type hi-
erarchies, potentially with typological advantages.
In Romance languages such as Spanish, where ad-
nominal modifiers are overwhelmingly post-head,
the directionality constraint for adjectives in (18)
could instead be stated as a default on a higher su-
pertype of all adnominals (where the few excep-
tions lexically override the default). Again, these
types of constraints are not possible in most HPSG
or CCG implementations. CCG without type hier-
archies lacks the language in which such general-
izations can be stated. Instead modifiers only form
a class meta-theoretically with shared information
stated redundantly. On the other hand, most HPSG
approaches typically do not offer a sufficiently con-
strained set of category types to state generaliza-
tions over modifiers. Generalizations over mod-
ifier classes must be stated heterogeneously as a
combination of lexical marking and pre- and post-
head adjunct constructions (or alternatively stated
in terms of independent linear precedence rules
(Kathol, 2000)). Thus combining these approaches
yields potential not easily realizable separately.
7 Conclusion
TCCG is an implemented CCG in an HPSG frame-
work that combines the advantages of both theo-
ries: well-organized, minimally redundant lexical
and grammatical information mixed with the theo-
retical elegance of CCG grammars. The combina-
tion allows for simplifications of common analyses
in both theories, even allowing for generalizations
that are more difficult to state in both theory. The
details discussed here are just a subset of TCCG;
for a full description see Beavers (2002).
Acknowledgements
The bulk of this work was done at the Univer-
sity of Edinburgh in 2002, with the support of The
Edinburgh-Stanford Link Grant #2KBA905 and the
LinGO project at CSLI at Stanford University.
I’d like to thank Jason Baldridge, Tim Baldwin,
Colin Bannard, Chris Callison-Burch, Ann Copes-
take, Dan Flickinger, Julia Hockenmaier, Martin
Kay, Geert-Jan Kruijff, Stephan Oepen, Ivan Sag,
Mark Steedman, Maarika Traat, Aline Villavicen-
cio, Michael White, and several anonymous review-
ers for their comments. I’d like to especially ac-
knowledge Ann Copestake and Aline Villavicen-
cio’s earlier CCG LKB implementation as an imme-
diate predecessor and influence on this one even if
the two diverge significantly. Any mistakes or omis-
sions are purely my own.

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