c© 2002 Association for Computational Linguistics
The Combinatory Morphemic Lexicon
Cem Bozsahin
∗
Middle East Technical University
Grammars that expect words from the lexicon may be at odds with the transparent projection of
syntactic and semantic scope relations of smaller units. We propose a morphosyntactic framework
based on Combinatory Categorial Grammar that provides flexible constituency, flexible category
consistency, and lexical projection of morphosyntactic properties and attachment to grammar in
order to establish a morphemic grammar-lexicon. These mechanisms provide enough expressive
power in the lexicon to formulate semantically transparent specifications without the necessity
to confine structure forming to words and phrases. For instance, bound morphemes as lexical
items can have phrasal scope or word scope, independent of their attachment characteristics but
consistent with their semantics. The controls can be attuned in the lexicon to language-particular
properties. The result is a transparent interface of inflectional morphology, syntax, and semantics.
We present a computational system and show the application of the framework to English and
Turkish.
1. Introduction
The study presented in this article is concerned with the integrated representation and
processing of inflectional morphology, syntax, and semantics in a unified grammar ar-
chitecture. An important issue in such integration is mismatches in morphological,
syntactic, and semantic bracketings. The problem was first noted in derivational mor-
phology. Williams (1981) provided examples from English; the semantic bracketings
in (1a–2a) are in conflict with the morphological bracketings in (1b–2b).
(1) a.
hydro electric
-ity
b.
hydro
electric -ity
(2) a.
G¨odel number
-ing
b.
G¨odel
number -ing
If the problem were confined to derivational morphology, we could avoid it by
making derivational morphology part of the lexicon that does not interact with gram-
mar. But this is not the case. Mismatches in morphosyntactic and semantic bracketing
∗ Computer Engineering and Cognitive Science, Middle East Technical University, 06531 Ankara, Turkey.
E-mail: bozsahin@metu.edu.tr.
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Computational Linguistics Volume 28, Number 2
also abound. This article addresses such problems and their resolution in a computa-
tional system.
1
M¨uller (1999, page 401) exemplifies the scope problem in German prefixes. (3a) is
in conflict with the bracketing required for the semantics of the conjunct (3b).
(3) a. Wenn [Ihr Lust] und [noch nichts anderes vor-]habt,
if you pleasure and yet nothing else intend
k¨onnen wir sie ja vom Flughafen abholen
can we them PARTICLE from.the airport pick up
’If you feel like it and have nothing else planned, we can pick them
up at the airport.’
b. Ihr Lust habt UND noch nichts anderes vorhabt
Similar problems can be observed in Turkish inflectional suffixes. In the coordi-
nation of tensed clauses, the tense attaches to the verb of the rightmost conjunct (4a)
but applies to all conjuncts (4b). Delayed affixation appears to apply to all nominal
inflections (4c–e).
(4) a. Zorunlu deprem sigortası [y¨ur¨url¨u˘ge girmi¸s] ama
mandatory earthquake insurance effect enter-ASP but
[tam anlamıyla uygulanamamı¸s]-tı
exactly apply-NEG-ASP-TENSE
’Mandatory earthquake insurance had gone into effect, but it had not
been enforced properly.’
b. y¨ur¨url¨u˘ge girmi¸s-ti ama tam anlamıyla uygulanamamı¸s-tı
c. Adam-ın [araba ve ev]-i
man-GEN car and house-POSS
’the man’s house and car’
d. Araba-yı [adam ve ¸cocuk]-lar-a g¨oster-di-m
Car-ACC man and child-PLU-DAT show-TENSE-PERS1
’(I) showed the car to the men and the children.’
e. Araba-yı sen-in [dost ve tanıdık]-lar-ın-a g¨oster-di-m
Car-ACC you-GEN friend and acq.-PLU-POSS-DAT showed
’(I) showed the car to the your friends and acquaintances.’
1 Our use of the term morphosyntax needs some clarification. Some authors, (e.g., Jackendoff 1997),
take it to mean the syntax of words, in contrast to the syntax of phrases. By morphosyntax we mean
those aspects of morphology and syntax that collectively contribute to grammatical meaning
composition. This is more in line with the inflectional-morphology-is-syntax view. In this respect, we
will not address problems related to derivational morphology; its semantics is notoriously
noncompositional and does not interact with grammatical meaning. Moreover, without a semantically
powerful lexicon such as Pustejovsky’s (1991), even the most productive fragment of derivational
morphology is hard to deal with (Sehitoglu and Bozsahin 1999).
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Bozsahin The Combinatory Morphemic Lexicon
Phrasal scope of inflection can be seen in subordination and relativization as well.
In (5a), the entire nominalized clause marked with the accusative case is the object
of want. In (5b), the relative participle applies to the relative clause, which lacks an
object. The object’s case is governed by the subordinate verb, whose case requirements
might differ from that of the matrix verb (5c). As we show later in this section, the
coindexing mechanisms in word-based unification accounts of unbounded extraction
face a conflict between the local and the nonlocal behavior of the relativized noun,
mainly due to applying the relative participle -di˘g-i to the verbal stem ver rather than
the entire relative clause. A lexical entry for -di˘g-i would resolve the conflict and
capture the fact that it applies to nonsubjects uniformly.
(5) a. Can [Ay¸se’nin kitab-ı oku-ma-sı]-nı iste-di
C.NOM A.-GEN book-ACC read-INF-AGR-ACC want-TENSE
’Can wanted Ay¸se to read the book.’
lit. ’Can wanted Ay¸se’s-reading-the-book.’
b. Ben [ Mehmet’in ¸cocu˘g-a/*-u ver ]-di˘g-i kitab-ı oku-du-m
I.NOM M-GEN child-DAT/*ACC give-REL.OP book-ACC read-TENSE-PERS1
’I read the book that Mehmet gave to the child.’
c. Ben [ Mehmet’in kitab-ı ver ]-di˘g-i ¸cocu˘g-u/*-a g¨or-d¨u-m
I.NOM M-GEN book-ACC give-REL.OP child-ACC/*DAT see-TENSE-PERS1
’I saw the child to whom Mehmet gave the book.’
The morphological/phrasal scope conflict of affixes is not particular to morpho-
logically rich languages. Semantic composition of affixes in morphologically simpler
languages poses problems with word (narrow) scope of inflections. For instance, fake
trucks needs the semantics (plu(faketruck)), which corresponds to the surface brack-
eting [fake truck]-s, because it denotes the nonempty nonsingleton sets of things that
are not trucks but fake trucks (Carpenter 1997). Four trucks, on the other hand, has the
semantics (four(plutruck)), which corresponds to four [truck]-s, because it denotes the
subset of nonempty nonsingleton sets of trucks with four members.
The status of inflectional morphology among theories of grammar is far from
settled, but, starting with Chomsky (1970), there seems to be an agreement that deriva-
tional morphology is internal to the lexicon. Lexical Functional Grammar (LFG)
(Bresnan 1995) and earlier Government and Binding (GB) proposals e.g. (Anderson
1982) consider inflectional morphology to be part of syntax, but it has been del-
egated to the lexicon in Head-Driven Phase Structure Grammar (HPSG) (Pollard
and Sag 1994, page 35) and in the Minimalist Program (Chomsky 1995, page 195).
The representational status of the morpheme is even less clear. Parallel develop-
ments in computational studies of HPSG propose lexical rules to model inflectional
morphology (Carpenter and Penn 1994). Computational models of LFG (Tomita 1988)
and GB (Johnson 1988; Fong 1991), on the other hand, have been noncommittal re-
garding inflectional morphology. Finally, morphosyntactic aspects have always
been a concern in Categorial Grammar (CG) (e.g., Bach 1983; Carpenter 1992; Dowty
1979; Heylen 1997; Hoeksema 1985; Karttunen 1989; Moortgat 1988b; Whitelock
1988), but the issues of constraining the morphosyntactic derivations and re-
solving the apparent mismatches have been relatively untouched in computational
studies.
We briefly look at Phrase Structure Grammars (PSGs), HPSG, and Multimodal
CGs (MCGs) to see how word-based alternatives for morphosyntax would deal with
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Computational Linguistics Volume 28, Number 2
the issues raised so far. For convenience, we call a grammar that expects words from
the lexicon a lexemic grammar and a grammar that expects morphemes a morphemic
grammar. A lexemic PSG provides a lexical interface for inflected words (X
0
s) such
that a regular grammar subcomponent handles lexical insertion at X
0
.
2
In (4d), the
right conjunct ¸cocuk-lar-a is analyzed as N
0
→ ¸cocuk-PLU-DAT (or N
0
→ N
0
prime -DAT,
N
0
prime → N
0
primeprime -PLU, N
0
primeprime → Stem, as a regular grammar). Assuming a syncategorematic
coordination schema, that is, X → X and X, the N
0
in the left and right conjuncts
of this example would not be of the same type. Revising the coordination schema
such that only the root features coordinate would not be a solution either. In (4e),
the relation of possession that is marked on the right conjunct must be carried over
to the left conjunct as well. What is required for these examples is that the syntac-
tic constituent X in the schema be analyzed as X-PLU(-POSS)-DAT, after N
0
and N
0
coordination.
What we need then is not a lexemic but a morphemic organization in which brack-
eting of free and bound morphemes is regulated in syntax. The lexicon, of course,
must now supply the ingredients of a morphosyntactic calculus. This leads to a the-
ory in which semantic composition parallels morphosyntactic combination by virtue
of bound morphemes’ being able to pick their domains just like words (above X
0
,
if needed). A comparison of English and Turkish in this regard is noteworthy. The
English relative pronouns that/whom and the Turkish relative participle -di˘g-i would
have exactly the same semantics when the latter is granted a representational status
in the lexicon (see Section 6).
Furthermore, rule-based PSGs project a rigid notion of surface constituency. Steed-
man (2000) argued, however, that syntactic processes such as identical element dele-
tion under coordination call for flexible constituency, such as SO (subject-object) in
the SVO & SO gapping pattern of English and SV (subject-verb) constituency in
the OSV & SV pattern of Turkish. Nontraditional constituents are also needed in
specifying semantically transparent constituency of words, affixes, clitics, and
phrases.
Constraint-based PSGs such as HPSG appeal to coindexation and feature passing
via unification, rather than movement, to deal with such processes. HPSG also makes
the commitment that inflectional morphology is internal to the lexicon, handled either
by lexical rules (Pollard and Sag 1994) or by lexical inheritance (Miller and Sag 1997).
We look at (5c) to highlight a problem with the stem-and-inflections view. As words en-
ter syntax fully inflected, the sign of the verb ver-di˘g-i in the relative clause (5c) would
be as in (6a), in which the SUBCAT list of the verb stem is, as specified in the lexi-
cal entry for ver, unsaturated. The participle adds coindexation in MOD|···|INDEX.
The HPSG analysis of this example would be as in Figure 1. Although passing the
agreement features of the head separately (Sehitoglu 1996) solves the case problem
alluded to in (5c), however, structure sharing of the NP
dat
with the SLASH, INDEX,
and CONTENT features of ver-di˘g-i is needed for semantics (GIVEE), but this conflicts
with the head features of the topmost NP
acc
in the tree. The relative participle as a
lexical entry (e.g., (6b)) would resolve the problem with subcategorization because its
SUBCAT list is empty (like the relative pronoun that in English), hence there would be
no indirect dependence of the nonlocal SLASH feature and the local SUBCAT feature
via semantics (CONTENT). Such morphemic alternatives are not considered in HPSG,
however, and require a significant revision in the theory. Furthermore, HPSG’s lexical
2 But see Creider, Hankamer, and Wood (1995), which argues that the morphotactics of human languages
is not regular but linear context free.
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Bozsahin The Combinatory Morphemic Lexicon
assignment for trace introduces phonologically null elements into the lexicon, which,
as we show later, is not necessary.
(6) a. ver-di˘g-i :=
















LOCAL













CAT





HEAD
bracketleftBigg
AGR
bracketleftBig
PERSON third
NUMBER sing
bracketrightBig
CASE dat
bracketrightBigg
SUBCAT <
3
NP[gen],
2
NP[acc],
1
NP[dat]>
MOD | MODSYN | LOCAL | CONT | INDEX
1





CONTENT



RELN give
GIVER
3
GIVEE
1
GIFT
2
















NONLOCAL | TO-BIND | SLASH
braceleftbig
1
bracerightbig
















b. -di˘g-i :=





LOCAL



CAT
bracketleftbigg
HEAD noun
bracketleftbig
acc or dat
bracketrightbig
SUBCAT <>
bracketrightbigg
CONTENT npro
bracketleftbig
INDEX
1
bracketrightbig



NONLOCAL | INHER | SLASH
braceleftbig
1
bracerightbig





MCGs (Hepple 1990a; Morrill 1994; Moortgat and Oehrle 1994) allow different
modes of combination in the grammar. In addition to binary modes such as wrapping
and commutative operations, unary modalities provide finer control over the cate-
gories. Heylen (1997, 1999) uses unary modalities as a way of regulating morphosyn-
tactic features such as case, number, and person for economy in lexical assignments.
For instance, Frau has the category ✷
case
✷
fem
✷
sg
✷
3p
✷
decl
N, which underspecifies it for
case and declension. Underspecification is dealt with in the grammar using inclusion
postulates (e.g., (7)). The interaction of different modalities is regulated by distribution
postulates.
(7) ✷
case
Γ turnstileleft X
✷
nom
Γ turnstileleft X
✷
case
Γ turnstileleft X
✷
acc
Γ turnstileleft X
Lexical assignments to inflected words carry unary modalities: boys has the type
✷
pl
N, in contrast to ✷
sg
N for boy. Although such regulation of inflectional features
successfully mediates, for example, subject-verb agreement or NP-internal case agree-
ment (as in German), it is essentially word-based, because type assignments are to
inflected forms; morphemes do not carry types. This reliance on word types neces-
sitates a lexical rule–based approach to some morphosyntactic processes that create
indefinitely long words, such as ki-relativization in Turkish (see Section 6.5). But lexical
rules for such processes risk nontermination (Sehitoglu and Bozsahin 1999). Our main
point of departure from MCG accounts is the morphemic versus lexemic nature of the
lexicon: The morphosyntactic and attachment modalities originate from the lexicon;
they are not properties of the grammar (we elaborate more on this later). This paves
the way to the morphemic lexicon by licensing type assignments to units smaller than
words.
Besides problems with lexical rules, the automata-theoretic power of MCGs is
problematic: Unrestricted use of structural modalities and postulates leads to Tur-
ing completeness (Carpenter 1999). Indeed, one of the identifiable fragments of Mul-
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Computational Linguistics Volume 28, Number 2
Figure 1
HPSG analysis of (5c).
timodal languages that is computationally tractable is Combinatory Categorial lan-
guages (Kruijff and Baldridge 2000), which we adopt as the basis for the framework
presented here. We propose a morphosyntactic Combinatory Categorial Grammar
(CCG) in which the grammar and the morphemic lexicon refer to morphosyntactic
types rather than syntactic types. We first introduce the syntactic CCG in Section 2.
Morphosyntactic CCG is described in Section 3. In Section 4, we look at the compu-
tational aspects of the framework. We then show its realization for some aspects of
English (Section 5) and Turkish (Section 6).
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Bozsahin The Combinatory Morphemic Lexicon
2. Syntactic Types
CG is a theory of grammar in which the form-meaning relation is conceived as a
transparent correspondence between the surface-syntactic and semantic combinatorics
(Jacobson 1996). A CCG sign can be represented as a triplet π − σ:µ, where π is the
prosodic element, σ is its syntactic type, and µ its semantic type. For instance, the
lexical assignment for read is (8).
3
(8) read := read − (S\NP)/NP:λx.λy.readxy
Definition (Syntactic Types)
• The set of basic syntactic categories: A
s
= {N,NP,S,S
−t
,S
+t
}
• The set of complex syntactic categories: B
s
— A
s
⊆B
s
— If X ∈B
s
and Y ∈B
s
, then X\Y and X/Y ∈B
s
The classical Ajdukiewicz/Bar-Hillel (AB) CG is weakly equivalent to Context-
Free Grammars (Bar-Hillel, Gaifman, and Shamir 1960). It has function application
rules, defined originally in a nondirectional fashion. The directional variants and their
associated semantics are as follows:
(9) Forward Application (>):
4
X/Y: fY: a ⇒ X: fa
Backward Application (<): Y: aX\Y: f ⇒ X: fa
CCG (Steedman 1985, 1987, 1988; Szabolcsi 1983, 1987) is an extended version of
AB that includes function composition (10), substitution, and type raising (11). These
extensions make CCGs mildly context sensitive.
(10) Forward Composition (>B): X/Y: fY/Z: g ⇒ X/Z:λx.f(gx)
Backward Composition (<B): Y\Z: gX\Y: f ⇒ X\Z:λx.f(gx)
(11) Forward Type Raising (>T):
5
X: a ⇒ T/(T\X):λf.f[a]
Backward Type Raising (<T): X: a ⇒ T\(T/X):λf.f[a]
Type raising is an order-preserving operation. For instance, Lambek’s (1958) cat-
egory S/(S\NP) is a positional encoding of the grammatical subject as a function
3 We take π to be the surface string for simplicity. We use the “result-first” convention for CG. For
instance, transitive verbs of English are written as (S\NP)/NP, which translates to (NP\S)/NP in the
“result-on-top” convention.
4 We omit the prosodic element for ease of exposition. For instance, the complete definition of forward
application is s
1
− X/Y: fs
2
− Y: a ⇒ s
1
• s
2
− X: fa, where • is prosodic combination and fa is the
application of f to a. The • will play a crucial role in the lexicalization of attachment later on.
5 The lambda term f[a] denotes internal one-step β-reduction of f on a. In parsing, we achieve the same
effect by partial execution (Pereira and Shieber 1987). λf.f[a] is encoded as (a^F)^F in Prolog, where ˆ
is lambda abstraction. We opted for the explicit f[a] notation mainly for ease of exposition (cf. the
semantics of raising verbs, relative participles, etc. in Section 6). Moreover, as Pereira and Shieber
noted, (a^F)^F is not a lambda term in the strict sense because a is not a variable.
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Computational Linguistics Volume 28, Number 2
looking for a VP (= S\NP) to the right to become S. The reversal of directionality such
as topicalization (e.g., This book, I recommend) requires another schema. The reversal
is with respect to the position of the verb, which we shall call contraposition and
formulate as in (12).
6
(<XP) is leftward extraction of a right constituent, and (>XP)
is rightward extraction of a left constituent, both of which are marked constructions.
Directionally insensitive types such as T|(T|X) cause the collapse of directionality in
surface grammar (Moortgat 1988a).
(12) Leftward Contraposition (<XP): X: a ⇒ S
+t
/(S/X):λf.f[a]
S
+t
/(S
+t
/X):λf.f[a]
Rightward Contraposition (>XP): X: a ⇒ S
−t
\(S\X):λf.f[a]
S
−t
\(S
−t
\X):λf.f[a]
The semantics of contraposition depends on discourse properties as well. We leave
this issue aside by (1) noting that it is related to type raising in changing the function-
argument relation and (2) categorizing the sentence as S
+t
(topicalized) or S
−t
(detopi-
calized), which are not discourse equivalent to S. Syntactic characterization as such
also helps a discourse component do its work on syntactic derivations.
CCG’s notion of interpretation is represented in the Predicate-Argument Structure
(PAS). Its organization is crucial for our purposes, since the bracketing in the PAS is
the arbitrator for reconciling the bracketings in morphology and syntax via proper
lexical type assignments. It is the sole level of representation in CCG (Steedman 1996,
page 89).
7
It is the level at which the conditions on objects of interpretation, such as
binding and control, are formulated. For instance, Steedman (1996) defines c-command
and binding conditions A, B, and C over the PAS. The PAS also reflects the obliqueness
order of the arguments:
Predicate ... Tertiary-Term Secondary-Term Primary-Term
Assuming left associativity for juxtaposition, this representation yields the brack-
eting in (13) for the PAS. Having the primary argument as the outermost term is
motivated by the observations on binding asymmetries between subjects and comple-
ments in many languages (e.g., *Himself saw John, *heself).
(13)
3. Morphosyntactic Types
A syntactic type such as N does not discriminate morphosyntactically. A finer dis-
tinction can be made as singular nouns, plural nouns, case-marked nouns, etc. For
6 In fact, topicalization of nonperipheral arguments (This book, I would give to Mary) requires that (12) be
finitely schematized over valencies, such as S, S/NP, S/PP (Steedman 1985).
7 We will not elaborate on the theoretical consequences of having this level of representation; see, for
instance, Dowty (1991) and Steedman (1996).
153
Bozsahin The Combinatory Morphemic Lexicon
n-relbase n-root
n-num
s-caus
s-reflex s-recip(x)
(r)
(n)
n-possn-comp (m)
n-case (c)
free 
(a)
s-tense
s-abil
s-neg
s-imp
s-pass
(s)
(m)
(t)
(g)
(i)
(p)
s-tense
n-base s-base
(b)
(t)
(v)(b)
(n)
s-person
s-modal
n-num
(f)
(a)
(c)
s-base  (v)
(l)
n-base (b)
(o)
(u)
free (f)
Figure 2
The lattice of diacritics for (a) Turkish and (b) English.
instance, the set of number-marked nouns can be represented as
n
✶N, where ✶ is a
morphosyntactic modality (“equals”) and n is a diacritic (for number). Books is of type
n
✶N, but book is not. The type for books can be obtained morphosyntactically by as-
signing -s (-PLU) the functor type
n
✶N\
b
✶N, where b stands for base. A syntactic type
such as N\N overgenerates.
Another modality, < (“up to and equals”), allows wider domains in morphosyn-
tactic typing. For instance,
n
< N represents the set of nouns marked on number or
any other diacritic that is lower than number in a partial order (e.g., Figure 2). The
inflectional paradigm of a language can be represented as a partial ordering us-
ing the modalities.
8
For instance, if the paradigm is Base-Number-Case, we have
υ(
b
< N) ⊆ υ(
n
< N) ⊆ υ(
c
< N), where υ(τ) is the valuation function from the mor-
phosyntactic type τ to the set of strings that have the type τ. The ✶ modality is more
strict than < to provide finer control; although υ(
n
< N) ⊆ υ(
c
< N), υ(
n
✶N) negationslash⊆ υ(
c
✶N),
because a noun can be number marked but not case marked or vice versa. Also,
υ(
i
✶N) ⊆ υ(
i
< N) for any diacritic i since, for instance, the set of nouns marked up to
and including case includes case-marked, number-marked, and unmarked nouns.
The lattice consistency condition is imposed on the set of diacritics to ensure
category unity.
9
In other words, the syntactic type X can be viewed as an abbreviation
for the morphosyntactic type
latticetop
< X where latticetop is the universal upper bound. It is the
8 See Heylen (1997) on use of unary modalities for a similar purpose in lexemic MCG.
9 In a lattice L, x ≤ y (morphosyntactically, x < y) is equivalent to the consistency properties x ∧ y = x
and x ∨ y = y. We use the join operator for this check, thus it suffices to have a join semilattice.
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Computational Linguistics Volume 28, Number 2
most underspecified category of X which subsumes all morphosyntactically decorated
versions of X. Figure 2 shows the lattice for English and Turkish.
Definition (Morphosyntactic Types)
•D= finite set of diacritics
• Join semilattice L =(D,≤, =)
• The set of basic morphosyntactic types: A
ms
.
—
i
< X ∈A
ms
and
i
✶X ∈A
ms
if i ∈Dand X ∈A
s
(see definition of
syntactic types for A
s
)
— (✶ corresponds to lattice condition =)
— (< corresponds to lattice condition ≤)
• The set of complex morphosyntactic types: B
ms
— A
ms
⊆B
ms
— If X ∈B
ms
and Y ∈B
ms
, then X\Y and X/Y ∈B
ms
For instance, the infinitive marker -ma in (14a) can be lexically specified to look
for untensed VPs—functions onto
a
< S—to yield a complex noun base (14b), which, as
a consequence of nominalization (result type N), receives case to become an argument
of the matrix verb. The adjective in fake trucks can be restricted to modify unmarked
Ns to get the bracketing [fake truck]-s (14c).
(14) a. Mehmet [[kitab-ı oku]-ma]-yı istiyor
M.NOM book-ACC read-INF-ACC wants
’Mehmet wants to read the book.’
b. -INF := ma −
b
< N\(
a
< S\
f
< NP
nom
):λf.f
c. fake := fake −
b
< N/
b
< N:λx.fakex
Different attachment characteristics of words, affixes, and clitics must be factored
into the prosodic domain as a counterpart of refining the morphosyntactic description.
In Montague Grammar, every syntactic rule is associated with a certain mode of at-
tachment, and this tradition is followed in MCG; attachment types are related with the
slash (e.g., /
w
for wrapping), which is a grammatical modality.
10
In the present frame-
work, however, attachment is projected from the lexicon to the grammar as a prosodic
property of the lexical items.
11
The grammar is unimodal in the sense that / and \
simply indicate the function-argument distinction in adjacent prosodic elements. The
lexical projection of attachment further complements the notion of morphemic lexicon
so that bound morphemes are no longer parasitic on words but have an independent
10 See Dowty (1996) and Steedman (1996) for a discussion of bringing nonconcatenative combination into
grammar.
11 There is a precedent of associating attachment characteristics with the prosodic element rather than the
slash in CG (Hoeksema and Janda 1988). In Hoeksema and Janda’s notation, arguments can be
constrained on phonological properties and attachment. For instance, the English article a has its NP/N
category spelled out as </CX/N,NP,Pref>, indicating a consonantal first segment for the noun
argument and concatenation to the left.
155
Bozsahin The Combinatory Morphemic Lexicon
Table 1
Attachment properties of some Turkish morphemes.
uzun (long) :=
s
◦ uzun −
b
< N/
b
< N
uzun yol
long road
’long road’
oku (read) :=
s
◦ oku −
v
< S\
f
< NP
nom
\
f
< NP
acc
adam kitab-ı oku-du
man book-ACC read-TENSE
’the man read the book.’
-EMPH :=
c
◦ de − X\X
Ben de yaz-ar-ım
I too write-TENSE-PERS
’I write too.’
-LOC :=
a
◦ de −
c
< N\
o
< N
Ben-de kalem var
I-LOC pen exist
’I have a pen.’
representational status of their own. We write
i
◦s to denote the attachment modality
i (affixation, syntactic concatenation, cliticization) of the prosodic element s.
Table 1 shows some lexical assignments for Turkish (e.g., the sign
a
◦s − X\Y:µ
characterizes a suffix). The morphosyntactic calculus of CCG is defined with the ad-
dition of morphosyntactic types and attachment modalities as follows (similarly, for
other combinatory rules):
(15) Forward Application (>):
i
◦s
1
− X/
α
1
✷
1
Y: f
j
◦s
2
−
α
2
✷
2
Y: a
>
k
◦(s
1
k
•s
2
) − X: fa
if α
2
✷
1
α
1
in lattice L, for: ✷
1
,✷
2
∈{✶,<},
α
1
,α
2
∈Din L,
i, j, k ∈{a, s, c},
i
◦
j
◦turnstileleft
a
k
◦
Forward Composition (>B):
i
◦s
1
− X/
α
1
✷
1
Y: f
j
◦s
2
−
α
2
✷
2
Y/Z: g
>B
k
◦(s
1
k
•s
2
) − X/Z:λx.f(gx)
if α
2
✷
1
α
1
in lattice L, for: ✷
1
,✷
2
∈{✶,<},
α
1
,α
2
∈Din L,
i, j, k ∈{a, s, c},
i
◦
j
◦turnstileleft
a
k
◦
The main functor’s argument specification (✷
1
of
α
1
✷
1
Y in (15)) determines the
lattice condition in derivations.
12
Hence the morphosyntactic decoration in lexical as-
signments propagates its lattice condition to grammar as in α
2
✷
1
α
1
(cf. Heylen [1997],
in which the grammar rule imposes a fixed partial order, e.g., X/Y combines with Z if
12 This coincides with Steedman’s (1991b) observation that directionality of the main functor’s slash is
also a property of the same argument. The main functor is the one whose result type determines the
overall result type (i.e., X/Y in (15)).
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Computational Linguistics Volume 28, Number 2
Z ≤ Y). This is another prerequisite that must be fulfilled for the morphemic lexicon
to project the lexical specification of scope.
The grammar is not fixed on the attachment modality either (unlike a lexemic
grammar, which is fixed on combination of words). Hence another requirement is the
propagation of attachment to grammar. This is facilitated by the lexical types
m
◦s−σ:µ,
where m is an attachment type. The attachment calculus
i
◦
j
◦turnstileleft
a
k
◦ in (15), which reads
“attachment types i and j yield type k,” relates attachment to prosodic combination in
the grammar.
13
It can be attuned to language-particular properties.
We can specify some prosodic properties of the attachment calculus for Turkish as
follows (´x indicates stress on the prosodic element x):
syntactic concatenation ´x
s
•´y = ´x´y
affixation ´x
a
•y = x´y
cliticization ´x
c
•y = ´x´y
4. Morpheme-Based Parsing
To contrast lexemic and morphemic processing, consider the Turkish example in (16a).
We show some stages of the derivation to highlight prosodic combination (•) as well.
Every item in the top row is a lexical entry. Allomorphs, such as that of tense, have the
same category in the lexicon (16b). Vowel harmony, voicing, and other phonological
restrictions are handled as constraints on the prosodic element. Constraint checking
can be switched off during parsing to obtain purely morphosyntactic derivations.
(16) a. Can Ay¸se nin kitab ı oku ması nı iste di
C.NOM -GEN(agr) book -ACC read -SUB1G -ACC want -TENSE
b
triangleleft N
b
triangleleft N
c
triangleleft NP
gen
\
o
triangleleft N
b
triangleleft N
c
triangleleft N
acc
\
o
triangleleft N
v
triangleleft S\
f
triangleleft NP
nom
o
triangleleft N\
f
triangleleft NP
gen
c
triangleleft N\
o
triangleleft NTV(
t
triangleleft S\
f
triangleleft NP)
\
f
triangleleft NP
acc
\(
a
triangleleft S\
f
triangleleft NP
nom
) \(
a
triangleleft S\
f
triangleleft NP)
.
.
.
iste
a
• di−
t
triangleleft S\
f
triangleleft NP
nom
kitab
a
• ı
s
• oku−
v
triangleleft S\
f
triangleleft NP
nom
\
f
triangleleft NP
acc
(kitab
a
• ı
s
• oku)
a
• ması−
o
triangleleft N\
f
triangleleft NP
gen
.
.
.
((ay¸se
a
• nin)
s
• (kitab
a
• ı
s
• oku)
a
• ması)
a
• nı− (
t
triangleleft S\
f
triangleleft NP
nom
)/(
t
triangleleft S\
f
triangleleft NP
nom
\
f
triangleleft NP
acc
)
.
.
.
can
s
• (ay¸se
a
• nin
s
• kitab
a
• ı
s
• oku
a
• ması
a
• nı)
s
• (iste
a
• di)−
t
triangleleft S
: want(readbookay¸se)can
’Can wanted Ay¸se to read the book.’
b. -TENSE :=
a
◦dı|di|du|d¨u|tı|ti|tu|t¨u − (
t
< S\
f
< NP)\(
a
< S\
f
< NP):λf.f
13 Clearly, much more needs to be done to incorporate intonation into the system. The motive for
attachment types is to provide the representational ingredients on behalf of the morphemic lexicon. As
one reviewer noted, CCG formulation of the syntax-phonology interface moved from autonomous
prosodic types (Steedman 1991a) to syntax-directed prosodic features (Steedman 2000b). The present
proposal for attachment modality is computationally compatible with both accounts: Combinatory
prosody can match prosodic types with morphosyntactic types. Prosodic features are associated with
the basic categories of a syntactic type in the latter formulation, hence they become part of the featural
inference that goes along with the matching of categories in the application of combinatory rules.
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Bozsahin The Combinatory Morphemic Lexicon
The lexicalization of attachment modality helps to determine the prosodic domain
of postconditions. For instance, for Turkish, vowel harmony does not apply over word
boundaries, which can be enforced by applying it when the modality is
a
◦ and
c
◦, but
not
s
◦. Voicing applies to
a
◦ and
s
◦, but not to
c
◦.
The basic categories N, NP, S, S
+t
, and S
−t
carry agreement features of fixed arity
(e.g., tense and person for S, S
+t
, and S
−t
, and case, number, person, and gender for N
and NP). Positional encoding of such information as in Pulman (1996) allows efficient
term unification for the propagation of these features.
14
Term unification also handles
the matching of complex categories in the CCG schema. For instance,
α
1
✷
1
A/(
α
2
✷
2
B\
α
3
✷
3
C)
combines with
β
2
✷
4
B\
β
3
✷
5
C via (>) for B, C ∈A
s
,ifβ
2
✷
2
α
2
, β
3
✷
3
α
3
(✷
i
∈{<,✶}). Apart
from the matching of syntactic types and agreement, unification does no linguistic
work in this framework, in contrast to structure-sharing in HPSG and slash passing
in Unification CG (Calder, Klein, and Zeevat 1988).
CCG is worst-case polynomially parsable (Vijay-Shanker and Weir 1993). This re-
sult depends on the finite schematization of type raising and bounded composition.
Assuming a maximum valence of four in the lexicon (Steedman 2000a), composition
(B
n
) is bounded by n ≤ 3. The refinement of the type raising schema (11) for finite
schematization is shown in (17).
(17) a. Revised Forward Type Raising (>T): NP: a ⇒ T/(T\NP):λf.f[a]
b. Revised Backward Type Raising (<T): NP: a ⇒ T\(T/NP):λf.f[a]
T ∈{S,S\NP, S\NP\NP, S\NP\NP\NP}.
The finite schematization of type raising suggests that it can be delegated to the
lexicon, for example, by a lexical rule that value-raises all functions onto NP to their
type-raised variety, such as NP/N to (S/(S\NP))/N. But this move presupposes the
presence of such functions in the lexicon, that is, a language with determiners. To be
transparent with respect to the lexicon, we make type raising and other unary schema
(contraposition) available in the grammar. Since both are finite schemas in the revised
formulation, the complexity result of Vijay-Shanker and Weir still holds. Checking the
lattice condition as in (15) incurs a constant factor with a finite lattice.
Type raising and composition cause the so-called spurious-ambiguity problem
(Wittenburg 1987): Multiple analyses of semantically equivalent derivations are pos-
sible in parsing. This is shown to be desirable from the perspective of prosody; for
example, different bracketings are needed to match intonational phrasing with syn-
tactic structure (Steedman 1991). From the parsing perspective, the redundancy of
analyses can be controlled by (1) grammar rewriting (Wittenburg 1987), (2) checking
the chart for PAS equivalence (Karttunen 1989; Komagata 1997), (3) making the proces-
sor parsimonious on using long-distance compositions (Pareschi and Steedman 1987),
or (4) parsing into normal forms (Eisner 1996; Hepple 1990b; Hepple and Morrill 1989;
K¨onig 1989; Morrill 1999). We adopt Eisner’s method, which eliminates chains of com-
positions in O(1) time via tags in the grammar, before derivations are licensed. There
is a switch that can be turned off during parsing to obtain all surface bracketings.
14 Mediating agreement via unification, type subsumption, or set-valued indeterminacy has important
consequences on underspecification, the domain of agreement, and the notion of “like categories” in
coordination (see Johnson and Bayer 1995; Dalrymple and Kaplan 2000; Wechsler and Zlati´c 2000).
Rather than providing an elaborate agreement system, we note that Pulman’s techniques provide the
mechanism for implementing agreement as atomic unification, subsumption hierarchies represented as
lattices, or set-valued features. The categorial ingredient of phrase-internal agreement can be provided
by endotypic functors when necessary (see Sections 5 and 6).
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Computational Linguistics Volume 28, Number 2
There is also a switch for checking the PAS equivalence, with the warning that the
equivalence of two lambda expressions is undecidable.
The parser is an adaptation of the Cocke-Kasami-Younger (CKY) algorithm (Aho
and Ullman 1972, page 315), modified to handle unary rules as well: In the kth iteration
of the CKY algorithm to build constituents of length k, the unary rules apply to the CKY
table entries T[α
i
,α
i+k
], i = 0, 1,..., n − k; that is, k-length results of binary rules are
input to potential unary constituents of length k. In practice, this allows, for instance,
a nominalized clause to be type-raised after it is derived as a category of type N.
The remaining combinatory schema is already in Chomsky Normal Form, as required
by CKY. The finite schematization of CCG rules and constant costs incurred by the
normal form and lattice checking provide a straightforward extension of CKY-style
context-free parsing for CCG. Komagata (1997) claims that the average complexity of
CCG parsing is O(n
3
) even without the finite schematization of type raising (based on
the parsing of 22 sentences consisting of around 20 words, with a lexicon of 200 entries
and no derivation of semantics in the grammar; a morphological analyzer provided
five analyses per second to the parser). Statistical techniques developed for lexicalized
grammars (e.g., Collins 1997), readily apply to CCG to improve the average parsing
performance in large-scale practical applications (Hockenmaier, Bierner, and Baldridge
2000). Both Collins and Hockenmeier, Bierner, and Baldridge used section 02-21 of the
Wall Street Journal Corpus of Penn Treebank for training, which contains 40,886 words
(70,151 lexical entries). A recent initiative (Oflazer, et al. 2001) aims to provide such a
resource of around one million words for Turkish. It encodes in the Treebank surface-
syntactic relations and the morphological breakdown of words. The latter is invaluable
for training morphemic grammars and lexicons.
In morpheme-based parsing, lattice conditions help eliminate the permutation
problem in endotypic categories. Such categories are typical of inflectional morphemes.
For instance, assume that three morphemes m
1
, m
2
, and m
3
have endotypic categories
(say N\N), that they can appear only in this order, and that they are all optional. The
categorization of m
i
as
κ
prime
i
< N\
κ
i
< N such that κ
prime
i
negationslash≤ κ
i
for all i, and κ
prime
j−1
≤ κ
j
for j = 1, 2, 3
allows omissions (18a–b) but rules out the permutations (18c–d).
15
(18) a. stem m
1
m
2
m
3
κ
0
< N
κ
prime
1
< N\
κ
1
< N
κ
prime
2
< N\
κ
2
< N
κ
prime
3
< N\
κ
3
< N
<
κ
prime
1
< N because κ
0
≤ κ
1
<
κ
prime
2
< N because κ
prime
1
≤ κ
2
<
κ
prime
3
< N because κ
prime
2
≤ κ
3
b. stem m
3
<
κ
prime
3
< N because κ
0
≤ κ
3
15 Three asterisks in the line indicate that the derivation is not licensed.
159
Bozsahin The Combinatory Morphemic Lexicon
c. *stem m
2
m
1
m
3
<
κ
prime
2
< N because κ
0
≤ κ
2
***
<
κ
prime
2
negationslash≤ κ
1
because κ
1
<κ
prime
1
≤ κ
2
<κ
prime
2
d. *stem m
1
m
3
m
2
<
κ
prime
1
< N because κ
0
≤ κ
1
<
κ
prime
3
< N because κ
prime
1
≤ κ
3
***
<
κ
prime
3
negationslash≤ κ
2
because κ
2
<κ
prime
2
≤ κ
3
<κ
prime
3
The lattice and its consistency condition on derivability offer varying degrees of
flexibility. A lattice with only latticetop and the relation ≤ would undo all the effects of
parameterization; it would be equivalent to a syntactic grammar in which every basic
category X stands for
latticetop
< X. To enforce a completely lexemic syntax, a lattice with latticetop
and free would define all functional categories as functions over free forms.
Morphological processing seems inevitable for languages like Turkish, and mor-
phological and lexical ambiguity such as that shown in (19) must be passed on to
syntax irrespective of how inflectional morphology is processed (isolated from or in-
tegrated with syntax). For the verbal paradigm, Jurafsky and Martin (2000) reports
Oflazer’s estimation that inflectional suffixes alone create around 40,000 word forms
per root. In the nominal paradigm, iterative processes such as ki-relativization (Sec-
tion 6.5) can create millions of word forms per nominal root (Hankamer 1989).
(19) a. kazma-ları
pickaxe-POSS3p
’their pickaxe’
b. kazma-lar-ı
pickaxe-PLU-POSS3p
’their pickaxes’
c. kazma-lar-ı
pickaxe-PLU-POSS3s
’his/her pickaxes’
d. kaz-ma-ları
dig-SUB-AGR
’their digging’
The questions that need to be answered related to processing are (1) What should a
(super)linear fragment of processing for morphology deliver to (morpho)syntax? and
(2) Is the syntax lexemic or morphemic? The problems with lexemic syntax, which
stem from mismatches with semantics, were highlighted in the introduction. In other
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Computational Linguistics Volume 28, Number 2
interpretation
syntax and
kazma
kaz
kazma−POSS3p
kazma−PLU−POSS3p
kazma−PLU−POSS3s
kaz−SUB−AGR
kazma
kaz
kazma−POSS3p
kazma−PLU−POSS3p
kazma−PLU−POSS3s
kaz−SUB−AGR
pairs
root lexicon
affix lexicon −ma
−lar
−i
−lari
kaz
kazma
−lar
−i
−lari
root lexicon
morpheme−
semantics
matching
morphological
parsing
lexicon
root and affix
morphological
parsing interpretation
syntax and
(a) Lexemic syntax and lexicon
(b) Morphemic syntax and split lexicon
(c) Morphemic syntax and lexicon
pairs
interpretation
syntax and
−ma
PF−LF
PF−LF
pairs
PF−LF
Phonological Form (PF)
Logical Form (LF)
Figure 3
The processing of kazmaları in three different architectures (see Example (19) for glosses).
words, a lexemic grammar (e.g., Figure 3a) is computationally nontransparent when
interpretation is a component of an NLP system.
Regarding the first question, let us consider two architectures from the perspective
of the lexicon for the purpose of morphology, morphemic syntax, and semantics inter-
face. The architecture in Figure 3b incorporates the current proposal as an interpretive
front end to a morphological analyzer such as Oflazer’s (1994), which delivers the anal-
yses of words as a stream of morphemes out of which the bound morphemes have to
be matched with their semantics from the affix lexicon to be interpretable in grammar.
The advantage of this model is its efficiency; morphological parsing of words is—in
principle—linear context free; hence, finite-state techniques and their computational
advantages readily apply. But the uninterpretable surface forms of bound morphemes
must match with those of the affix lexicon, and this is not necessarily a one-to-one
mapping because of multiple lexical assignments for capturing syntactic–semantic dis-
tinctions (e.g., dative case as a direct object, indirect object, or adjunct marker or -i
as a possessive and/or compound marker). Surface form–semantics pairing is not a
trivial task, particularly in the case of lexically composite affixes, which require se-
mantic composition as well as tokenization. The matching process needs to be aware
of all the syntactic contexts in which certain affix sequences act as a unit, for exam-
ple, relative participles and agreement markers (-di˘g-i relative participle as -OP-POSS
or -OP-AGR), possessive and compound markers, etc., for Turkish. The factorization
of syntactic issues into a morphological analyzer would also make the separate mor-
phological component nonmodular or expand its number of states to factor in these
concerns (e.g., treating the -OP-POSS sequence as a state different from -OP followed
161
Bozsahin The Combinatory Morphemic Lexicon
Table 2
Parsing performance.
Average number
Sample text Number of items of parses/grammatical Average CPU time
type in text input per test (milliseconds)
Normal Normal
PAS form PAS form
tests words morphs check parse Unrestr. check parse
Word order and 58 216 384 1.26 3.68 39 39 30
case
Subordination 14 70 137 3.00 5.09 267 270 180
Relativization 23 130 232 2.04 2.32 796 783 266
Control verbs 33 147 291 1.42 3.34 166 163 137
Possessives and 26 109 200 1.23 2.47 137 135 98
compounds
Adjuncts 14 57 100 1.12 4.87 89 88 72
-ki relatives 24 66 179 1.07 1.54 36 36 35
Note: CPU times are for a Sun UltraSparc-4 running SICStus Prolog; lexical items include stems and inflec-
tional affixes.
by -POSS, in which -POSS is not interpreted with the semantics of possession but that
of agreement marking). Not knowing how many of the syntactic distinctions are han-
dled by the morphological analyzer, a subsequent interpreter may need to reconsult
the grammar if scoping problems arise.
The architecture in Figure 3c describes the current implementation of the pro-
posal. Bound morphemes are fed to the parser along with their interpretation. This
model is preferred over that presented in Figure 3b for its simplicity in design and
extendibility.
16
The price is lesser efficiency due to context-free processing of inflec-
tional morphology. By one estimate (Oflazer, Gocmen, and Bozsahin 1994), Turkish
has 59 inflectional morphemes out of a total of 166 bound morphemes, and Oflazer
(personal communication) notes that the average number of bound morphemes per
word in unrestricted corpora is around 2.8, including derivational affixes. In a news
corpus of 850,000 words, the average number of inflections per word is less than two
(Oflazer et al. 2001). This is tolerable for sentences of moderate length in terms of the
extra burden it puts on the context-free parser. Table 2 shows the results of our tests
with a Prolog implementation of the system on different kinds of constructions. The
test cases included 10 lexical items on average, with an average parsing time of 0.32
seconds per sentence. A relatively long sentence (12 words, 21 morphemes) took 2.9
seconds to parse. The longest sentence (20 words, 37 morphemes) took 40 seconds.
The lexicon for the experiment included 700 entries; 139 were free morphemes and
561 were bound morphemes compiled out of 105 allomorphic representations (includ-
ing all the ambiguous interpretations of bound morphemes and the results of lexical
rules). For a rough comparison with an existing NLP system with no disambiguation
16 The morphological analyzer would be in no better position to handle morpheme–semantics pairing if
the architecture in Figure 3b were implemented with an integrated lexicon of roots and affixes. For
instance, -POSS would still require distinct states because of the difference in the semantics of
possession and agreement marking coming from the lexicon.
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Computational Linguistics Volume 28, Number 2
aids, G ¨ung¨ord ¨u and Oflazer (1995) reported average parsing times of around 10 sec-
onds per sentence for a lexicon of 24,000 free morphemes, and their morphological
analyzer delivered around two analyses per second to a lexemic grammar. Oflazer’s
later (1996) morphological analyzer contained an abstract morphotactic component of
around 50 states for inflections, which resulted in compilation to 30,000 states and
100,000 transitions when the morphophonemic rules were added to the system.
In conclusion, we note that the current proposal for a morphemic lexicon and
grammar is compatible with both a separate morphological component (Figure 3b) and
syntax-integrated inflectional morphology (Figure 3c). The architecture in Figure 3b
may in fact be more suitable for inflecting languages (e.g., Russian) in which the
surface forms of bound morphemes are difficult to isolate (e.g., m´este, locative singular
of m´esto) but can be delivered as a sequence of morpheme labels by a morphological
analyzer (e.g. m´esto-SING-LOC) to be matched with the lexical type assignments to
-SING and -LOC for grammatical interpretation.
It might be argued that in computational models of the type in Figure 3b, the lattice
is not necessary, because the morphological analyzer embodies the tactical component.
But not only tactical problems (cf. Example (18) and its discussion) but also transparent
scoping in syntax and semantics is regulated by the use of lattice in type assignments,
and that is our main concern. We show examples of such cases in the remainder of the
article. Thus the nonredundant role of the lattice decouples the morphemic grammar–
lexicon from the kind of morphological analysis performed in the back end.
5. Case Study: The English Plural
In this section, we present a morphosyntactic treatment of the English plural mor-
pheme. The lattice for English is shown in Figure 2b. We follow Carpenter (1997) in
categorizing numerical modifiers and intersective adjectives as plural noun modifiers:
four boys is interpreted as four(pluboy) and green boxes as green(plubox). This bracketing
reflects the “set of sets” interpretation of the plural noun; four(pluboy) denotes the set
of nonempty nonsingleton sets of boys with four members. The type assignments in
(20) correctly interpret the interaction of the plural and these modifiers (cf. 21a–b).
The endotypic category of the plural also allows phrase-internal number agreement
for languages that require it; the agreement can be regulated over the category N
before the specifier is applied to the noun group to obtain NP.
(20) -PLU :=
a
◦s −
n
< N\
b
< N:λx.plux
four :=
s
◦four −
n
< N/
n
✶N:λx.fourx
green :=
s
◦green −
n
< N/
n
< N:λx.greenx
(21) a. four boy -s
n
< N/
n
✶N
b
< N
n
< N\
b
< N
<
n
< N: pluboy
>
n
< N :four(pluboy)
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Bozsahin The Combinatory Morphemic Lexicon
b. four boy -s
***
>
n
< N:fourboy
n
< N\
b
< N
because n-base negationslash= n-num
***
n
< N:*plu(fourboy)
Carpenter (1997) points out that nonintersective adjectives (e.g, toy, fake, alleged)are
unlike numerical modifiers and intersective adjectives in that their semantics requires
phrasal (wide) scope for -PLU, corresponding to the “set of things” interpretation
of the plural noun. Thus, toy guns is interpreted as plu(toygun) because the plural
outscopes the modification. It denotes a nonempty nonsingleton set of things that are
not really guns but toy guns. *toy(plugun) would interpret plu over guns. The situation
is precisely the opposite of (21); we need the second derivational pattern to go through
and the first one to fail. The following category for nonintersective adjectives derives
the wide scope for -PLU but not the narrow scope:
(22) toy :=
s
◦toy −
b
< N/
b
< N:λx.toyx
(23) a. toy gun -s
<
b
< N/
b
< N
n
< N:plugun
***
n
< N :*toy(plugun)
because n-num negationslash≤ n-base
b. toy gun -s
b
< N/
b
< N
b
< N
n
< N\
b
< N
>
b
< N:toygun
<
n
< N :plu(toygun)
Carpenter (1997) avoided rebracketing because of the plural through lexical type
assignments to plural nouns and a phonologically null lexical entry to obtain differ-
ent semantic effects of the plural. In our formulation, there is no lexical entry for
inflected forms and no phonologically null type assignment to account for the dis-
tinction in different types of plural modification; there is only one (phonologically
realized) category for -PLU.
17
The modifiers differ only in the kind and degree of mor-
phosyntactic control. Strict control (✶)onfour disallows four boy, and flexible control
(<)ongreen also handles green box. Four green boxes is interpreted as four(green(plubox)),
17 This is not to say that there is only one model-theoretic interpretation of plu. “Sets of sets” and “set of
individuals” valuations of plu can be carried over the PAS.
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Computational Linguistics Volume 28, Number 2
not as *four(plu(greenbox)), and four toy guns is interpreted as four(plu(toygun)), not as
*plu(four(toygun)). These derivations preserve the domain of the modifiers and the
plural without rebracketing.
6. Case Study: Turkish Morphosyntax
There have been several computational studies to model morphology–syntax inter-
action in Turkish. These unification-based approaches represent varying degrees of
integration. G ¨ung¨ord ¨u and Oflazer (1995) isolates morphology from syntax by having
separate modules (a finite-state transducer for the former, and an LFG component for
the latter), that is, the syntax is lexemic. The morphological component is expected to
handle all aspects of morphology, including inflections and derivations. In Sehitoglu
and Bozsahin (1999), lexical rules implement inflectional morphology, and derivations
are assumed to take place in the lexicon. Hoffman’s (1995) categorial analysis of Turk-
ish is also lexemic; all lexical entries are fully inflected. Interpretive components of
these systems face the aforementioned difficulties because of their commitment to lex-
emic syntax. Inflectional morphology is incorporated into syntax in another categorial
approach (Bozsahin and G¨o¸cmen 1995), but morphotactic constraints are modeled with
nonmonotonic unification, such as nonexistence checks for features and overrides. The
system cannot make finer distinctions in morphosyntactic types either. The result is an
overgenerating and nontransparent integration of morphology and syntax because of
the possibility of rebracketing and the unresolved representational basis of the lexicon.
In this section, we outline the application of the proposed framework to Turkish.
We analyze a large fragment of the language, without any claims for a comprehensive
grammar. The phenomena modeled here exhibit particular morphosyntactic problems
described in the preceding sections. We assume the binding theory in Steedman (1996),
which is predicated over the PAS. In each section, we provide a brief empirical observa-
tion about the phenomenon, propose lexical type assignments, exemplify derivations
of the parser, and briefly discuss the constraints imposed by morphosyntactic types.
Because of space considerations, we sometimes use abbreviated forms in derivations
such as the genitive affix’s (N/(N\N))\N category for (
o
< N/(
o
✶N
pn
\
o
✶N
pn
))\
o
< N
pn
,
but the parser operates on full morphosyntactic representations.
6.1 Case Marking and Word Order
Turkish is regarded as a free constituent order language; all permutations of the
predicate and its arguments are grammatical in main clauses, being subject to con-
straints on discourse and semantic properties such as definiteness and referentiality
of the argument and topic–focus distinctions. The mapping of surface functions to
grammatical relations is mediated by case marking. Word order variation has lesser
functionality in embedded clauses because embedded arguments are less accessible
to surface discourse functions like topic and focus. Embedded clauses are verb fi-
nal.
6.1.1 Lexical Types. We start with the lexical type assignments for the verbs. We use
the abbreviations in (24a) when no confusion arises about the arguments’ case or mor-
phosyntactic type. Verb-final orders are regarded as basic, which suggests the category
S\NP\NP for transitive verbs. But Janeway (1990) argued that such underspecification
for verb-peripheral languages causes undesirable ambiguity. Grammatical relations of
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Bozsahin The Combinatory Morphemic Lexicon
the arguments are determined not by directionality but by case in such languages. The
category S\NP
nom
\NP
acc
resolves the ambiguity (24b–c).
(24) a. IV = S\NP
TV = S\NP\NP
DV = S\NP\NP\NP
b. sev (like) :=
s
◦ sev −
v
< S\
f
< NP
nom
\
f
< NP
acc
:λx.λy.likexy
c. ver (give) :=
s
◦ ver −
v
< S\
f
< NP
nom
\
f
< NP
dat
\
f
< NP
acc
:λx.λy.λz.giveyxz
d.
v
< S\
f
< NP
nom
\
f
< NP
acc
:λx.λy.likexy ⇒
v
< S\
f
< NP
+ref
acc
\
f
< NP
nom
:λy.λx.likexy
e. -ACC :=
a
◦ i|ı|u|¨u|yi|yı|yu|y¨u −
c
< N
acc
\
o
< N:λf.f
f. -LOC :=
a
◦ de|da|te|ta − (
α
< S/
α
< S)\
o
< N:λx.λf.atfx
Gapping behavior seems to indicate that Turkish is verb final, not just SOV. SO
and OS syntactic types must be distinguished to account for SO & SOV, OS & OSV,
*SO & OSV and *OS & SOV. The OS & OSV pattern requires the lexical category
S\NP
acc
\NP
nom
for the verb (Bozsahin 2000b). SOV and OSV base orders can be cap-
tured uniquely in the lexicon in set-CCG notation as S\{NP
acc
,NP
nom
}. Set-CCG is
strongly equivalent to CCG (Baldridge 1999). We distinguish SOV and OSV lexically,
however, because OSV requires referential objects (25a–b). OSV is generated from SOV
by a lexical rule (24d). This is genuine lexical ambiguity, because the two related entries
differ in semantics (referentiality).
(25) a. Kitab-ı adam oku-du
Book-ACC man.NOM read-TENSE
’The man read the book.’
b. *Kitap adam oku-du
Book man.NOM read-TENSE
Regarding the relationship between case and the specifiers, it is questionable
whether Turkish has a discernible syntactic category for determiners. There is no lex-
ical functor that takes an N and yields an NP. The only article, the indefinite bir (’a’),
makes a distinction in discourse properties (26). Specifying case as a determiner (e.g.,
NP\N) does not alleviate the problem, either. Ignoring the problem of case stacking
for a moment, zero marking of the surface subject and the indefinite object takes us
back to where we started.
(26) ¸Cocuk ye¸sil bir elma/elma/elma-yı ye-mi¸s
child.NOM green an apple/apple/apple-ACC eat-TENSE
’The child ate a green apple.’ (indefinite but referential apple)
’The child ate green apple.’ (indefinite and nonreferential apple)
’The child ate the green apple.’ (definite and referential apple)
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Computational Linguistics Volume 28, Number 2
Making the nouns lexically ambiguous (N or NP) would also require that all func-
tions onto nouns be ambiguous (N\N and NP\NP for inflections, N/N and NP/NP for
adjectives, etc.). Redundancy of this kind in the lexicon is not desirable, since it is in-
troduced purely for formal reasons with no distinction in meaning. We accommodate
these concerns by positing a special case of type raising for Turkish (27). Similarly,
contraposition turns Ns into functors looking for NPs.
(27) Type Raising for Turkish: N
agr
: a ⇒ T/(T\
f
< NP
agr
):λf.f[a]
⇒ T\(T/
f
< NP
agr
):λf.f[a]
T ∈{S,S\NP,S\NP\NP, S\NP\NP\NP}
The noun that is type raised can be a syntactically derived noun (28). SO (and OS)
constituency required for gapping is provided by >T and >B.
(28) Mehmet k¨u¸c¨uk ye¸sil kitab-ı, ¸cocuk da yeni gelen dergi-yi oku-du
M.NOM little green book-ACC child-COORD new come mag.-ACC read-TENSE
N
nom
N
acc
N
nom
N
acc
S\NP
nom
\NP
acc
>T >T
S/(S\NP
nom
)(S\NP)
/(S\NP\NP
acc
)
.
.
.
>B >B
S/(S\NP
nom
\NP
acc
)S/(S\NP
nom
\NP
acc
)
&
S/(S\NP
nom
\NP
acc
)
>
S
’Mehmet read the little green book, and the child, the newly arrived magazine’.
Our lexical type assignment to case morphemes (24e–f) departs from other CCG
analyses of case (e.g., Steedman 1985, 1991a, Bozsahin 1998). These studies correlate
morphological case with type raising of arguments, in the case of Bozsahin (1998), via
a value-raised category assignment to case morphemes. Evidence from NP-internal
case agreement and case stacking (Kracht 1999) challenges the type-raising approach.
Agreement phenomena require that case (which can be marked on articles, adjectives,
and nouns) be regulated as an agreement feature within the category N before the
case-marked argument looks for the verb via type raising. Kracht observes that, in
case stacking, there may be other morphemes between two case morphemes. Thus,
treating the two cases as composite affixes for the purpose of type raising is not
feasible. If the first case type-raises the noun to say, T/(T\NP), the second case would
require a category, (T/(T\NP))\(T/(T\NP)); that is, it is endotypic. Hence, an endotypic
category for case (like other inflections in the paradigm) subsumes the type-raising
analysis of case provided that type raising is available in the grammar, not necessarily
anchored to case.
We analyze case as an endotypic functor of type N\N (24e)—hence allow for
phrase-internal agreement for languages that require it and provide type raising in
grammar as in (27). Abandoning the type-raising analysis of case does not necessitate
taking liberties in the directionality of the categories, such as the use of nondirectional
slash (|) in multiset-CCG (Hoffman 1995). Contraposition and type raising in grammar
167
Bozsahin The Combinatory Morphemic Lexicon
can account for free word order and gapping facts with fully directional syntactic types
(Bozsahin 2000a).
6.1.2 Derivations. The wide scope of case is captured by treating its argument type as
non-case-marked N (
o
< N) and the type of noun modifiers as functions onto non-case-
marked nouns of a particular domain, for example,
b
< N for nonintersective adjectives
and
n
< N for intersective adjectives (29a). The same strategy in type assignments to
other nominal inflections allows them to outscope nominal modification, for exam-
ple, (29b).
(29) a. Mehmet [[oyuncak araba ] -lar ] -ı sev-er
M.NOM toy car -PLU -ACC like-TENSE
<B
b
< N
nom
b
< N/
b
< N
b
< N
n
< N\
b
< N
c
< N
acc
\
o
< N
t
< S\
f
< NP
nom
:mehmet :λx.toyx : car :λx.plux :λf.f \
f
< NP
acc
>T
S/(S\
f
< NP
nom
) :λx.λy.likexy
:λf.f [mehmet]
>
b
< N:toycar
<
n
< N:plu(toycar)
<
c
< N
acc
:plu(toycar)
>T
(S\NP)/(S\NP\
f
< NP
acc
):λg.g[plu(toycar)]
>
t
< S\
f
< NP
nom
:λy.like(plu(toycar))y
>
S:like(plu(toycar))mehmet
’Mehmet likes toy cars.’
b. Adam-ın [k¨u¸c¨uk kırmızı araba]-sı
Man-GEN little red car-POSS
’the man’s little red car’ = poss(little(redcar))man
A word-based alternative for reconciling the semantic (wide) scope of inflections
and their morphological (narrow) attachment to stems runs into difficulties even if
we assume that morphemes carry type assignments—and hence have representational
status—but that they always combine with stems first. We use syntactic types to show
the problem. If -PLU and -ACC in (29a) combine with the stem first, only the narrow-
scope reading of the plural and case is possible (30a). Plu(toycar) is not derivable with
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Computational Linguistics Volume 28, Number 2
word-based modification. The morphosyntactic categories, however, are transparent
to the scope of nominal modification (cf. (29a) and (30b)).
(30) a. oyuncak [[araba] -lar] -ı
toy car -PLU -ACC
N/NNN\NN
acc
\N
:λx.toyx : car :λx.plux :λf.f
<
N:plucar
<
N
acc
:plucar
>
N:∗toy(plucar)
b. [ye¸sil [araba] -lar] -ı
green car -PLU -ACC
n
< N/
n
< N
b
< N
n
< N\
b
< N
c
< N
acc
\
o
< N
:λx.greenx : car :λx.plux :λf.f
<
n
< N:plucar
>
n
< N:green(plucar)
<
c
< N
acc
:green(plucar)
Surface case annotations on categories enable the grammar to capture the correct
PAS in all permutations of S, O, and V while maintaining the discourse-relevant dis-
tinctions (31). Verb-final subordinate clauses are enforced by the directionality of the
subordination morphemes in the lexicon.
(31) a. S O V
>T >T
S/(S\
f
< NP
nom
)(S\NP)/(S\NP\
f
< NP
acc
)S\NP
nom
\NP
acc
>
S\NP
nom
>
S
b. O S V
>T >T
S/(S\
f
< NP
acc
)(S\NP)/(S\NP\
f
< NP
nom
)S\NP
acc
\NP
nom
>
S\NP
acc
>
S
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Bozsahin The Combinatory Morphemic Lexicon
c. O V S
>T >XP
(S\NP)/(S\NP\
f
< NP
acc
)S\NP
nom
\NP
acc
S
−t
\(S\NP
nom
)
>
S\NP
nom
<
S
−t
d. S V O
>T >XP
(S\NP)/(S\NP\
f
< NP
nom
)S\NP
acc
\NP
nom
S
−t
\(S\NP
acc
)
>
S\NP
acc
<
S
−t
e. V S O
>XP >XP
S\NP
nom
\NP
acc
S
−t
\(S\NP
nom
)S
−t
\(S
−t
\NP
acc
)
<B
S
−t
\NP
acc
<
S
−t
f. V O S
>XP >XP
S\NP
acc
\NP
nom
S
−t
\(S\NP
acc
)S
−t
\(S
−t
\NP
nom
)
<B
S
−t
\NP
nom
<
S
−t
6.2 Subordination
Subordinate clauses can be classified as unmarked clauses (32a), infinitival clauses
(32b), verbal nouns (32c), and nominalizations (32d). The latter two types require a
genitive embedded subject, which agrees with the subordinate verb.
(32) a. Mehmet [ ¸cocuk ev-e git-ti ] san-dı
M.NOM child.NOM house-DAT go-TENSE assume-TENSE
’Mehmet assumed that the child went home.’
b. ¸Cocuk [ kız-a kalem-i ver-me ] -yi unut-tu
child.NOM girl-DAT pen-ACC give-SUB1i -ACC forget-TENSE
’The child forgot to give the pen to the girl.’
c. [ ¸Cocu˘g-un araba-da uyu-ma-sı] Mehmet’i kız-dır-dı
child-GEN car-LOC sleep-SUB1g-POSS M-ACC anger-CAUS-TENSE
’Child’s sleeping in the car made Mehmet angry.’
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Computational Linguistics Volume 28, Number 2
d. Deniz [ ¸cocu˘g-un uyu-du˘g-u] -na inan-m-ıyor
D.NOM child-GEN sleep-SUB2g-POSS -DAT believe-NEG-TENSE
’Deniz does not believe the child’s sleeping.’
(33) a. Deniz
i
[kendisi-nin
i
uyu-ma-dı˘g-ı]-nı s¨oyle-di
D.NOM self-GEN sleep-NEG-SUB2g-POSS-ACC2 say-TENSE
’Deniz
i
said that he
i
did not sleep.’
b. *kendisi
i
[Deniz’in
i
uyu-ma-dı˘g-ı]-nı s¨oyle-di
c. Deniz
i
adam-ı
j [
kendi
i/j
arkada¸s-ı-nın g¨or-d¨u˘g-¨u ]-ne inan-ıyor
D.NOM man-ACC self friend-POSS see-SUB2g-POSS-DAT2 believe-TENSE
’Deniz
i
believes that his
i/j
friend saw the man
j
.’
d. Deniz
i
adam-a
j [
kendi
i/∗j
kitab-ı-nı oku-du˘g-u ]-nu s¨oyle-di
D.NOM man-DAT self book-POSS-ACC2 read-SUB2g-POSS-ACC2 say-TENSE
’Deniz
i
told the man
j
that he read his
i/∗j
book.’
6.2.1 Lexical Types. The asymmetries in (33) show that the obliqueness order in bind-
ing relations is preserved in subordination. This suggests the following bracketing, in
which the embedded clause’s position in the PAS of the matrix predicate is determined
by its grammatical function.
Matrix-Pred ...Matrix-Argument ...Embedded-Clause ...Matrix-Argument
(34) -SUB1i (-ma) :=
a
◦ ma −
b
< N\(
a
< S\
f
< NP
nom
):λf.f
(infinitive)
-SUB1g (-ması) :=
a
◦ ması −
o
< N\
f
< NP
agr
\(
a
< S\
f
< NP
nom
):λf.f
(verbal noun)
-SUB2g (-dı˘gı) :=
a
◦ dı˘gı −
o
< N
case=obl
\
f
< NP
agr
\(
a
< S\
f
< NP
nom
):λf.f
(nominalization)
The wide scope of case markers on subordinate clauses implies that the subor-
dinate markers themselves must have phrasal scope as well. Since case is a nominal
inflection, the category of a subordinate marker must be a function onto N. Its ar-
gument is IV for infinitives and NP
agr
\IV for others, which require genitive subjects
(34). This yields two families of functors for subordination. The verb-final characteris-
tics of the embedded clauses is ensured by the backward-looking main functor of the
subordinate marker.
For morphosyntactic modality, the resulting nominalized predicate can receive
only case, hence it has
o
< N control. Verbal nouns refer to actions, and nominaliza-
tions refer to facts. Subordinate markers for the former are tenseless. A subordinate
marker replaces the tense of the subordinate verb in nominalizations, yielding
a
< S
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Bozsahin The Combinatory Morphemic Lexicon
control on the verb. For subject raising, the result may undergo any nominal inflection
(
b
< N).
Word order variation within the subordinate clause is constrained by the subject
on the left and the verb on the right. This constraint is achieved by categorizing the
embedded subjects as NP
agr
and having a result category of N for all subordinate mark-
ers. If there were any contraposed element NP in the embedded clause, the category
of the clause would be S\NP, and the clause could not combine with the contraposed
category such as S
−t
\(S\NP) on the right because the extraction category combines
with a subordinate marker first, which is onto N, not S\NP, hence composition (<B)
could not take place.
6.2.2 Derivations. Example (35a) is the derivation of subject raising (we use N
↑
as
an abbreviation for a type-raised N when space is limited). We use Steedman’s (1996)
ana function to denote the binding of the embedded subject. Infinitive -SUB1i has
phrasal scope in this example; the DV must be reduced to an IV before the infinitive
can apply. Hence the subordination of intransitive clauses is only a special case in
which the morphological scope of the infinitive works without rebracketing. Subject
raising and coindexation with the matrix subject are made explicit in the raising cate-
gory of unut. The systematic relationship between the raised and nonraised category
of such verbs can be captured by a lexical rule, for example, TV:λx.λy.forgetxy ⇒
TV:λf.λy.forget(f[anay])y.
(35b–c) contrast subject and nonsubject nominalizations. The difference is cap-
tured with the case distinction of the result type (
o
< N) for -SUB1g and -SUB2g. These
examples also show the possibility of affix composition in the lexicon. For instance,
we write -ması in (35b), which marks subordination and agreement together, instead
of -ma-sı. Otherwise, -ma (SUB1g) would have to look to the right as a functor to
enforce agreement, and the verb-final property of subordination could not be as-
sured.
(35) a. ¸Cocuk kız-a kalem-i ver -me -yi unut-tu
child.NOM girl-DAT pen-ACC give -SUB1i -ACC forgot
>T >T >T <B
N
↑
nom
N
↑
dat
N
↑
acc
DV
b
< N\(
a
< S\
f
< NP
nom
)
c
< N
acc
\
o
< NTV
:λf.f[child] :λg.g[girl] :λh.h[pen] :λx.λy.λz. :λf.f :λf.f :λf.λx.
giveyxz forget
(f[anax])x
>
v
< S\
f
< NP
nom
\
f
< NP
dat
>
v
< S\
f
< NP
nom
<
b
< N
<
c
< N
acc
>T
(S\NP)/(S\NP\
f
< NP
acc
)
>
t
< S\
f
< NP
nom
>
t
< S:forget(givegirlpen(anachild))child
’The child forgot to give the pen to the girl.’
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Computational Linguistics Volume 28, Number 2
b. ¸Cocu˘g-un uyu -ması Mehmet’i kızdır-dı
child-GEN sleep -SUB1g M-ACC anger-TENSE
>T >T <B
NP
agr
IV N\NP
agr
\IV IV/TV TV
< >
N\NP
agr
IV
<
N
>T
S/IV
>
S:anger(sleepchild)mehmet
’The child’s sleeping angered Mehmet.’
c. * ¸Cocu˘g-un uyu-du˘gu Mehmet’i kızdır-dı
sleep-SUB2g
6.3 The Morphosyntax of Control
The control verb’s controlled argument is marked by the infinitive -ma, and the re-
sulting nominalized embedded clause can undergo nominal inflections (36a–b). The
infinitive -ma has the lexical type in (34). A potential conflict between an object con-
trol verb’s subcategorization and PAS is resolved by case decoration: zorla ’force’ and
tavsiye et ’recommend’ differ in their case requirements and what is controlled (36b–c).
tavsiye et’s infinitive complement is accusative, whereas zorla’s is dative.
(36) a. ¸Cocuk [kitab-ı oku-ma]-ya ¸calı¸s-tı
child.NOM book-ACC read-SUB1i-DAT try-TENSE
’The child
i
tried [to
i
read the book].’
b. Mehmet ¸cocu˘g-u [kitab-ı oku-ma]-ya zorla-dı
M.NOM child-ACC book-ACC read-SUB1i-DAT force-TENSE
’Mehmet
j
forced the child
i
[to
i/∗j
read the book].’
c. Mehmet ¸cocu˘g-a/*-u [kitab-ı oku-ma]-yı/*-ya tavsiye et-ti
M.NOM child-DAT/ACC book-ACC read-SUB1i-ACC/DAT recommend-TENSE
’Mehmet recommended the child
i
[to
i
read the book].’
6.3.1 Lexical Types. Subject control verbs (e.g., ¸calı¸s ’try’; s¨oz ver ’promise’) and object
control verbs (e.g., zorla; tavsiye et) have the control property indicated in their PAS
(37). The nonraising variety of these verbs is obtained via a lexical rule.
(37) ¸calı¸s:=
s
◦ ¸calı¸s − TV:λq.λz.try(q[anaz])z
s¨oz ver :=
s
◦ s¨oz ver − DV:λq.λz.λw.promisez(q[anaw])w
zorla :=
s
◦ zorla − DV:λz.λq.λw.force(q[anaz])zw
tavsiye et :=
s
◦ tavsiye et − DV:λzλqλw.recommend(q[anaz])zw
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Bozsahin The Combinatory Morphemic Lexicon
6.3.2 Derivations. The types in (37), coupled with the raising category of the infinitive,
yield the derivations in (38). These examples compose the infinitive complement before
a case can be applied on the nominalized predicate. This is possible because of the
phrasal scope of -ma and the case markers. (38b) shows that although there may be two
accusative-marked NPs, the arguments of the infinitive complement are identifiable;
the IV scope of -ma implies that any (di)transitive subordinate verb must find its
nonsubject arguments before the matrix verb gets its arguments. This type assignment
strategy handles word order variations inside the infinitive complement and the matrix
clause transparently.
(38) a. ¸Cocuk kitab-ı oku -ma -ya ¸calı¸s-tı
child.NOM book-ACC read -SUB -DAT try-TENSE
>T >T <B
S/IV IV/TV TV N\IV N
dat
\NTV
>
IV
<
N
<
N
dat
>T
IV/TV
>
IV
>
S:try(readbook(anachild))child
’The child tried to read the book.’
b. Mehmet ¸cocu˘g-u kitab-ı oku -ma -ya zorla-dı
M.NOM child-ACC book-ACC read -SUB -DAT force-TENSE
>T >T >T <B
S/IV IV/TV IV/TV TV N\IV N
dat
\NDV
>
IV
<
N
<
N
dat
>T
TV/DV
>
TV
>
IV
>
S:force(readbook(anachild))childmehmet
’Mehmet forced the child to read the book.’
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Computational Linguistics Volume 28, Number 2
6.4 Relativization
There are two strategies for forming relative clauses: the subject participle strategy
(SP) and the nonsubject participle strategy (OP). SP is realized by the affixes -(y)An,
-(y)AcAk, and -mI¸s, and OP by -dIk- and -(y)AcAk-. OP triggers agreement similar to
that of possessive constructions between the subject and the predicate of the relative
clause (39b).
(39) a. kitab-ı oku-yan adam
book-ACC read-SP man
’the man that read/reads the book’
b. adam-ın oku-du˘g-u kitap
man-GEN(AGR) read-OP-POSS(AGR) book
’the book that the man read’
6.4.1 Lexical Types. The categories in (40) make explicit the unbounded nature of
relativization; type raising and composition can combine an indefinitely large sequence
of constituents onto S\NP.
(40) -SP :=
a
◦ yan − (N
↑
/
f
< N)\(
a
< S\
f
< NP
nom
)
:λP.λx.λQ.and(Q[x])(P[x])
-OP.AGR :=
a
◦ dı˘gı − (N
↑
/
f
< N)\(
a
< S\
f
< NP
case=obl
)
(argument) :λP.λx.λQ.and(Q[x])(P[x])
-OP.AGR :=
a
◦ dı˘gı − (N
↑
/
f
< N)\
a
< S
(adjunct) :λP.λx.λQ.and(Q[x])(at(P[x])x)
We present a formulation of relativization without any use of empty categories,
traces, or movement. We follow the Montagovian treatment of relative clauses as noun
restrictors of the semantic type λP.λQ.and(Q[x])(P[x]), where P is the semantics of the
relative clause and Q is the semantics of the predicate taking the relativized noun
(x) as the argument. Montagovian analysis assumes a generalized quantifier (GQ)
category for the determiner; that is, NP is the functor and VP is the argument. The
determiner takes the relativized noun (and its semantically type-raised category) as an
argument as well. In a language with determiners, the functor category of the overall
NP can be made explicit by lexically value-raising the determiner with GQ semantics
from, for example, NP/N to (S/(S\NP))/N=(S/VP)/N. To achieve the same effect in
a language that lacks determiners, we make NP the functor by lexically value-raising
the relative participle from (N/N)\(S\NP) to (N
↑
/N)\(S\NP), in which N
↑
/N denotes
a value-raised noun, since N
↑
is a type-raised category. The category of the relative
participle unfolds to ((S/(S\NP))/N)\(S\NP) and (((S\NP)/(S\NP\NP))/N)\(S\NP).
Relativization is strictly head final in Turkish. This implies that all relative par-
ticiples are backward-looking functors that differ only in case requirements (cf. En-
glish relatives, which require different directionality, e.g., (N\N)/(S\NP) for subjects
and (N\N)/(S/NP) for nonsubjects). For morphosyntactic modality, the head noun has
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Bozsahin The Combinatory Morphemic Lexicon
flexible control (
f
< N), because any further grammatical marking on the head must be
shared (41).
(41) Adam-ın g¨or-d¨u˘g-¨u¸cocuk-lar uyu-du
man-GEN see-OP-POSS child-PLU sleep-TENSE
’The children that the man saw slept.’ = and(sleep(pluchild))(see(pluchild)man)
negationslash=*and(sleep(pluchild))(seechildman)
Morphologically, the agreement marker -POSS in OP strategy is a function over
the -OP morpheme, but syntactically, the -OP morpheme triggers the agreement in
the relative clause. Hence -OP-POSS can be treated as a lexically composite affix and
glossed as -OP.AGR. This also ensures the verb-final property of the relativized clause
by not positing a rightward-looking functor for -OP. As for attachment modality, rel-
ative participles are bound morphemes that are affixed to the predicate.
6.4.2 Derivations. (42a–d) show example derivations for subject, object, indirect object,
and adjunct relativization. All nonsubject arguments are handled by a single -OP type
(42b–c). Relativizing the specifier of an argument uses the same strategy as the argu-
ment. This phenomenon calls for another well-regulated lexical assignment schema,
for example, (N
↑
/N)\(N\N)\IV for the relativized specifier of the subject. (42e) is an ex-
ample of relativizing the subject’s specifier. Configurationality within the noun group
is maintained by backward directionality of the categories.
(42) a. kitab-ı oku -yan adam uyu-du
book-ACC read -SP man sleep-TENSE
>T <B
IV/TV TV (N
↑
/N)\IV N IV
:λf.f[book] :λx.λy.readxy :λP.λx.λQ.and(Q[x])(P[x]) :man :λx.sleepx
>
IV:λy.readbooky
<
N
↑
/N:λx.λQ.and(Q[x])(readbookx)
>
N
↑
=S/(S\NP):λQ.and(Q[man])(readbookman)
>
S:and(sleepman)(readbookman)
’The man who read the book slept.’
b. adam-ın g¨or -d¨u˘g¨u¸cocuk uyu-du
man-GEN read -OP.AGR child sleep-TENSE
< <B
NP
agr
TV (N
↑
/N)\IV
agr
NIV
<
IV
agr
<
N
↑
/N
<
N
↑
=S/IV
>
S:and(sleepchild)(seechildman)
’The child whom the man saw slept.’
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Computational Linguistics Volume 28, Number 2
c. ¸cocu˘g-un kitab-ı ver -di˘gi adam uyu-du
child-GEN book-ACC give -OP.AGR man sleep-TENSE
< >T <B
NP
agr
TV/DV DV (N
↑
/N)\IV
agr
NIV
>
TV
<
IV
agr
<
N
↑
/N
>
N
↑
=S\IV
>
S:and(sleepman)(givemanbookchild)
’The man to whom the child gave the book slept.’
d. ¸cocu˘g-un uyu -du˘gu araba bozul-du
child-GEN sleep -OP.AGR car break-TENSE
< <B
NP
agr
IV (N
↑
/N)\SN IV
<
S
<
N
↑
/N
>
N
↑
=S/IV
>
S:and(breakcar)(at(sleepchild)car)
’The car that the child slept in broke.’
e. ¸cocu˘g -u uyu -yan adam kız-dı
child -POSS sleep -SP man anger-TENSE
<B
NN\N\NIV(N
↑
/N)\(N\N)\IV N IV
< <
N\N(N
↑
/N)\(N\N)
<
N
↑
/N
>
N
↑
=S/IV
>
S:and(sleep(posschildman))(angerman)
’The man whose child slept got angry.’
As these examples indicate, -SP and -OP do not range over the verb stem in
semantic scope; they cover the entire relative clause. The wide scope of -SP and -OP
resolves the inconsistency pointed out in the introduction (5b–c), which was mainly
due to coindexation in unification accounts and the lexemic nature of the lexicon.
Isolating the relative participle inflections in a morphological component undermines
the transparency of derivations. Note also that -OP is categorially transparent to the
arity of the verb; a DV must be reduced to an IV before -OP applies to the verb
complex (42c). This is possible only when -OP has phrasal scope.
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Bozsahin The Combinatory Morphemic Lexicon
6.5 Ki-relativization
Ki-relativization is a morphosyntactic process that can generate indefinitely long words
of relative pronouns and relative adjectives. -ki can be attached to case-marked nouns
whose case relation is one of possession, time, or place (i.e., the genitive and the
locative). Its effect is to create a nominal stem on which all inflections can start again
(43a–b). It produces relative pronouns (43c) and relative adjectives (43d) with the
locative and relative pronouns with the genitive.
(43) a. araba-da-ki
car-LOC-REL
’the one in the car’
b. ¸cocu˘g-un ev-i-nde-ki-ler-in-ki
child-GEN house-POSS-LOC2-REL-PLU-GEN-REL
lit. ’The one that belongs to the ones that are in the child’s house’
c. Ben ev-de-ki-ni hi¸c kullan-ma-dı-m
I.NOM house-LOC-REL-ACC2 never use-NEG-TENSE-PERS.1s
’I never used the one at home.’
d. ev-de-ki hediye
house-LOC-REL present
’the present
i
, the one
i
at home’
6.5.1 Lexical Types.
(44) a. -PROki :=
a
◦ ki −
l
✶N\
c
✶N
loc
:λx.λf.and(atPROx)(f[PRO])
(locative)
b. -ADJki :=
a
◦ ki − (
l
✶N/
n
< N)\
c
✶N
loc
:λx.λy.λf.and(atxy)(f[y])
c. -PROki :=
a
◦ ki −
l
✶N\N
↑
gen
:λx.λf.and(possPROx)(f[PRO])
(genitive)
d. sabahki :=
s
◦ sabahki −
l
✶N/
n
< N:λx.λf.and(atmorningx)(f[x])
e. ki (that) :=
c
◦ ki − (N
↑
\
f
< N)/(
v
< S\
f
< NP
nom
)
:λP.λx.λQ.and(Q[x])(P[x])
N
↑
gen
is a shorthand for the N/(N\N) category of a type-raised genitive. In (43c),
pronominal one (PRO) cannot be bound to ev (44a). Adjectival interpretation (43d)
associates the relative adjective with the relativized noun (44b). For morphosyntac-
tic modality, ki-marked nouns behave like possessive-marked nouns in case marking,
which requires strict control over the possessive (
o
✶N). This presents a dilemma: Mor-
phologically, -ki creates a nominal stem that can undergo all nominal inflections again,
but, as (45a) indicates, the stem does not take the CASE (ACC, DAT, etc.) that is com-
mon to nouns unmarked on the possessive. Thus CASE2 in (45c) must refer to another
diacritic (n-relbase, or
l
✶) to eliminate (45b). This diacritic controls the result category
of -ki. The value-raised varieties of (44a–c) are assigned a type similar to the type of
relative participles. Inherently temporal nouns such as sabah (’morning’) can take -ki
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Computational Linguistics Volume 28, Number 2
without the locative. They can be lexicalized without overgeneration with the help of
the morphosyntactic modality
l
✶ (44d).
(45) a. *ev-de-ki-yi
house-LOC-REL-ACC
b. *ev-ni
house-ACC2
c. ev-de-ki-ni
house-LOC-REL-ACC2
d. ev-i
house-ACC
6.5.2 Derivations. -ki ranges over the case-marked noun, which, as (46a–b) indicate,
can be lexical or phrasal. In a lexemic analysis, the entire ki-marked noun would have
to be rebracketed before the adjective k¨u¸c¨uk can apply to its right scope (which is ev,
not ¸cocuk).
(46) a. ev -de -ki
house -LOC -PROki
b
< N
c
< N\
o
< N
l
✶N\
c
✶N
loc
<
c
< N
loc
<
l
✶N:λf.and(atPROhouse)(f[PRO])
’the one that is in the house’
b. k¨u¸c¨uk ev -de -ki ¸cocuk
little house -LOC -ADJki child
b
< N/
b
< N
b
< N
c
< N\
o
< N (
l
✶N/
n
< N)\
c
✶N
loc
b
< N
>
b
< N
<
c
< N
loc
<
l
✶N/
n
< N
>
l
✶N:λf.and(at(littlehouse)child)(f[child])
’the child
i
, the one
i
at the little house’
There is another ki in Turkish that forms nonrestrictive relative clauses as post-
modifiers. It is a Persian borrowing and follows the Indo-European pattern of relative
clause formation (47). It can be distinguished from the bound morpheme -ki lexically.
Its attachment characteristic is also different than that of -ki (44e).
(47) Adam ki hep uyur
man that always sleep-TENSE
’the man, who always sleeps’
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Bozsahin The Combinatory Morphemic Lexicon
6.6 Possessive Constructions and Syntactic Compounds
The grammatical marking of possession is realized through the genitive case on the
possessor (N
gen
) and the possessive marker on the possessee (N
poss
). N
gen
and N
poss
must
agree in person and number (48a), and the resulting noun group is configurational.
Possessives can be nested (48c).
(48) a. ev-in kapı-sı
house-GEN3 door-POSS3s
’the door of the house’
b. * ev-in kapı / *ev-in kapı-lar (door-PLU)
c. ben-im arkada¸s-ım-ın ev-i-nin kapı-lar-ı
I-GEN1 friend-POSS1s-GEN3 house-POSS3s door-PLU-POSS3s
’my friend’s house’s doors’
d. ben-im arkada¸s-ım-ın
i
dost-u-nun
j
kendisi
∗i/j
I-GEN1 friend-POSS1s-GEN3 buddy-POSS3s-GEN3 self
’my friend’s buddy himself’
e. Her ¸calı¸san-ın bazı hak-lar-ı vardır
every worker-GEN3 some right-PLU-POSS3s exists
∀x∃y((worker(x) ∧ right(y)) → has(x, y))
but not ∃y∀x(right(y) ∧ (worker(x) → has(x, y)))
6.6.1 Lexical Types for Possessives. Type assignments for the genitive and the pos-
sessive can be schematized over person (p) and number (n) features, as in (49).
(49) -GEN
pn
:=
a
◦ s − (
o
< N/(
o
✶N
pn
\
o
✶N
pn
))\
o
< N
pn
:λx.λy.possyx
-POSS
pn
:=
a
◦ s − (
o
✶N
pn
\
o
✶N
pn
)\
n
< N
pn
:λf.f
The possessive marker’s result category is a functor because it enforces agreement
with the type raised specifier.
18
(48d–e) indicate that the genitive marker is a type
raiser; the possessor scopes over the possessee. For morphosyntactic modality, the
genitive marker can be attached to nouns that are inflected up to and including a
possessive marker (
o
< N). Moreover, nesting in possessives implies that the specifier
may be a genitive. Hence, the stem’s category must be
o
< N.
But there is a finer control over the possessee argument’s category, because it must
be inflected with the possessive marker to signify relation of possession (cf. (48a–b)).
Semantically, the possessive must outscope nominal modification. For instance, (50a)
has the PAS as indicated, hence both markers must range over a noun group, not just
18 An “inert” category such as N may be motivated by the prodrop phenomenon, in which the specifier
may be dropped under pragmatically conditioned circumstances. But this analysis disregards the point
that binding relations (hence semantics) still require the coindexation of the specifier with some overt
referent, which can be inferred from the discourse. Such an interface phenomenon seems to be better
suited for handling by interactions in the components of a multidimensional grammar, rather than as a
purely syntactic phenomenon.
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Computational Linguistics Volume 28, Number 2
the stem. Binding relations require an organization of the type (possposseepossessor)
(50b–c).
(50) a. ya¸slı adam-ın k¨u¸c¨uk kız-ı
old man-GEN3 little daughter-POSS3s
’old man’s little daughter’ = poss(littledaughter)(oldman)
b. adam
i
-ın kendi
i
-si
man-GEN self-POSS
’the man himself’
c. *kendi
i
adam
i
-ı
6.6.2 Derivation of Possessive Constructions. Example (51) shows the wide scope of
the genitive (51a) and nested genitives (51b).
(51) a. ya¸slı adam -ın k¨u¸c¨uk kız -ı
old man -GEN little daughter -POSS
b
< N/
b
< N
b
< N
o
< N/(
o
✶N\
o
✶N)\
o
< N
b
< N/
b
< N
b
< N
o
✶N\
o
✶N\
n
< N
> >
b
< N
b
< N
< <
o
< N/(
o
✶N\
o
✶N)
o
✶N\
o
✶N
>
o
< N:poss(littledaughter)(oldman)
’old man’s little daughter’
b. ben -im arkada¸s -ım -ın ev -i
I -GEN friend -POSS -GEN house -POSS
NN/(N\N)\NNN\N\NN/(N\N)\NNN\N\N
< < <
N/(N\N) N\ \N
>
N
<
N/(N\N)
>
N: posshouse(possfriendi)
’my friend’s house’
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Bozsahin The Combinatory Morphemic Lexicon
6.6.3 Lexical Types for Compounds. Syntactic compounds exhibit syntactic patterns
similar to possessive constructions, but they signify semantic relations of a different
kind. In what follows, we use the function comp to signify that the arguments in the
PAS form a compound but say nothing about the range of productivity of this function.
The lexical semantics of the arguments and a qualia structure (Pustejovsky 1991) may
indicate the function’s range of applicability. Lexical type assignments for compound
markers are as in (52).
(52) -COMP :=
a
◦ s −
m
✶N\
n
< N\
b
✶N:λx.λy.compxy
-COMP2 :=
a
◦ s −
m
✶N\
m
✶N\
n
< N\
b
✶N:λx.λy.λz.comp(compxy)z
(nested comp)
Syntactic compounds are formed by means of compound markers that are attached
to the head of the compound. For morphosyntactic modality, nonreferentiality of the
head implies no inflection (
b
✶N) or modification (53a–b). The left component can be
a noun group (53c) in which there is ambiguity in the scope of modification. This
is regulated by typing, for example, the intersective adjectives ambiguous as noun
modifiers (
n
< N/
n
< N) and compound modifiers (
m
✶N/
m
✶N).
19
The overall compound
may be inflected only for case (see, e.g., (53d) and (53e)).
(53) a.otob¨us bilet-i
bus ticket-COMP
’bus ticket’
b.*otob¨us ye¸sil bilet-i
green
c.ye¸sil otob¨us bilet-i
green bus ticket-COMP
green(compticketbus)
or comp(ticket(greenbus))
d.otob¨us bilet-i-ni
ticket-COMP-ACC2
e.*otob¨us bilet-i-si
ticket-COMP-POSS
Compound markers serve the dual function of compounding and agreement in
possessive constructions; double marking of the possessive is suppressed (cf. 54a–b).
The -COMP2 type assignment in (52) handles nested compounds.
(54) a.banka-nın faiz oran-ı
bank-GEN interest rate-COMP.POSS
’interest rate of the bank’
b.*banka-nın faiz oran-ı-sı
rate-COMP-POSS
We claim that plural compounds are lexically composite functions in a similar
vein. This claim has some empirical support from the lexicalization of -leri as a
third person plural possessive marker; see (55b–c). It follows that -leri has the lexi-
19 I am grateful to the anonymous reviewer who proposed this alternative.
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Computational Linguistics Volume 28, Number 2
cal types of -COMP and -COMP2 with plural and possessive composition: λx.λy.plu
(compxy).
(55) a.otob¨us bilet-leri
bus ticket-COMP.PLU
’bus tickets’
b.onlar-ın ev-leri
they-GEN3 house-POSS3p
’their house’
c.onlar-ın ev-ler-i
they-GEN3 house-PLU-POSS3s
’their houses’
6.6.4 Derivation of Compounds. (56) exemplifies derivations with the type assign-
ments in (52). (56a–b) show that both the narrow and the wide scope of the modifier
can be accounted for. (56c–d) show that the compound marker interacts with the pos-
sessive. Hence, it must carry both poss and comp in possessive constructions involving
compounds. (56e–f) are examples of nested compounds. (56f–g) show the effect of
strict control (
b
✶N) over the compound’s head.
(56) a. ye¸sil otob¨us bilet -i
green bus ticket -COMP
n
< N/
n
< N
b
< N
b
< N
m
✶N\
n
< N\
b
✶N
> <
n
< N
m
✶N\
n
< N
<
m
✶N:compticket(greenbus)
b. ye¸sil otob¨us bilet -i
<
m
✶N/
m
✶N
b
< N
m
✶N\
n
< N
<
m
✶N
>
m
✶N:green(compticketbus)
c. banka -nın faiz oran -ı
bank -GEN interest rate -COMP.POSS
NN/(N\N)\NN NN\N\N\N
> <
N/(N\N) N\N\N
<
N\N
>
N:poss(comprateinterest)bank
’interest rate of the bank’
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Bozsahin The Combinatory Morphemic Lexicon
d. banka -nın faiz oran -ları
bank -GEN interest rate -COMP.POSS.PLU
NN/(N\N)\NN N N\N\N\N
> <
N/(N\N) N\N\N
<
N\N
>
N:poss(plu(comprateinterest))bank
’interest rates of the bank’
e. kredi kart -ı faiz oran -ı
credit card -COMP interest rate -COMP2
NNN\N\NN NN\N\N\N
< <
N\ \N\N
< <
NN\N
<
N:comp(comprateinterest)(compcardcredit)
’credit card interest rate’
f.kredi kart-ı yıllık faiz oran-ı
annual
’credit card annual interest rate’
g.*kredi kart-ı faiz yıllık oran-ı
7. Conclusion
Theoretical and computational commitment to word-based grammar—and to regard
inflectional morphology as a word-internal process—puts artificial limits on specify-
ing the syntactic and semantic domains of all meaning-bearing elements and on the
transparent projection of scope from the lexicon. Designating words as minimal units
of the lexicon is too constraining for many languages. This traditional notion is also
challenged in current linguistic theorizing (e.g., Jackendoff 1997 and Keenan and Sta-
bler 1997). Marslen-Wilson (1999) argues on psycholinguistic grounds that the lexicon
must be morphemic even for morphologically simpler languages such as English.
We have argued in this article that the key to the integration of inflectional mor-
phology and syntax is granting representational status to morphemes, which, in a
computational system, requires certain precautions. What we propose is enriching the
expressive power of the combinatory morphemic lexicon to factor in morphosyntactic
types and attachment modalities. Coupled with flexible constituency in the grammar
and directionality information coming from the lexicon, these extensions provide the
grammar with the information it requires to compute the transparent semantics of
morphosyntactic phenomena. This flexibility causes neither inefficiency in parsing nor
uncontrolled expressivity. The extensions do not affect the polynomial worst-case com-
plexity results, and category unity is preserved by lattice consistency. The result is a
morphemic grammar–lexicon with computationally desirable features such as mod-
ularity and transparency. The system is available at ftp://ftp.lcsl.metu.edu.tr/pub/
tools/msccg.
184
Computational Linguistics Volume 28, Number 2
Acknowledgments
I am very grateful to four anonymous CL
reviewers for extensive commentary and
suggestions. Thanks to Wolf K¨onig and
Stefan M ¨uller for the data; and to Jason
Baldridge, Gann Bierner, Aysenur Birt ¨urk,
Ruken ¸Cakici, Nissim Francez, Stasinos
Konstantopoulos, Markus Kracht, Geert-Jan
Kruijff, Alan Libert, Mark Steedman,
¨
Umit
Turan and Deniz Zeyrek for comments,
advice, and criticism.

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