what is coordination?

What is coordination?$

Annabel Cormack*, Neil Smith

Department of Linguistics, University College London, Gower Street, London WC1E 6BT, UK

Received 25 August 2003; accepted 25 August 2003

Available online 17 December 2003

Abstract

We argue that there are no devices in the grammar specific to coordination. The grammar is only

capable of providing asymmetric structures, through particular lexical entries relating to semantic

conjunction. Such entries produce adjunction structures, rather than head-complement structures.

The interpretation of conjunction structures is a joint function of such lexical entries, processing

properties, and pragmatics. Coordination phenomena are the result of an unresolved ambivalence

between a ‘head initial’ and a ‘head final’ asymmetric conjunction structure, with the effect that there

are parallel representations.

# 2003 Elsevier B.V. All rights reserved.

Keywords: Coordination; Conjunction; Adjunction; Syntax; Semantics; Lexicon; Minimalism; CCG

1. Introduction

Our purpose in this paper is to argue for the position that there are no devices in the

grammar specific to coordination. Coordination appears to be symmetric, but the

grammar is only capable of providing asymmetric structures. In a standard Principles

and Parameters version of projection, two phrasal categories can be related in either of

two ways. They may be linked (asymmetrically) to a particular head as specifier or

complement of that head, or they may be linked (again asymmetrically) as adjunct and

host. We see the adjunct�host relation, like the complement�specifier relation, as also

essentially head-mediated and, in the case of conjunction, we argue that the particular

lexical entries encoding semantic conjunction relate the two conjuncts as adjunct and

Lingua 115 (2005) 395–418

$ This is a revised version of the paper given at the 4th NWCL International Conference ‘Coordination,

syntax, semantics and pragmatics’ at Salford in November 2001.* Corresponding author. Tel.: þ44-20-7679-7173; fax: þ44-20-7383-4108.

E-mail addresses: [email protected] (A. Cormack), [email protected] (N. Smith).

0024-3841/$ – see front matter # 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.lingua.2003.09.008

host, rather than as specifier and complement.1 The interpretation of conjunction

structures is then a joint function of such lexical entries, processing considerations,

and pragmatics. We argue that the grammar exploits both asymmetric (subordinating)

and symmetric (coordinating) conjunction structures, but that coordination requires no

further elaboration of the grammar: coordination phenomena result from the occurrence

of parallel ‘head initial’ and ‘head final’ asymmetric conjunction structures.

We first clarify the terminology and notation we use. Conjunction ‘^’, disjunction ‘_’,

and implication ‘�’ are logical operators—specifically, two-place operators. Negation is

a one-place logical operator. Lexical items (connectives) like and, but, and because, or,and if, are either Natural Language two-place operators corresponding to traditionaltruth-functional operators for the non-pragmatic part of their meaning, or they aremarkers, much like agreement markers, which are associated with such aNL operator(which may itself be phonologically null).

Coordination is a particular syntactic manifestation of conjunction (or disjunction),

which is symmetric with respect to the conjuncts/disjuncts (i.e. the conjuncts/disjuncts

have the same syntactic status). Without theoretical commitment, we may use &, instead of

^, to indicate that conjuncts are coordinated, and refer to this as coordinating conjunc-tion. Subordination, e.g. as induced by implication (if), is asymmetric: there is an

adjunct and a host. We may use $ to indicate asymmetric conjunction, instead of ^ (see

Smith, 1999). We mostly use a ‘bare’ category notation, where V, for instance, stands for

some projection of a verb. For the operators, we use the full categorial notation, which

includes the selection categories.

Our analysis of coordination exploits a simplified version of Minimalism, with the

addition of Combinators from Combinatorial Categorial Grammar (CCG). In such a theory,

most of the work of the grammar is done by the lexicon. We assume that the combinators

are included in the lexicon: they have syntax, semantics, and (null) phonology.

In contradistinction to standard CCG, but consistent with Minimalism, we assume that

Merge produces an LF representation within NL syntax, with LF being the representation

presented to the Conceptual-Intentional Interface for non-linguistic inferential processing.

All merge is driven by selection.2 We assume that the LF representation, like the PF

representation, is ordered: the unmarked option is that selector precedes selected.3 PF

ordering is derivative, and obtained by displacement. In particular, the PF-part of a head or

phrase may be displaced to some other position because of the morphological selection

properties of the head at that position. This process, which we refer to as PF-attraction, or

simply attraction, has no effect on LF ordering. For expository convenience, we talk of

‘movement’, though we have argued elsewhere (Cormack and Smith, 2001a) that there is

no real movement in the grammar of NL.

1 See Cinque (1994, 1999) for adjectival and adverbial phrases as Specifiers. Sportiche (1994) suggests for

adjuncts only a Spec-Complement relation. See also discussion in Cormack (1999).2 Cormack and Smith (1994); this assumption is fundamental in Categorial Grammar. Chomsky

(2000: 133–134) endorses this principle for ordinary heads, but excludes adjuncts.3 Of course, we do not know how a tree structure, or a tree with a precedence relation defined over it, is

represented in the mind/brain. However, given items of fixed arity, ‘functor first’ allows a linear bracket-free

representation of a tree with a suitable precedence relation (see Partee et al., 1990: 439; for Polish notation, see

McCawley, 1981).

396 A. Cormack, N. Smith / Lingua 115 (2005) 395–418

Arguments are discharged one at a time, resulting in binary branching. Because

argument noun phrases (DNPs) are always headed by a determiner which has the semantic

and syntactic selection properties of a generalised quantifier, noun phrase arguments never

have type hei, but rather hhe, ti, ti and so on.4 Hence, these arguments are functors over VPs

of type he, ti, and so typically precede the lexical selecting V head (though a movement

account from an underlying head-initial order would not be incompatible with our

analysis). VO order at PF is obtained by movement of V to some head Agr, equivalent

in effect to Larson’s (1988) higher V, Bowers’ (1993) Pr head, or Chomsky’s (1995: 60,

352) AgrO or ‘little v’. A comparable treatment of phrasal adjuncts requires either that they

be headed by a two-place operator, selecting first for the rest of the adjunct and finally for

the host, or that they be adjoined by means of some two-place operator which selects for the

adjunct and then for the host. This gives rise in the unmarked case to the order

‘Adjunct < ðprecedesÞ Host’.

We take it that syntax exploits the lexicon under the operation of a principle of default

reasoning which goes by a number of names, including most notably the ‘Penguin

Principle’.

(1) Penguin Principle: Default Reasoning (Elsewhere Condition; Panini Principle)5

If two rules/operations can apply to the same input and their application would

give rise to different outputs, then the one which applies more specifically to the

input has priority

That is, lexical entries compete, with more highly specified entries outranking more

general ones. For example, for the past tense form of the verb give, the competition is

between the form gived, arising from the general rule, and the form gave which is

idiosyncratically specified. It is the more specific form which wins.

By hypothesis, the grammar contains combinators. These occupy the head positions that

we have labelled Agr in our examples. We have suppressed most reference to combinators in

this paper but, if we exploit them fully, we can eliminate the ‘head-final’ versus ‘head initial’

microparameters from the grammar (Cormack and Smith, 2001b: Appendix).

We do not here offer an analysis of all aspects of coordination, omitting in particular

many issues relating to noun phrase coordination (including agreement and set-taking

predicates), and multiple conjunction structures. We concentrate on the syntactic asym-

metry versus symmetry issue, and the theoretical status of coordination itself.

2. Asymmetric versus symmetric conjunction

Ever since the introduction of X-bar theory, the symmetry of coordination has been a

problem. Standardly, X0 theory offers head-mediated phrasal relations between specifier

4 See also Cormack (1999). For an example with a proper name, see (48b). To take care of object and oblique

noun phrase arguments, we assume polymorphic quantifiers (see discussion in Heim and Kratzer, 1998: 180–182).5 See Briscoe et al. (1995) and Asher and Morreau (1991) for discussion, and also Gazdar (1987), Evans and

Gazdar (1989). For uses in phonology and morphology, see Kiparsky (1973), Anderson (1992: 132), Stump

(2001, e.g., 23 ff). Our informal formulation is based on the latter characterisations, for concreteness.

A. Cormack, N. Smith / Lingua 115 (2005) 395–418 397

and complement, or adjunct and host. Neither of these is a symmetric relation.6

Nevertheless, we argue that the symmetry of coordination can be accounted for using

the adjunction relation. In order to do this, we must first explore ASYMMETRIC con-

junction.

Consider the contrast between the two logical connectives and and if. What we get with

the logical connective if is ASYMMETRIC, with a host and an adjunct of differing status.

Extraction is possible from the host, but not from the adjunct, as we see in (2). In contrast,

what we see with and as the logical connective, in examples like (3), is SYMMETRIC, with

extraction allowed from NEITHER conjunct.

(2) a [[If [John takes the car]], [you will go by bus]]

b How, [[if [John takes the car]], [will [you taux go t]]]?

c �What, [if [John takes t]], [will [you taux go by bus]]?

(3) a [^ [You will go by bus] [and [John must take the car]]]

b �How [^ [will [you taux go t]] [and [John must take the car]]]

c �What [^ [ you will go by bus] [and [must [John taux take t]]]]

This syntactic symmetry or asymmetry reflects, and is motivated by, the inferential

symmetry in relation to the two operands of logical operators like and and or, in contrast

to the inferential asymmetry of the logical operator if. The differences between symmetric

and asymmetric operators can be seen clearly with closely related operators. Consider the

examples in (4).

(4) a John will leave soon, since Mary has left

What, since Mary has left, will John do? since: asymmetric

b John will leave soon, because Mary has left�What, because Mary has left, will John do? because: symmetric

The difference in grammatical status parallels differences in inferential status. In (4a),

that Mary has left is assumed to be already known, and so is the inferential/causal

connection between John’s leaving and Mary’s leaving. That John will leave soon is

asserted, and asserted to have been deducible from known information. In (4b), both

that John will leave soon and that Mary has left are asserted, as is the inferential/causal

connection.

We show next that not all conjunction is coordinating or SYMMETRIC. Indeed, not only is

subordinating, or ASYMMETRIC conjunction widespread, but coordinating (i.e. SYMMETRIC)

6 For a summary and bibliography of work on coordination, see Progovac (1998a,b). Attempts to base a

theory of coordination on the specifier–complement relation include Kayne (1994), Johannessen (1998), and

Zoerner (1999). Munn (1993, 2000), Thiersch (1996), Buring and Hartmann (1998), Velde (2000), and others

argue for a basis of adjunction. Borsley (1994) enumerates problems for symmetric coordination with most such

analyses. Many authors (e.g. Johannessen, 1998; Munn, 2000) claim that asymmetries in agreement point to an

inherent asymmetry in conjunction. We see this as an orthogonal issue.


conjunction is derivative, and hence not anomalous. We base our arguments on symmetries

and asymmetries in EXTRACTION, SELECTION, and SEMANTIC TYPE.

We confine our comparison of asymmetric and symmetric operators mainly to the

logical connectives conjunction and implication, associated with and and if. Both the

logical connectives are semantically two-place operators, i.e. they select for two operands.

The default assumption is that their syntactic selection is the same. Given binary Merge, we

expect these operands to be selected one at a time, so that if if is the phonological realisation

of implication, the simplest structure is as in (5). We show this with the operator preceding

its operands, and indexed to show its arity.

(5) [[2if Q] P]

In general, a phrasal adjunct such as [if Q] is headed by a two-place operator, which

selects initially for the ADJUNCT Q and then for the HOST P. What differentiates minor heads

like if, which introduce adjuncts, from lexical or functional projections, is that the syntactic

category of the mother projection is not that of the head, but that of the host (i.e. the final

operand).7 The general two-place operator induces a tree like that in (6a i), exemplified as

shown in (6a ii) for the operator if. Using the Categorial Grammar notation, we code this in

the lexicon by assigning the operator the category shown in (6b), or (6c) for if. The features

with slashes represent the selections, with the selection discharged first being outermost.

Selection features are deleted as they are discharged.

Convention: variables over phrases of a given category, such as X, Y, will be used in such

a way that the alphabetic or subscript order reflects the LF linear order of the operands.

The assumption in (5) and (6c) is that the head if is the two-place connective. However,

there are reasons to suppose that a more elaborate structure might be needed for some

connectives. For example, we might propose the structures in (7), for if. Here, the

conditional operator itself is phonologically null, but there is an associated semantically

7 See Keenan and Faltz re modifiers (1985: 118 ff for a one-place adjunct, 197 for a two-place adjunct). The

categorial notation X/X for an adjunct instantiates Grimshaw’s (1991: 29) claim that functional categories may

be category neutral, transmitting the category of their complement.


trivial one-place operator if on the antecedent of the conditional, and an optional one-place

operator then on the consequent, which are effectively MARKERS of agreement with the

phonologically empty two-place operator head.

(7) [[2� [1if Q]] [(1then) P]]

We will use the simpler version for if, although the other is probably right. Analogously,

one might expect conjunction structures of the form in (8):

(8) a [[2^ [(1both) Q]] [1and P]]

b [[2^ [(1either) Q]] [1or P]]

That and is a marker rather than a two-place operator is suggested by the fact that it occurs

in other conjunction-related and non-conjunction structures. Examples are alternately hot

and cold (where alternately is a two-place operator), and ‘modal subordination’ cases such

as Try and come and Come any closer and I’ll shoot. The last is syntactically as well as

semantically a conditional structure, as witness the licensing of any in the antecedent. But a

structure such as (7) still leaves the symmetry of coordination unexplained. Since we will

not give our explanation of symmetric coordination until Section 8, we may use structures

like (9) for conjunction.

(9) [^ [ Q] [and P]]

We will assume that in the unmarked case a head precedes its complements or operands.

3. Symmetric (coordinating) operators

3.1. Semantics and pragmatics

There is a sense in which conjunction is the most primitive binary operator. Assertion of

‘P’, followed by assertion of ‘Q’, is semantically (but not pragmatically) equivalent to

assertion of the conjunction ‘P ^ Q’. It is not surprising then that this operator may be

phonologically null (see Payne, 1985: 25–27).

We follow the now standard assumption that where logical conjunction is used, there

may be varied pragmatically derived implicatures or explicatures (Grice, 1967/1989;

Sperber and Wilson, 1995; Carston, 1988, 2002). The interpretations in (10) are plausible

and regularly available:

(10) a He [did some weeding and wrote a few pages

of the paper]

simple conjunction

b Hermione got pregnant and looked for a husband temporal ordering

c Jenny hit Billy and he began to cry cause-effect

d Lucinda nibbled biscuits and read a book simultaneity


We see these same meanings arising in other languages, and for phonologically null

instances of the conjunction operator. In the asymmetric interpretations, the asymmetry is

based on ICONICITY, with temporal events paralleling the temporal appearance of the

relevant phrases, and the cause-effect ordering relying on the temporal non-commutativity

of cause and effect. We have argued in previous work (Cormack and Smith, 1999), that the

ordering underlying the iconicity should be identified not at PF, but at an ordered LF. We

return to this later.

3.2. Syntax

Informally, coordination behaves as if it were regulated by the following rule of thumb:

(11) Rule of thumb for coordination structures:

Each conjunct or disjunct behaves as if it were the host

In particular, each must have the same category and semantic type, or rather, each must

have a category and semantic type which is fit for the environment in which the whole

structure occurs (the ‘external homogeneity condition’ of Hohle, 1991). As shown in Sag

et al. (1985), conjuncts of mismatched category are not excluded by the grammar. The

structures in (12) are possible because predicational be is eclectic in its c-selection options,

accepting projections of P, V, A and N, and all the conjuncts are of the appropriate type, that

of a predicate, type he, ti:

(12) a John is [& [P in a temper] [and [V surrounded by fools]]

b John is [& [A hungry] [and [P in a temper]]]

The ‘rule of thumb’ permits distinct categories of conjuncts, each apparently acting as host,

as in the examples in (12), but says nothing about what the mother category is in the

conjunct phrase. In GPSG and HPSG, a cover-category corresponding to a lexical

projection (Lex) exploiting the features [�N, �V] is used. But this still leaves a puzzle

as to why the features should not project, in coordination, or if they do project, why they do

not clash, when in other circumstances the [�N,�V] features from the head must project in

order that there can be differential selection of a projection, say for A but not N. Our

coordination solution will sidestep this problem.8

We presume without argument that constituent conjunction is permitted. We assume

the combinatory account, using S (see Steedman, 1987, 1989, 1990, 1993, and

Szabolcsi, 1992).9 Under this account, although the lexical entry for the binary

operator of conjunction is of type ht, ht, tii (i.e. expecting two propositional arguments

to return a truth value), it may also combine with two operands of type a, where ais some unsaturated type such as he, ti. In effect, it behaves as if it had, type ha, ha, tii

8 See also Bayer (1996) for discussion.9 S is defined by the identity ðSfgÞx ¼ f ðxÞ � gðxÞ. That is, Sfg ¼ lx½f ðxÞ � gðxÞ�.


(see Gazdar, 1980 or Keenan and Faltz, 1985 for theories assigning this type in the

lexicon). Concomitantly, there is a wide variety of syntactic categories that can be

coordinated.

The rule of thumb predicts correctly that there cannot be extraction from just one

conjunct. In (13b), [a father of twins] cannot be host, because [Who is John a father of

twins] is ungrammatical, so [a father of twins] and [fond of t] fail the rule of thumb test and

cannot be coordinated; and in (13c) [fond of his wife] cannot be host, because [How many

children is John fond of his wife] is ungrammatical, so that again, the two putative conjuncts

fail the rule of thumb test.

(13) a John is [[a father of twins] [and [fond of his wife]]]

b �Who is John taux [& [N a father of twins]] [and [A fond of t]]]?

c �How many children is John taux [& [the father of t] [and [fond of his wife]]]

There are of course other coordinating operators, such as or, but we will not discuss these

in detail here.

4. Asymmetric operators

Logical operators like^ (‘and’) and_ (‘or’) are symmetric with respect to the contribution

of the two operands, and may give rise to coordination structures. Other binary operators like

� (‘if’) are asymmetric. Asymmetric binary operators in natural language usually give rise to

asymmetric structures which are distinct from coordination structures. Since we are going to

argue that some conjunction structures in Natural Language are asymmetric rather than

symmetric, we discuss some of the relevant properties of structures headed by asymmetric

operators first, exemplifying with English if.

Subordinating operators are less promiscuous in their selection possibilities than

coordinating conjunction is, but do allow some variation. Consider again if. In (14), in

both the (a) and (b) versions, unless there is massive deletion we have two operands of type

he, ti.

(14) a Raw fish T is [[dangerous to eat] [if stale]]

b Raw fish T [[is dangerous to eat] [if stale]]

The semantics offered for constituent conjunction extends readily to the conditional, so we

may take this as prima facia evidence that if too may appear to have type ha, ha, tii for

appropriate a.

More interestingly, the asymmetric connective if may have semantically and syntacti-

cally unmatched operands. Stroik (1990) and Pesetsky (1995: 161) showed by using

binding possibilities that adjuncts can be attached lower in the clause than one might

expect. For example, in (15a), a bound variable reading is possible, so that the indirect

object must have scope over, and hence c-command, the adjunct. We assume that the


underlying LF structure is something like that in (15 b), with the adjunct attached at the

lowest V-projection level. ‘Head movement’ of the verb to Agr gives the PF-order in (15a).

(15) a John gives [each girl]k money if shek asks for it (but not the boys)

b [John T [Agr [each girl]k [money [V [[if [C shek asks for it]][V gives]]]]]]

c if category: V/V/C; semantics: IF, where if ¼ lulv [u ! v] for u and v of

type hti

Here, if needs to select for operands headed by C and V. Of these, only the host, V, is

compatible with the higher selecting element, T. Not only do the categories of the two

operands of the connective if not match, but the types do not. The first operand of if is of

type hti, and the second is of type he, he, he, tiii. It is straightforward to give an appropriate

syntactico-semantic account of such a structure using the combinators of CCG. We assume

that if has type ht, ht, tii here, so that it combines with its first operand, the clause, by

function-argument application (A) as usual, giving type ht, ti. The next Merge however

must use generalised function composition, using the combinator B (Steedman, 1989,

1990, 1993).10 The representation of the VP in (16a) gives the correct semantics, equivalent

to (16b), and the correct syntax, in parallel.11

(16) a [B [ A IFht, ht, ti [SHE ASKS FOR IT]hti]ht, ti [GIVES]he, he, he, tiii]he, he, he, tiiib lz ly lx [[IF.[SHE ASKS FOR IT]][GIVES.z.y.x]

An example showing details is given in Appendix A.

We are crucially assuming that there are no traces which represent variables in the

grammar, so that extraction requires the use of the combinator B, which in effect passes the

selection information relating to the ‘gap’ up the tree. The use of B will permit adjunction

of some category to a host which is less saturated, as above, but not to a host which is more

saturated, so that it is predicted within CCG that there can be extraction from the host but

not the adjunct in an adjunction structure. It is essentially this fact that gives us an

explanation of the restrictions on extraction from constructions with conjunction that we

discuss below. Steedman (1987) shows that using the combinator S allows extraction from

both operands, giving parasitic gap structures.

5. Asymmetric conjunction

5.1. Head-initial and head-final operators

In this section, we illustrate instances of conjunction exhibiting asymmetries compar-

able to those shown by if, supporting our claim that the structures involved are adjunction

structures. We begin in Section 5.2 with examples of noun modification and of secondary

10 The combinator B is defined by ðBfgÞx ¼ f ðgðxÞÞ, so that in effect it allows the immediate combination of

f and g in anticipation of x ðBfgÞ ¼ lxf ðgðxÞÞ so that we may combine f having category X/Y and type hb, ai and

g having category Y/Z and type hg, bi to give a constituent of category X/Z and type hg, ai.11 Here, we have taken the pronouns to be referential, for simplicity.


predication, where the conjunction operator is head-initial; and then in Section 5.3 we

argue that, somewhat surprisingly for English, there are other cases of adjunction to a

verbal head where the conjunction operator is head-final. In all these cases, we argue that

conjunction gives the correct semantics for the structures.

5.2. Head-initial asymmetric conjunction

Our first example concerns the modification of nouns. In the typical case of noun

modification, the relation between the meanings of the modifier and the noun is INTER-

SECTIVE, in the sense that if the modifier meaning and the noun meaning are taken to

correspond to sets, then the meaning of the whole corresponds to the intersection of the two

sets. In such cases we can represent the modification as headed by the conjunction operator,

as shown in (17).

(17) [D every [N ^ [Ared] [Nball]]]

Semantics: The conjunction entails that the phrase correctly represents ‘being red AND

being a ball’. Simply adjoining the adjective to the noun fails to give any syntax-semantics

correspondence.12

Syntax: Symmetric conjunction would require that D could select both N and A. But this

is not correct: D may only select N. If we have asymmetric conjunction, $, then only the

host category projects, and so the whole may properly be selected by D.

PF: There are two relevant observations concerning the phonological status of the

conjunction head. In the example cited, it is phonologically null, but in some languages it

may be overt, or there may be an overt marker (Rubin, 1996, Rebuschi this volume).

Indeed, there are cases in English where asymmetric conjunction is overtly marked, as we

will see in Section 5.3.

More importantly, the syntax we have proposed gives the wrong ordering for some noun

modification, as for example in (18b), where we now assume that the conjunction head is an

asymmetric head initial operator, shown as $.

(18) a [N [$ [P with red spots on]] N ball]]

b [N [$ [A proud of her successes]] N girl]

To handle this problem, we propose that the $ head PF-attracts a category Lex [�V]

(i.e. N or A). In (18a), this must be the N projection.13 In (17) or (18b), it might be the N

or A projection. We have argued in Cormack and Smith (2000) that word order

indeterminacies may be settled by Soft Constraints (understood as in OT), and suggest

12 The conjunction operator syntactically and semantically produces ‘predicate composition’ (Chomsky,

2002: 16), but this notion is not what is required for adjuncts with heads such as if.13 The alternative, of taking prenominal adjectives to be one-place operators of type hhe, ti, he, tii rather than

as predicates of type he, ti, is not viable in the light of the contrast between (i) �[the children happy] and (ii) [the

children at school and happy]. However, non-intersective adjectives like former and mere must be one-place

operators of category N/N.


the same here. In these cases, there are conflicting desiderata. Moving the A projection

leaves the LF and PF orders in correspondence. Moving the N projection leaves a ‘heavy’

A projection last. We can postulate that English ranks the Soft Constraint HEAVY LAST

higher than PRESERVE CORRESPONDENCE, so that A moves in (17) and N in (18b) (see

Abeille and Godard, 2000 for French).

These considerations suggest that we need a lexical entry for asymmetric conjunction

whose syntax is as in (19) (where the information in parentheses is a reminder for the

reader, not part of the entry).

(19) N/N/X ^ head PF-attracts N or A (modification of N)

Such an entry licenses trees such as those shown in (20 a and b).14

The unspecified category X correctly allows for modification by any category of type he, ti,including PP, AP, passive and progressive VP, and relative clauses.

Our second example concerns adjunction to verbs in secondary predication structures. In

Cormack and Smith (1999), we argued that depictives and resultatives in English should be

given an account in terms of asymmetric conjunction. We take adjectives to be unac-

cusatives, assigning their semantically overt (internal) role to the object, but simulta-

neously selecting for an external argument with semantically vacuous role: that, is one

which contributes nothing to the associated meaning postulates. The analysis of a subject

depictive is illustrated in (21):

(21) a PF: Jo rode the horse weary

b LF: [Jo PAST Agr [VP [THE HORSE [V $ [AP WEARY t]] [V RODE ]]

adjunction to V0

14 On the standard definition of c-command, the noun in (20b) is apparently lowered to the position of the

conjunction head. It is however intuitively clear that a two-place operator should command both its operands,

and we take it that the relevant definition of command needs to be formulated accordingly.


It is well-known that English does not have subject-orientated resultatives, but in languages

such as Korean, sentences comparable to (21a) do have such a reading (Kim and Maling,

1998). In Cormack & Smith (1999: 266f.), we argued that the difference lay in the head

initial versus head final setting for $ in these structures. Resultative readings of conjunction

structures depend on a pragmatic exploitation of iconicity, with causes preceding effects. In

(22a), but not (22b), the fall may be taken as the cause of the fracture.

(22) a Letitia fell over and broke her wrist

b Letitia broke her wrist and fell over

However, there are two possible representations over which this iconicity may be

exploited: PF and LF. Consider (21) again. There is a plausible causal connection between

riding a horse and becoming weary; the relevant iconicity is instantiated in the PF

(ride < weary), but not in the LF (weary < ride). We proposed then that pragmatic

interpretation depending on iconicity uses LF representations, not PF representations, so

that given a head-initial conjunction, (21) is correctly predicted not to have a subject-

orientated resultative reading.15 It may, of course, have a depictive reading and, for suitable

adjoined predicates, there may be a cause-effect interpretation, but it must be the adjunct

which gives the cause, as in (23), with IN A FIT OFtemper < break.

(23) a Mary broke the vase in a fit of temper

b [Mary PAST Agr [VP [THE VASE [V $ [AP IN A FIT OF TEMPER t]] [V BROKE ]]]]

The PF for these examples could be obtained by PF-attraction of V0 to Agr. However,

replacing the simple verb by a phrasal verb, shows that this is not sufficient.

(24) a Jo rubbed down the horse angry

b Jo rubbed the horse down angry

In (24a), we may suppose that the whole phrasal verb complex, which is arguably a V0

projection, moves to Agr. In (24b) however, the particle is stranded before the adjective. We

propose that there is PF-attraction of the V-projection to $, followed by the PF-attraction of

some V0 projection to Agr. The implication is that the lexical entry for conjunction required

for such examples is as in (25):

(25) V/V/X ^ head PF-attracts V (resultatives and depictives)

Crucially, our explanation for the absence of subject-orientated resultatives in English

relies on the $ being head-initial. In contrast, in a language such as Korean where subject-

orientated resultatives are grammatical, we postulate head-final $.

15 An alternative structure consisting of a single event gives rise to the object orientated resultative, without

appeal to iconicity (Cormack and Smith, 1999).


Both the kinds of example discussed in this section have conjuncts mismatched for

selection by a higher head, which requires that the conjunct is asymmetric. In both, there is

displacement of some head or projection of a head to the syntactic position of the

conjunction operator: such displacement gives evidence that the operator is syntactically

present, even if phonologically null.16

5.3. Head-final asymmetric conjunction

So far, the $ position has been, as one would expect for English, head-initial. However,

that we need an ostensibly head-final $ can be shown not only for standard head-final

languages like Korean, but for English too.17

We can argue for head-final asymmetric conjunction on the basis of quasi-serials. At first

sight, examples like (26), discussed in Lakoff (1986), seem to allow extraction from either

conjunct:18

(26) a John ran to the shop and bought a paper

b Which shop did John run to t and buy a paper?

c What did John run to the shop and buy t?

However, in Cormack and Smith (1994, 1999), we argue that the correct analysis for such

sentences involves the conjunction at the canonic transitive level of two verbs or verb

projections, as in our analysis of a Serial Verb Construction. Further, the final result must be

a ‘QUASI-LEXICAL’ complex predicate in the sense that it has the syntactic and semantic

properties appropriate to a verbal lexical entry and must describe a ‘single event’. The

structure requires a ‘transitive’ form of run (available to unaccusative motion verbs), which

assigns a semantically null theta-role to an internal object argument (distinct from the goal

argument). This means that in (45), the argument a paper may be shared by run to the

shop and buy, which are conjoined as indicated in (27a). The whole complex V0 phrase is

PF-attracted to Agr to give the PF form. The occurrence of head-final conjunction is now

no obstacle to the extraction of a paper, as shown in (27b).

(27) a John T Agr [a paper [V [run to the shop] [[and buy] $] ]]

b Whatk did John T Agr [tk [V run to the shop] [[and buy] $] ]]

c Which shop did John T Agr [a paper [V [run [to t]] [[and buy] $] ]]?

In (27c), we have extraction from the first conjunct. If $ is head-final, then the first conjunct

will be the host, so that extraction is permitted, as discussed in Section 4.

16 Compare Steedman (1990: 215), where and is a marker, but the conjunction head is a combinator which is

not represented as a lexical item.17 Arguments for a host-initial adjunction version of asymmetric conjunction are made for German by

Thiersch (1996). For the asymmetries in German, see also discussion in Hohle (1989), Heycock and Kroch

(1994), Buring and Hartmann (1998), and Velde (2000).18 Lakoff was indeed arguing against the ‘Coordinate Structure Constraint’. The alternative we put forward

for the examples in this section can be seen as following the line suggested by Pauline Jacobson which is

recorded in the Appendix to Lakoff (1986).


We conclude that there can be asymmetric conjunction with head-final $ in English. In

such examples, an overt marker and appears on the second conjunct. This suggests a lexical

entry for asymmetric conjunction of the form in (28):

(28) V/V/V{and} Head final; quasi-lexical

The feature on the adjunct selection in (28) is to force the one-place marker 1and to be

attached to this operand. The occurrence can be forced because 1and is a semantically and

syntactically trivial entity, which may be freely introduced into the array of lexical items to

be merged when required by syntax, rather than occurring essentially as part of the

meaning which is being constructed. When it occurs, it projects a feature {and} to the

mother category, as shown in (29).

Our second example is also from Lakoff (1986). Consider (30) and (31). For us, (30) is

acceptable or at worst only mildly deviant, while (31), with extraction from the second

conjunct, is unacceptable (Lakoff, 1986 gave both (30) and (31) as acceptable—see below).

If (31) is ungrammatical, then we suppose that we have head-final conjunction, so that not

get cancer is the adjunct of the adjunct�host pair. We may account for the extraction in

(30) as in (33a or b). In (33a), the parse has extraction from the first conjunct only. In (33b),

the conjuncts are mismatched for type, being of types he, he, tii and he, ti, respectively, as

are the operands of if in Stroik-style examples such as (15) in Section 4. Following the

discussion in Section 4, both these require that the first conjunct is the host in an adjunction

structure, and hence either of these bracketings entails that we have head-final asymmetric

conjunction, as shown.

(30) [What kind of herbs]k can you eat tk and not get cancer?

(31) �[What forms of cancer]k can you eat herbs and not get tk? (our�)

(32) �[What forms of cancer]k can you [eat herbs] and [[not get tk] $]

(33) a [What kind of herbs]k can you [V [V eat tk] [and [V not get cancer]] $]

b [What kind of herbs]k can you [V tk [V [V eat] [and [V not get cancer] ] $] ]


We argue below that the structure for (30) too is quasi-lexical, so that the right form is that

in (33b).

Although the postulation of head-final conjunction for (30) and (31) gives the right

results for us, it is not right for Lakoff. Since Lakoff can extract from either conjunct of

(30), we need an explanation similar to that we gave for the dual extraction possibilities

from (26a). For this, we need get to assign a null thematic role to its patient argument, and

to take cancer as an oblique argument. Since cancer here is clearly not a canonic patient,

and get cancer can be paraphrased with ‘become ill with cancer’, where become is

unaccusative, this is not implausible. This will allow a shared argument what kind of herbs

to be extracted. If for Lakoff the conjunction is head-initial, then the second conjunct is the

host, and so alternatively, there can be extraction of what kind of cancer. The structures are

indicated in (34), where the null theta role assignment is correlated with selection for an

underdetermined type hnili.

(34) a [What kind of herbs]k can you [VP tk [V [$ [V eat]he, he, tii]

[and [V not get cancer]he, hnil, ti ]]

b [What forms of cancer]k can you [VP herbs [[$ [eat]he, he, tii]

and [[not get tk]he, he, hnil, tii]]

If this theta role assignment is available to all speakers for get, the conjunction of eat and

not get cancer may be at the canonic transitive level, allowing a quasi-lexical interpreta-

tion. In this instance, we see not get cancer as a state holding simultaneously with the eat

herbs process, so that we have something akin to a depictive, in (30), and to a result in

(34b), comparable to a resultative. Then for both Lakoff and ourselves, the required

selection is as in (28) above, with an obligatory quasi-lexical reading. The difference

resides only in the headedness of $ when the unaccusative is the second of the pair of

verbs.19

We have shown in this section that asymmetric head-initial conjunction is needed in the

analysis of noun modification, and of resultatives and depictives. We have also shown that

asymmetric head-final conjunction is available in some cases of sub-sentential conjunction

of verbal projections. On the assumption that symmetric (coordinating) conjunction also

exists, this finding leads immediately to the question of the distribution of the various kinds

of conjunction.

6. New question

Given both symmetric and asymmetric conjunction, how do we know when conjunction

must be symmetric, and when it must be asymmetric? It is clear that we must both answer

19 We believe that all Lakoff’s apparent violations of the coordinate structure constraint can be explained

away, and that one essential ingredient is an appeal to the option of null theta selection for the object argument

which may be associated with a subset of unaccusative verbs. We see his type A versus type B distinction as

having an essentially pragmatic explanation.


this and provide some account of how symmetric conjunction emerges. We saw a contrast

between asymmetric if and necessarily symmetric and in examples (2) and (3), and the very

hypothesising of a coordinate structure constraint entails that not all examples of

coordination can be re-analysed as asymmetric structures.

Let us start with the question why coordination, i.e. symmetric conjunction, exists at

all, given its apparently anomalous status in the grammar. Unlike operators such as if,

conjunction and disjunction are inherently symmetric in their logical properties, and we

take it that this is the reason for their syntactic symmetry. Coordination is the unmarked

option.

What then is the motivation for introducing asymmetric conjunction? Our examples in

the last section were noun modification, and various adjuncts to verb projections, where the

product of the conjunction was a complex predicate of some sort. Let us suppose that it is

required on the grounds of expressive power and lexical parsimony that complex predicates

can be formed: that is, we do not want distinct lexical items to encode every complex of the

kind given by red ball or iron dry. Then in a language where adjectives, nouns, and verbs

belong to distinct syntactic categories, we NEED asymmetric conjunction. We do not

similarly expect asymmetric disjunction, because disjunctive concepts are of little if any

utility (cf. grue Goodman, 1955: Chapter 3). Accordingly, we need to set up lexical

selection restrictions licensing asymmetric conjunction, which we expect to be more

restricted that those for symmetric conjunction.

However, when we consider the distribution of symmetric and asymmetric conjunc-

tion, we have a problem. The distributions seem to overlap. We must have symmetric

conjunction of A and N projections in copular complements, as in (35a), but in noun

modification, we must have asymmetric conjunction of A and N projections, as in

(35b).

(35) a John is [& [A fond of his wife] [N and [N a happy man]]]

b the [$ [A happy] [N man]]

Similarly, we must have symmetric conjunction of V and A projections in (36a), but

asymmetric conjunction in resultatives and depictives as in (36b).

(36) a John is [& [A unhappy] [V and [V pursued by debtors]]]

b Mary [the vase [$ [P in a fit of temper t] [V broke]]] (¼(23))

Finally, we have symmetric conjunction of two V projections in examples like (37a), but

asymmetric conjunction in examples like those in (37b and c)

(37) a John [rare books] [& [V bought from the public] [V and [V sold to dealers]]]

(where neither PP can be extracted)

b John a paper [[V run] [V and [V fetch]] $]

c You can [those herbs [[V eat] [V and [V not get cancer]] $]


For structures like (37), we claim that the condition restricting asymmetric conjunction to a

quasi-lexical interpretation of the whole is sufficient. In Cormack and Smith (1999) we

attempted to instantiate this in terms of event structure, and hence ultimately giving an

account in terms of a restriction on the types of the conjuncts. Although our account there is

flawed, we think this is the right approach, and will assume here that no further stipulation is

needed. For structures like those in (35) and (36), we suggest that the required distribution can

be obtained by exploiting checking theory to place restrictions on the lexical entries of the

host categories, where we restrict the host to being a projection of V or N.20

The solution we propose turns on special properties of V and N. In English, N must be

licensed by D, which is why characteristically determiners turn up in predicate NPs in

English.21 Comparably, V must be licensed by Inflection, which we have argued in

Cormack and Smith (1997) to be always a separate head in English, even when associated

with Tense. Consider the following LF structures:22

In the symmetric examples in (38), the required Determiner and Infl nodes are INSIDE the

scope of the conjunction; in the asymmetric examples in (39), the one relevant to the host

may be OUTSIDE.

We now tighten up our initial proposals for lexical entries for asymmetric conjunction,

given in (19), (25) and (29). The requirement for a checking feature is coded by requiring

the host to be of the form N{\D} or V{\Infl}, where the curly brackets indicate an

‘uninterpretable’ checking feature. We envisage that a feature {\X} is deleted under

sisterhood with X, perhaps after percolation.

(40) Revised lexical entries for the binary conjunction operator:

20 This means that there are no adjective or prepositional phrase modifiers which are adjoined by means of

covert conjunction. All such modifiers have to be headed by overt operators. As far as we can see, this is

harmless; the typical modifiers in both cases are measure phrases such as almost, as in almost hot, or almost out

of sight.21 We take it that in Bill is president, there is a null Determiner licensing president.22 It is of course also possible for there to be two instance of a Tense node, one in each conjunct.


Note that because we have imposed the {\Infl} restriction on the host in (29), as in (40c),

any structure satisfying the syntactic description in (40c),23 which stipulates that the

conjunction operator must be head-final, will also satisfy (40b), where the conjunction

operator is head-initial. However, the various syntactic specifications are competing entries

in the lexicon, so that the Penguin Principle operates. Since the entry in (40c) is more

highly specified with respect to the items to be coordinated than that in (40b), it will

override the latter when applicable. In particular, quasi-serial constructions and examples

like Lakoff’s will always have $ final and an overt and.

It now seems that we predict incorrectly that structures with passives or progressives as

adjuncts, like that in (41a), instead of falling under (40b) as we assumed in Section 5.2, would

fall under (40c). This cannot be correct, since (40c) would require a form like that in (41b).

(41) a John ate his breakfast [standing up]/[surrounded by children]

b �John ate his breakfast and [standing up]/[surrounded by children]

Our reply is that passive and progressive phrases cannot occur in quasi-lexical projections

(see Cormack and Smith, 1997). If the fixed conditions of (40c) are not met, then this

specification cannot be used, and (40b) will be utilised.24

The question arises as to why it is the checking features {\Infl} and {\D} that are used to

restrictasymmetricconjunction.Weassumethat thefeaturesmustbecategorial, and thatusing

ordinary selection features would be incompatible with the ‘modification’ effects required of

the structures. If this is right, then a prerequisite for asymmetric conjunction is that the host

head is obligatorily associated with some higher head. Infl and D are local heads obligatorily

related to V and N, respectively, in English. Since we have not discussed all the variants of

asymmetric conjunction that we believe to occur in English, and do not have comparable

information from other languages, further generalisation and explanation must wait.

7. Coordination

Finally, we get to our proposal for symmetric conjunction. This has to meet the following

demands:

(42) i There are to be no principles of the grammar introduced especially for

coordination

ii In coordination, every conjunct behaves as if it were the head

iii We already have the three lexical entries given in (40) for the conjunction

operator

23 For Lakoff’s grammar, (40c) must presumably be replaced by two entries:

where the feature [location] is a cover term for the motion and location verbs possible with quasi-serials.24 It is possible that passive and progressive phrases do not even fall under the category V, but under Pass or

Mood, and Prog or Asp, respectively.


Taking these three together leaves us with little room for manoeuvre. All we can do is to

construct further lexical entries. What is needed for an arbitrary coordination of X and Y, to

appear at LF in that linear order? In order for X to be the host, we need a head-final

conjunction operator, as specified in (43b). In order for Y to be the host, we need a

specification as in (43a):

(43) a Y/Y/X

b X/X/Y head final

For English, however, the marker and is mandatory in coordination, so we add this. The

entries shown amended in (45a and b) give rise to the trees in (44a and b).

We now argue that given these two lexical entries, the processing system will indeed parse

the appropriate strings as coordination structures. We show the whole collection of

specifications for the conjunction operator in (45).

(45) Lexical entries for the binary Conjunction operator:

Suppose we wish to conjoin P and Q, where none of the conditions for asymmetric

conjunction in (45c–e) is met. Then the less specified entries (a) and (b) are available.

Which is chosen? We claim not only that the speaker does not WANT the hearer to choose

between (a) and (b), but that the processing system is such that the hearer CANNOT choose

between them. There are two subparts to this claim, one about choosing, and the other

about the consequences of not choosing. We discuss each in turn.


First, the grammar is normally set up in such a way as to minimise indeterminacy in

processing. Minimalism avoids optionality (Chomsky, 1991: 433). In most OT accounts,

this is enshrined in the requirement that soft constraints be totally rather than partially

ordered (Legendre, 2001: 3–5). In acquisition, Clark (1993) postulates a ‘Principle of

Contrast’ which states that ‘‘Speakers take every difference in form to mark a difference in

meaning’’. In the adult lexicon, there is a strong tendency for alternative items with the

same meaning to become differentiated (e.g. sheep, mutton). Where this appears not to

have happened, as with the free choice between mowed and mown, a decision is forced on

the speaker by the fact that although the items are identical semantically and equally

specified syntactically, they differ at PF (and almost certainly differ in related encyclo-

paedic content). In our case, although the two entries lead to distinct LF representations, the

two options are identical at the interfaces. That is, the PF output induced is the same for

both and, at the Conceptual�Intentional interface, we have first the contribution from the

symmetric logical operator conjunction, and secondly, any additional implicatures or

explicatures derived from the LF ordering of the conjuncts—which is the same for the

lexical options in (a) and (b). If the two entries lead to interface-identical output, there is no

basis for any decision, and no decision will be made.

This leads to the second question. How can a representation be indeterminate in this

way? There have been arguments for underspecified representations for both syntactic and

semantic ambiguity. For syntactic underspecification, see discussion in Gorrell (1995: §3.3

and §3.4), and for semantic underspecification, see Pinkal (1996), who says ‘‘Full

disambiguation may not even improve the usefulness of the utterance information, in

certain cases’’ (p. 186). It may be possible to produce an underspecified representation for

coordination from which the relevant syntactic and semantic inferences could be made.

Here, we assume that processing is done in parallel, with many options considered and

most rejected as the parse proceeds.25 If at the end there are still two viable representations,

so be it. That this is within human capacity is supported by the ubiquity of puns, where

because two distinct parses of some PF string are accessed almost simultaneously, both the

associated readings remain available, as in (46):

(46) a CHEMIST. WE DISPENSE WITH ACCURACY.

b The superconductivity revolution has come. Resistance is useless.

Our claim then is that there are two parallel parses as the proper output for a coordinate

structure.26 We are not claiming for our case, as others have done for other cases, that there

is real optionality in the grammar: we claim only that one cannot choose between equally

good syntactic possibilities.

25 We might assume some version of Ranked Parallel parsing: see Gorrell (1995) §3.6 and also §3.5 for an

introduction. It is clear that not all options can be pursued with equal commitment until shown non-viable, under

parallel processing, because of memory costs and the lack of explanation for Garden Path effects. That at least

limited parallel processing is necessary is argued for by Gorrell (1992), but see Gorrell (1995: 132) for an

alternative account.26 This makes our solution a bit like that of Goodall (1987): there are parallel structures in coordination. But

Goodall’s parallel structures contain material which is not identical at the Interfaces, whereas ours do not.


Coordination, or symmetric conjunction, is essentially an ambivalent instance of

asymmetric conjunction. The symmetric properties of coordination arise from this

ambivalence. Either of the two conjuncts can be construed as the host, and the other

as the adjunct. Thus, as required, the two operands in certain conjunctions have equal

syntactic status for selection and extraction. Because there is no single representation, with

a single mother, for coordination, the problem of the category of the mother when

categorially mismatched conjuncts are coordinated disappears.

The symmetries of coordination are accounted for without the need to postulate any

symmetric structures in the grammar.

8. Conclusion

We have shown, we hope, several things. First, pretheoretically, grammars exhibit both

symmetric and asymmetric conjunction. Asymmetric conjunction is much like any other

adjunction structure, while symmetric conjunction is apparently anomalous. Secondly, we

have sketched a theory under which all the relevant distinctions, possibilities, and related

facts about selection, extraction, and so on, can be encoded in the lexicon. Coordination is a

by-product of an ambivalence in the lexicon.

Apart from the lexical entries themselves, what we have exploited in reaching this

solution is the background theory of CCG and Minimalism, pragmatics, and the Penguin

Principle interpretation of the lexicon. We needed crucially to claim that where the lexicon

provides no decision procedure for which choice of entries to make, no decision can be

made, and both offerings are to be used simultaneously.

Our take home message then is: There are no devices specific to coordination in the

grammar. Coordination is a syntactic pun.

Acknowledgements

We are grateful to Bob Borsley and to an anonymous referee for useful questions and

criticism, and to Deirdre Wilson for discussion of puns.

Appendix A. Adjunction with host and adjunct of unmatched types

We show in more detail here that the use of the combinator B derives the correct

meaning for an adjunction structure where adjunct and host have unmatched types

(Section 4). In the context in (47), the if clause needs to be part of the VP predicated of

Johnny, in order to give the natural sloppy reading where Tommy doesn’t cry if he,

Tommy, loses. The meaning of this VP is constructed on the lines of the simplified

representation in (48a). The subject is constructed as in (48b), where we assume that a

proper name is a noun, and that nouns must be associated with determiners—in this case,

a null determiner with the semantics of a type lifter. The whole is put together as in (48c),

which gives the correct meaning.


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