\input avm.sty
\input amssym.tex
\input path.sty
\input pstricks
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\def\l{\char"AA}
\def\savm#1#2{[\feat{#1}~#2]}
\def\type#1{\hbox{\exhyphenpenalty=10000\it #1\/}}
\def\ger#1{{\it#1\/}}
\def\feat#1{{\sc#1}}
\def\rel#1{{\ss#1}}
\def\nocorr{\kern0pt }
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\def\sec#1{\vskip\parskip\leftline{\bigrm#1}\nobreak}
\def\ssec#1{\vskip\parskip\leftline{\notsobigrm#1}\nobreak}
\def\pt{\phantom`}
\def\ps{\phantom*}
\def\smnp{\hbox{\itss np}}
\def\smvp{\hbox{\itss vp}}
\def\smap{\hbox{\itss ap}}
\def\smconj{\hbox{\itss conj}}
\def\np{\type{np}}
\def\vp{\type{vp}}
\def\ap{\type{ap}}
\def\conj{\type{conj}}
\def\nom{\type{nom}}
\def\gen{\type{gen}}
\def\acc{\type{acc}}
\def\dat{\type{dat}}
\def\plural{\type{plural}}
\def\singular{\type{singular}}
\def\smacc{\hbox{\itss acc}}
\def\smdat{\hbox{\itss dat}}
\def\Gen{\hbox\feat{gen}}
\def\Acc{\hbox\feat{acc}}
\def\Dat{\hbox\feat{dat}}
\def\Nom{\hbox\feat{nom}}
\def\Mas{\hbox\feat{masc}}
\def\Fem{\hbox\feat{fem}}
\def\Case{\hbox\feat{case}}
\def\Neut{\hbox\feat{neut}}
\def\Sg{\hbox\feat{sg}}
\def\Pl{\hbox\feat{pl}}
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\rm
\centerline{On a Type-Based Analysis of Feature Neutrality and the
Coordination of Unlikes\oldfn{*}{This paper is an updated version of
\cite{daniels02}. Thanks go to Chris Brew, Martin Jansche, Bob Levine,
Roger Levy, Detmar Meurers, Carl Pollard, Ivan Sag, and Neal Whitman
for detailed comments on earlier drafts.}}
\centerline{Michael W. Daniels}
\centerline{The Ohio State University}
\centerline{Pre-candidacy paper \#1}

\sec{1. Introduction}

All theories of syntax aspire to be able to analyze any construction
found in any language. Thus Ingria's (1990)\nocite{ingria90} argument
that both feature neutrality and the coordination of unlikes pose
fundamental problems for unification-based theories presents a
formidable challenge to those theories; moreover, it has often been
assumed to automatically apply to their successors -- constraint-based
theories of grammar, exemplified by Head Driven Phrase Structure
Grammar [HPSG] \cite{pollard94}.

This paper shows that this claim does not in fact apply to HPSG.
Instead, the nature of the type hierarchy used by HPSG for ontological
specification provides a means to adequately and accurately analyze
these phenomena without recourse to novel data structures.

I will first describe the phenomena under discussion and then discuss
previous work on this topic; this will be followed by the proposed
analysis, and finally a comparison of this analysis with another
HPSG-based approach.

\sec{2. Overview of the Phenomena}
\ssec{2A. Feature Neutrality}

Many languages allow for a word to be neutral between two or more
values of a morphosyntactic feature; that is, the word's morphology
does not uniquely identify a value for the feature. These words may
appear in configurations where otherwise-conflicting constraints would
be imposed on that word -- in effect, the neutral form simultaneously
possesses both feature values. The German data in (\refn{first})
present an example of this phenomenon in a coordination construction.

\lbegin
\item{\eqdef{second}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & findet & und & hilft & M\"anner.\cr
& \ps he & finds & and & helps & men.\Acc\cr
}}
\item{\eqdef{third}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & findet & und & hilft & Kindern.\cr
& \ps he & finds & and & helps & children.\Dat\cr
}}
\item{\eqdef{first}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Er & findet & und & hilft & Frauen.\cr
& \ps he & finds & and & helps & women.\Acc/\Dat\cr
}}
\lend

The verb \ger{findet} requires its object to be accusative, while
\ger{hilft} requires a dative object. Thus the noun \ger{M\"anner} in
(\refn{second}), which cannot be dative, cannot occur with
\ger{hilft\nocorr}, while the noun \ger{Kindern} in (\refn{third}),
which cannot be accusative, cannot occur with
\ger{findet\nocorr}.\footnote{Switching the order of the conjuncts
does not affect acceptability.} The noun \ger{Frauen\nocorr}, however,
is neutral between accusative and dative case and is therefore
acceptable in this configuration.

Neutrality is distinguished from the familiar phenomenon of ambiguity
by precisely this property of simultaneity. The German subject-verb
agreement\footnote{In this paper, I use the terms {\it agreement\/}
and {\it concord\/} interchangeably; the traditional distinction
revolving around information flow is not relevant here.} data in
(\refn{am-1}) -- (\refn{am-3}) give an illustration of an ambiguous
form.

\lbegin
\item{\eqdef{am-1}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Sie & singt\cr
& \ps she & sings.\Sg\cr
}}
\item{\eqdef{am-2}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Sie & singen\cr
& \ps they & sing.\Pl\cr
}}
\item{\eqdef{am-3}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Sie & singt & und & singen\cr
& \ps she/they & sing.\Sg & and & sing.\Pl\cr
}}
\lend

While the form \ger{sie} can act as either singular or plural, it
cannot act as both at the same time. It is therefore considered
ambiguous rather than neutral.\footnote{Several articles, including
\cite{zaenen84} and \cite{pullum86}, discuss other ways to distinguish
neutrality from ambiguity; given that such a distinction exists, such
tests are orthogonal to the analysis of neutrality itself.}

A disjunctive description (for instance, \savm{case}{$\acc\lor\dat$})
represents a state of partial information: we know that \feat{case} is
either \type{acc} or \type{dat\nocorr}, but we don't know which. These
descriptions are quite suitable for ambiguous forms, as the form's
context will fill in the missing information by indicating which way
the disjunction should be resolved.

It has been recognized since \cite{zaenen84} that disjunctive
descriptions cannot be used to accurately model neutrality. If the
object corresponding to \ger{Frauen} in (\refn{first}) were specified
by \savm{case}{$\acc\lor\dat$}, sentence (\refn{first}) could not be
licensed: such a specification would have to describe an object with
either \savm{case}{\acc} (which fails to satisfy the selectional
requirements of \ger{hilft}) or \savm{case}{\dat} (which fails to
satisfy the requirements of \ger{findet}). \footnote{This problem also
holds when the lexicon contains two words with the phonological form
of \ger{Frauen}: one with \savm{case}{\acc} and one with
\savm{case}{\dat}.}

In the examples analyzed so far, we have focussed on a single aspect
of morphosyntax: case. In general, however, one affix or word often
encodes the value of multiple morphosyntactic features, as shown for
German in (\refn{3-a}).

\lbegin
\item{\eqdef{3-a}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
&\pt der & Antrag & des & oder & der & Dozenten\cr
&\pt the & petition & of-the.\Gen.\Sg & or & of-the.\Gen.\Pl &
docent.\Mas.\Gen.(\Sg/\Pl)\hfil\cr
&\multispan{6}`the petition of the docent(s)'\hfil\cr
}}
\lend

It is not enough to say that \ger{Dozenten} is neutral between
singular and plural: \ger{Dozenten} cannot be taken as singular in
(\refn{3-b}).

\lbegin
\item{\eqdef{3-b}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *der & Dozenten & ist & hier.\cr
& \ps the.\Nom.\Sg & docent.\Nom.\Sg & is.\Sg & here.\cr
}}
\lend

Instead, any theory of neutrality needs to be able to constrain the
neutrality of one feature based on the value of another. Here, while
it is true that \ger{Dozenten} is neutral between singular and plural,
a particular token of \ger{Dozenten} can only act as singular while
its case is not nominative.

One further wrinkle arises from the fact that many languages have
NP-internal agreement (for example, determiner-noun agreement or
noun-adjective agreement) in addition to NP-external agreement (for
example, subject-verb). When multiple elements of a noun phrase are
neutral, the resulting NP acts externally as if its agreement
properties were the intersection of the individual neutralities. This
is illustrated in (\refn{dd-1}) -- (\refn{dd-3}).

\lbegin
\item{\eqdef{dd-1}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Er & hilft & Dozenten.\cr
& \ps he & helps & docents.\Dat.\Pl\cr
}}
\item{\eqdef{dd-2}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Er & hilft & den & Dozenten.\cr
& \ps he & helps & the.\Dat.\Pl & docents.\Dat.\Pl\cr
}}
\item{\eqdef{dd-4}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Er & hilft & der & Frau.\cr
& \ps he & helps & the.\Dat.\Sg.\Fem & woman.\Dat.\Sg\Fem\cr
}}
\item{\eqdef{dd-3}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & hilft & der & Dozenten.\cr
& \ps he & helps & the & docents\cr
}}
\lend

Sentences (\refn{dd-1}) -- (\refn{dd-2}) show that \ger{Dozenten} is a
valid object of \ger{hilft} and therefore can manifest dative case.
Sentence (\refn{dd-4}) shows that the definite article \ger{der} can
also manifest dative case. In sentence (\refn{dd-3}), however, we see
that the combined noun phrase \ger{der Dozenten} cannot manifest
dative case. Thus it is insufficient for each word to individually
meet the case requirements of the verb: the NP itself may often be
less neutral than its component forms. This may seem trivial, but it
will be shown in section 3 that much of the existing literature on
this topic has not dealt with this problem.

\ssec{2B. Coordination of Unlikes}

Now consider the problem of determining the \feat{case} value of the
coordinate noun phrase \ger{M\"anner und Kindern\nocorr}. Items
(\refn{cu-3}) -- (\refn{cu-4}) show that this phrase cannot be
selected by a verb requiring an accusative object (like \ger{findet})
or by one requiring a dative object (like \ger{hilft}).

\lbegin
\item{\eqdef{cu-3}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & findet & M\"anner & und & Kindern.\cr
& \ps he & finds & men.\Acc & and & children.\Dat\cr
}}
\item{\eqdef{cu-4}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & hilft & M\"anner & und & Kindern.\cr
& \ps he & helps & men.\Acc & and & children.\Dat\cr
}}
\lend

This is the case even when the verb in question could occur with
either case individually, as shown in (\refn{leh-1}) --
(\refn{leh-3}).

\lbegin
\item{\eqdef{leh-1}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Er & lehrt & Kinder.\cr
& \ps he & teaches & children.\Acc\cr
}}
\item{\eqdef{leh-2}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps Er & lehrt & Kindern.\cr
& \ps he & teaches & children.\Dat\cr
}}
\item{\eqdef{leh-3}}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & lehrt & M\"anner & und & Kindern.\cr
& \ps he & teaches & men.\Acc & and & children.\Dat\cr
}}
\lend

The verb \ger{lehren} can take either the accusative \ger{M\"anner} or
the dative \ger{Kindern\nocorr}, but not the coordinate \ger{M\"anner
und Kindern\nocorr}. Thus the verb \ger{lehren} is said to have
ambiguous selectional requirements: it can take either of two values,
but not both simultaneously.

Ambiguous selectors like \ger{lehren} stand in contrast to those in
other languages with neutral selectional requirements. For instance,
in Russian, some verbs under certain circumstances can take either
accusative or genitive complements, as well as a coordinate complement
where one of the conjuncts is accusative and the other is genitive.
This is shown by the data from \cite{levy01} in (\refn{ru-1}).

\lbegin
\item{\eqdef{ru-1}}\vtop{\offinterlineskip\halign{\strut#\hfil&& # \hfil\cr
\pt V\v cera & ves' & den' & on & o\v zidal & svoju & podrugu\cr
\pt yesterday & all & day & he & expected & self's.\Acc & girlfriend.\Acc\cr
\noalign{\vskip2pt}
\pt Irinu & i & zvonka & ot & svoego & brata & Grigorija\cr
\pt Irina.\Acc & and & call.\Gen & from & self's.\Gen & brother.\Gen &
Gregory.\Gen\cr
\noalign{\vskip2pt}
\multispan{8}\strut`Yesterday he waited all day [for his girlfriend
Irina] and\hfil\cr
\multispan{8}\strut\pt[for a call from his brother Gregory].'\hfil\cr
}}
\lend

We can draw a parallel between this phenomenon and that of the
coordination of unlike categories, as discussed in e.g. \cite{sag85}.
This term traditionally refers to the coordination of distinct parts
of speech, as in (\refn{cu-2}) -- (\refn{cu-4}).

\lbegin
\item{\eqdef{cu-2}} He is [a republican] and [proud of it].
\item{\eqdef{cu-3}} I consider that [a rude remark] and [in very poor taste].
\item{\eqdef{cu-4}} Robin walks [slowly] and [with great care].
\lend

In (\refn{cu-2}), the conjuncts are a noun phrase and an adjective
phrase; in (\refn{cu-3}), a noun phrase and a prepositional phrase;
and in (\refn{cu-4}), an adverb and a prepositional phrase. In each
case, the coordinate phrase as a whole is a dependent of the verb.

In HPSG, the concept of category (i.e. the value of the \feat{cat}
feature) allows for fine-grained distinctions: since the conjuncts in
(\refn{cu-3}) have different values of \feat{case} (a subfeature of
\feat{cat}), they too can be said to be unlike categories.

Thus, as pointed out by \cite{bayer96}, the coordination of unlikes is
effectively the dual of feature neutrality: instead of multiple
constraints needing to be true of a single object, a single constraint
needs to be true of multiple objects. These two phenomena are linked
by a single question: If we take coordinate phrases to have the same
ontological status as non-coordinate phrases, then any feature
appropriate for a normal phrase (\feat{val}, \feat{case}) must also be
appropriate for a coordinate phrase. What are the values of those
features?

Before answering this question, I review some of the previous and
current work in this area.

\sec{3. Related Work}
\ssec{3A. Ingria 1990}

Ingria uses data related to feature neutrality to criticize the
standard treatment of agreement in unification-based grammars, in
which objects are subject to token-identity constraints (i.e. the
value of feature \feat{x} must unify with \type{y}). Instead, he
argues that agreement constraints should have the form of a
non-distinctness check (i.e. the value of feature \feat{x} must not
contradict \type{y}). For example, this check would say that since
\savm{case}{$\acc\lor\dat$} is non-distinct from both
\savm{case}{\dat} (the selectional requirement of \ger{hilft}) and
\savm{case}{\acc} (the selectional requirement of \ger{findet}), it is
an acceptable \feat{case} value for \ger{Frauen\nocorr}.

It is unclear how, in the absence of unification, the problem of
NP-internal agreement can be dealt with. Clearly the non-distinctness
check is insufficient on its own: in example (\refn{dd-3}) above, both
\ger{der} and \ger{Dozenten} are non-distinct with \feat{dat}, yet
\ger{der Dozenten} is an unacceptable object for \ger{hilft\nocorr}.

Ingria's objection to the use of token-identity is based on the
assumption that anything that \feat{case} values must be disjoint:
anything that can unify with a certain \feat{case} value cannot unify
with any other \feat{case} value. For instance, in a sentence like
(\refn{first}), the verb \ger{hilft} requires \savm{case}{\dat} to
hold of its object, while the verb \ger{findet} requires
\savm{case}{\acc}. No single object can meet both of these
constraints. I will show in section 4 an analysis that falsifies this
assumption.

\ssec{3B. Bayer and Johnson 1995}

Working within the framework of Lambek categorial grammar, Bayer and
Johnson (1995)\nocite{bayer95} present an account of feature
neutrality and unlike coordination that takes advantage of a certain
type-logical theory of categories. Their analysis of (\refn{first}) is
given in (\refn{cg}).

\lbegin
\item{\eqdef{cg}}{\mid\hfil\vtop{\offinterlineskip\halign{%
&\hfil#\hfil&\hskip1ex#\cr
\strut findet&&$[\smnp\land\smacc\land\smdat]^1$&&&&hilft&&
$[\smnp\land\smacc\land\smdat]^2$\cr
\cfill Lx&&\cfill P&&&&\cfill Lx&&\cfill P\cr
\strut$\smvp/\smnp\land\smacc$&&$\smnp\land\smacc$%
&&&&$\smvp/\smnp\land\smdat$&&$\smnp \land \smdat$\cr
\multispan3\cfill/E&&&&\multispan3\cfill/E\cr
\multispan3\strut\hfil$\smvp$\hfil&&\hfil%
und\hfil&&\multispan3\strut\hfil$\smvp$\hfil\cr
\multispan3\cfill/I$^1$&&\cfill Lx&&\multispan3\cfill/I$^2$\cr
\multispan3\strut\hfil$\smvp / \smnp \land \smacc \land
\smdat$\hfil&&\hfil$\smconj$\hfil&&\multispan3\hfil$\smvp / \smnp \land
\smacc \land \smdat$\hfil&&Frauen\cr
\multispan9\cfill Co&&\cfill Lx\cr
\multispan9\strut\hfil$\smvp / \smnp \land \smacc \land
\smdat$\hfil&&\hfil$\smnp \land \smacc \land \smdat$\cr
\multispan{11}\cfill/E\cr
\multispan{11}\strut\hfil$\smvp$\hfil\cr}}\hfil}
\lend

The derivation starts with instances of lexical access (rule Lx). The
verb \ger{findet} has category $\vp/\np\land\acc$, representing the
fact that it wants an accusative object; \ger{hilft} has category
$\vp/\np\land\dat$, as it wants a dative object; and \ger{Frauen} has
category $\np\land\acc\land\dat$, representing its neutrality between
accusative and dative case.

Then the category for \ger{Frauen} is hypothesized after each
conjunct. The first hypothesis is then weakened (rule P) from
$\np\land\acc\land\dat$ to $\np\land\acc$, and the second to
$\np\land\dat$. This allows each verb to combine (rule /E) with the
introduced argument, forming in each case the category $\vp$. The
hypothesis is then discharged (rule /I) for each conjunct, forming
categories $\vp/\np\land\acc\land\dat$.

Since the conjuncts have the same category, the conjunction rule (rule
Co) can be applied to form a single conjoined
$\vp/\np\land\acc\land\dat$ category. As the last step, this category
combines with the actual argument \ger{Frauen} (rule /E).

In this example, the hypothesized object was weakened by meet
elimination: the change from $a\land b$ to $a$. Categories can also be
weakened by join introduction: the change from $a$ to $a\lor b$. This
is used in the analysis of unlike coordination, as illustrated in
(\refn{cg2}).

\lbegin
\item{\eqdef{cg2}}{\mid\hfil\vtop{\offinterlineskip\halign{%
&\hfil#\hfil&\hskip1ex#\cr
\strut &&wealthy&&&&a republican\cr
&&\cfill Lx&&&&\cfill Lx\cr
\strut&&$\smap$&&and&&$\smnp$\cr
&&\cfill Wk&&\cfill Lx&&\cfill Wk\cr
\strut became&&$\smnp\lor\smap$&&$\smconj$&&$\smnp\lor\smap$\cr
\cfill Lx&&\multispan5\cfill Co\cr
\strut$\smvp/\smnp\lor\smap$&&\multispan5\hfil$\smnp\lor\smap$\hfil\cr
\multispan7\cfill/E\cr
\multispan7\strut\hfil$\smvp$\hfil\cr
}}\hfil}
\lend

Here, the lexicon assigns \ger{wealthy} category $\ap$, \ger{a
republican} category $\np$, and \ger{became} category
$\vp/\np\lor\ap$. Each of the conjuncts is then weakened (rule P) to
$\np\lor\ap$; these categories are then conjoined to form a single
$\np\lor\ap$ category, which can combine with the category of
\ger{became}.

While this seems to be a quite elegant solution to the problem,
\cite{bayer96} points out problems with the use of $\land$ to
represent the conjunction of orthogonal features as well as neutral
feature values. In particular, a form neutral between \Nom.\Pl\ and
\Gen.\Sg\ is represented by the meet of $(\np\land\nom\land\plural)$
and $(\np\land\gen\land\singular)$, which is
$(\np\land\nom\land\plural\land\gen\land\singular)$. This category can
be weakened to $(\np\land\gen\land\plural)$, thus predicting that such
a neutral form could be used in a context where \Gen.\Pl\ was
required. This is contradicted by the Finnish data in \cite{zaenen84},
where the form \ger{kirjansa} can be used for \Nom.\Sg, \Gen.\Sg, and
\Nom.\Pl, but not \Gen.\Pl.\footnote{The work of D\"orre and Manandhar
(1995)\nocite{doerre95} on constraint-based Lambek calculi may provide
an approach to features in categorial grammar that resists this
criticism (Martin Jansche, p.c.).}

\ssec{3C. Dalrymple and Kaplan 2000}

Dalrymple and Kaplan (2000)\nocite{dalrymple00} provide an LFG-based
analysis of both feature neutralization and unlike coordination. In
their account, coordinate phrases contrast with non-coordinate phrases
by corresponding to a set of f-structures rather than a single
f-structure. A constraint then holds of a set of f-structures exactly
when it holds of each member of the set. Neutrality is represented by
assigning the feature the set of those values between which the form
is neutral.

Thus in their analysis of (\refn{first}), \ger{Frauen} has
\savm{case}{$\{\acc, \dat\}$}. The verb \ger{hilft} requires that its
argument's \feat{case} value have \type{dat} as a member, and
similarly \type{acc} for \ger{findet\nocorr}. \ger{Frauen} meets these
conditions and (\refn{first}) is licensed.

This analysis shares some properties with Ingria's analysis and
suffers from some of the same problems. As agreement is effected
through what is in effect a subsumption check rather than a shared
object, NP-internal agreement must be treated as a separate
phenomenon. While Dalrymple and Kaplan acknowledge the existence of
this problem (p. 795), they do not provide an analysis for it. Nor is
any account given of neutrality across features

This approach also strips sets of having any intrinsic meaning in the
LFG framework, increasing the possibility for unwanted interactions.
Sets can be used to represent collections of arbitrary numbers of
items, neutral values, coordinations, and feature decompositions.

\ssec{3D. Levy 2001}

Levy (2001)\nocite{levy01}, along with \cite{levy-pollard02}, presents
an HPSG-based approach developed contemporaneously with this paper
that centers around certain sets of sets (which Levy refers to as
double-sets). Further discussion of Levy's approach will be deferred
until the analysis in section 4 has been presented; this will allow
for a detailed comparison of the two approaches.

It should be noted that Levy's theory only presents an analysis of
single-feature neutralization. He speculates, however, that his theory
can handle neutrality across features (pp. 27--29) and suggests some
potential avenues for further exploration.

\sec{4. A Type-Based Approach}

The analysis presented in this section differs from the proposals
discussed in the previous section in two main ways. It adds no new
data structures or mechanisms to the framework and it retains the use
of structure-sharing in effecting agreement. As such it explicitly
rejects Levy's (2001)\nocite{levy01} claim that ``the problems
presented by [feature neutrality and unlike coordination] cannot be
solved solely with the structural tools made available by HPSG's type
hierarchy''.

\ssec{4A. The Phrase Structure of Coordination}

Before the analysis can be presented, I will present some baseline
assumptions about the phrase structure of coordinate structures. I
take the type \type{coord-phrase} to be a subtype of
\type{non-headed-phrase\nocorr}. Following \cite{sag85}, I assume two
subtypes of \type{coord-phrase} for English:
\type{bin(ary)-coord-ph(rase)} and
\type{iter(ated)-coord-ph(rase)\nocorr}.

A \type{bin-coord-ph} is licensed whenever the first daughter has
\savm{marking}{$\alpha_0$} and the second daughter has
\savm{marking}{$\alpha_1$} for some $\alpha$. \cite{sag85} gives the
requirement $\alpha \in \{\{$both, and$\}, \{$either, or$\},
\{$unmarked, but$\}\}$ while noting that the set of possible values
for $\alpha$ is highly subject to idioletical variation.

Similarly, an \type{iter-coord-ph} is licensed whenever the first
daughter has \savm{marking}{$\beta_0$}, the last daughter has
\savm{marking}{$\beta_2$}, and all other daughters have
\savm{marking}{$\beta_1$} for some $\beta$. Here $\beta \in
\{\{$unmarked, and, and$\}, \{$unmarked, unmarked, and$\},
\{$unmarked, unmarked, or$\}, \{$unmarked, or, or$\}, \{$neither, nor,
nor$\}\}$; this too may vary widely among idiolects.

\ssec{4B. Feature Neutrality}

The analysis of feature neutrality developed in this paper is based on
the \cite{levine01} treatment of case-consistency for parasitic gaps.
As is standard in GPSG- and HPSG-style analyses of parasitic gaps, the
local properties of both the host and parasitic gaps are represented
by a single object: all constraints affecting one affect the other.
When different case requirements are imposed on the two gaps, then,
the resulting sentence is only acceptable when the filler is
case-neutral. This is illustrated in (\refn{fourth}) and
(\refn{fifth}).

\lbegin
\item{\eqdef{fourth}} *whom even friends of \gap\ believe \gap\ should
be closely watched.
\item{\eqdef{fifth}} \ps who even friends of \gap\ believe \gap\
should be closely watched.
\lend

Here the preposition \ger{of} requires its object to have accusative
case, while the verb \ger{should} requires its subject to have
nominative case. The accusative pronoun \ger{whom} cannot satisfy both
of these constraints, but the case-neutral pronoun \ger{who} can.

To analyze this, Levine et al. (2001)\nocite{levine01} augment the
type hierarchy for \feat{case} values with three new types: a neutral
type \type{p-nom-acc} and two `pure' subtypes \type{p-nom} and
\type{p-acc}, as given in the portion of the signature shown in
(\refn{nahier}).\footnote{Typenames have been slightly modified from
the \cite{levine01} version for consistency with later sections.}

\lbegin
\item{\eqdef{nahier}}{\hfil\xymatrix@-1pc{
&&\ar@{-}[dl]\ar@{-}[dr]\txt{case}\cr
&\ar@{-}[dl]\ar@{-}[dr]\txt{acc}&&\ar@{-}[dl]\ar@{-}[dr]\txt{nom}\cr
{\txt{p-acc}}&&{\txt{p-nom-acc}}&&{\txt{p-nom}}\cr}\hfil}
\lend

Here, the type \type{p-nom-acc} represents neutrality between
nominative and accusative case\footnote{When reading the type names,
it is important to take the \type{p-} prefix as having scope over the
rest of the name. For instance, the type \type{p-nom-acc} is the pure
type corresponding to the neutralization of nominative and accusative
case, not the neutralization of \type{p-nom} and \type{acc\nocorr}.};
a type like \type{p-nom} represents a pure (non-neutral) case value.

Under this scheme, the only maximally specific types are
\type{p-nom\nocorr}, \type{p-nom-acc\nocorr}, and \type{p-acc\nocorr}.
Case-neutral pronouns like \ger{who\nocorr}, as well as common and
proper nouns, are listed in the lexicon as
\savm{case}{\type{p-nom-acc}}, while case-specific pronouns like
\ger{he} or \ger{whom} are listed as \savm{case}{\type{p-nom}} or
\savm{case}{\type{p-acc}}, as appropriate.

The remaining types -- \type{nom\nocorr}, \type{acc\nocorr}, and
\type{case} (which is equivalent to $\nom\lor\acc$) -- are only used
in object descriptions, such as those found in valence specifications.
For instance, a typical finite English verb selects a subject with
\savm{case}{\nom} and selects complements with \savm{case}{\acc}.

With this hierarchy, a description like \savm{case}{\acc} abbreviates
the disjunction (\savm{case}{\type{p-acc}} $\lor$
\savm{case}{\type{p-nom-acc}}). Thus \savm{case}{\acc} and
\savm{case}{\nom} now unify to \savm{case}{\type{p-nom-acc}}. In
effect, we are now able to model the intuition that \ger{who} is both
nominative and accusative.

The central distinction in this hierarchy, then, is between types
which begin with \type{p-} (the pure types) and those that do not (the
non-pure types). Pure types are maximally specific; they are the types
found on linguistic objects. Non-pure types, in contrast, are found on
linguistic descriptions (e.g. subcategorization requirements). Every
non-pure type corresponds to a pure type. The non-pure type is usually
the immediate supertype of the pure type, with one exception: the most
neutral type (here, \type{p-nom-acc}) is both pure and
non-pure.\footnote{We could avoid this awkwardness by introducing a
type \type{nom-acc} in the place of \type{p-nom-acc} that would then
only dominate \type{p-nom-acc\nocorr}, but such unary branching in a
type hierarchy is seen as equally awkward by many.}

Just as (\refn{nahier}) serves as a case hierarchy for English, so may
a similar hierarchy be constructed for German, which has a four-case
system. I will assume that such a type hierarchy would only contain
those pure types which correspond to attested patterns of
neutralization in the language, rather than containing a pure type for
every potential subset of cases. For instance, no form in German is
neutral between nominative, accusative, and genitive cases (to the
exclusion of dative), and so there is no \type{p-nom-acc-gen} type in
the hierarchy. (See section 4D for an illustration of the effect this
has on a sample case hierarchy.)

The analysis of (\refn{first}) (repeated below) is now
straightforward.

\lbegin
\item{(\refn{first})}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& Er & findet & und & hilft & Frauen.\cr
& he & finds & and & helps & women.\Acc/\Dat\cr
}}
\lend

Under the system described above, the verb \ger{findet} imposes the
constraint \savm{case}{\acc} on its object and \ger{hilft} imposes the
constraint \savm{case}{\dat} on its object. The constraint in
(\refn{cps-1}) models the fact that each verb's selectional
specifications must be satisfied by the dependents of the coordination
(an outgrowth of what is often referred to as Wasow's generalization
\cite{pullum86}).

\lbegin\avmoptions{center}
\item{\eqdef{cps-1}} \type{coord-phrase} $\to$ \avm\[ \feat{val} & \@2
\cr \feat{dtrs} & \<\[\feat{val} & \@2\],\[\feat{val} & \@2\]\>\]\endavm
\lend

Thus the constraint that the coordination of the two verbal heads
\ger{findet und hilft} imposes on its object is the logical
conjunction of the constraints \savm{case}{\acc} and
\savm{case}{\dat}: namely, \savm{case}{\type{acc-dat}}.

Returning to (\refn{first}), the word \ger{Frauen\nocorr}, as a word
neutral between all four cases, is listed in the lexicon as
\savm{case}{\type{p-nom-acc-dat-gen}}; this is consistent with
\savm{case}{\type{acc-dat}} and \ger{Frauen} is therefore an
acceptable object for \ger{findet und hilft\nocorr}.

\ssec{4C. Coordination of Unlikes}

Recall that the data in (\refn{cu-3}) -- (\refn{cu-4}) (repeated
below) show that the \feat{case} value of the coordinate noun phrase
\ger{M\"anner und Kindern} cannot be either \type{dat} or \type{acc}
(or any subtype thereof), or else it would be selectable by either
\ger{findet} or \ger{hilft\nocorr}.

\lbegin
\item{(\refn{cu-3})}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & findet & M\"anner & und & Kindern.\cr
& \ps he & finds & men.\Acc & and & children.\Dat\cr
}}
\item{(\refn{cu-4})}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & hilft & M\"anner & und & Kindern.\cr
& \ps he & helps & men.\Acc & and & children.\Dat\cr
}}
\lend

Instead, it must be a type more specific than \type{case} but less
specific than \type{acc} or \type{dat}: a type that in effect reifies
$\acc\lor\dat$. I therefore introduce a new type \type{p-nom+acc} into
the hierarchy, as shown in (\refn{nachier}).

\lbegin
\item{\eqdef{nachier}}{\hfil\xymatrix@-1pc{
&&\ar@{-}[dl]\ar@{-}[d]\ar@{-}[dr]\txt{nom+acc}\cr
&\ar@{-}[dl]\ar@{-}[dr]\txt{acc}&{\txt{p-nom+acc}}%
&\ar@{-}[dl]\ar@{-}[dr]\txt{nom}\cr
{\txt{p-acc}}&&{\txt{p-nom-acc}}&&{\txt{p-nom}}\cr}\hfil}
\lend

Just as the hyphen mnemonically represents neutrality, the plus sign
indicates coordination. With this addition, the placement of the pure
types has become completely predictable: no pure type dominates any
other type, and every pure type is either equal to its corresponding
non-pure type or is immediately dominated by it. Thus we can
considerably simplify these diagrams by leaving out the pure types;
their presence will be implicit from now on. Under this convention,
(\refn{nachier}) appears as in (\refn{nacnphier}).

\lbegin
\item{\eqdef{nacnphier}}{\hfil\xymatrix@-1pc{
&&\ar@{-}[dl]\ar@{-}[dr]\txt{nom+acc}\cr
&\ar@{-}[dr]\txt{acc}&&\ar@{-}[dl]\txt{nom}\cr
&&{\txt{nom-acc}}&&\cr}\hfil}
\lend

To more fully illustrate the range of possibilities, it will be
helpful to consider a three-valued case system. The corresponding
simplified diagram for such a system appears as (\refn{natnphier}).

\lbegin
\item{\eqdef{natnphier}}{\hfil\xymatrix@-1pc{
&&\ar@{-}[lld]\ar@{-}[d]\ar@{-}[drr]\txt{a+n+g}\cr
\ar@{-}[d]\ar@{-}[drr]\txt{a+n}%
&&\ar@{-}[lld]\ar@{-}[drr]\txt{a+g}%
&&\ar@{-}[lld]\ar@{-}[d]\txt{n+g}\cr
\ar@{-}[d]\ar@{-}[drrrrr]\txt{a+g-n}%
&&\ar@{-}[drrr]\ar@{-}[d]\txt{n+a-g}%
&&\ar@{-}[d]\ar@{-}[dr]\txt{g+n-a}\cr \ar@{-}[d]\txt{a}&&%
\ar@{-}[d]\txt{n}&&%
\ar@{-}[d]\txt{g}&%
\ar@{-}[dlllll]\ar@{-}[dlll]\ar@{-}[dl]\txt{a-n+a-g+n-g}\cr
\ar@{-}[d]\ar@{-}[drr]\txt{a-n+a-g}%
&&\ar@{-}[dll]\ar@{-}[drr]\txt{a-n+n-g}%
&&\ar@{-}[dll]\ar@{-}[d]\txt{a-g+n-g}\cr
\ar@{-}[drr]\txt{a-n}&&\ar@{-}[d]\txt{a-g}&&\ar@{-}[dll]\txt{n-g}\cr
&&{\txt{a-n-g}}\cr}\hfil}
\lend

Note that in any expression containing both $\mathord-$ and
$\mathord+$ signs, the $\mathord-$ takes scope over the $\mathord+$.

In one sense, these names are purely iconic: none of the constraints
presented in this paper would fail if we replaced type names like
\type{a-n} and \type{a+n} with types like \type{banana} and
\type{pineapple}. On the other hand, if we want to talk about how
these hierarchies are developed, it helps to consider the types as
members of the free bounded distributive lattice over the basic cases
(here, \type{a}, \type{n}, and \type{g}) with operators $\mathord+$
and $\mathord-$ serving as meet and join. Thus the lack of a row of
types with the form \type{(a+g)-n} is deliberate: by distribution,
this is equivalent to \type{a-n+g-n}.

The hierarchy in (\refn{natnphier}) represents that of a fully
neutralizing language: every possible neutralization of the basic
cases has an instantiation. Not all natural languages are fully
neutralizing, however. For example, \cite{dyla84} shows that in
Polish, there are forms neutral between accusative and genitive case
exist, but there are no forms neutral between nominative and
accusative case.

A sample hierarchy for a three-case language where this particular
combination of cases (nominative and accusative) fails to neutralize
is given in (\refn{napnphier}).

\lbegin
\item{\eqdef{napnphier}}{\hfil\xymatrix@-1pc{
&&\ar@{-}[lld]\ar@{-}[d]\ar@{-}[drr]\txt{a+n+g}\cr
\ar@{-}[d]\ar@{-}[drr]\txt{a+n}%
&&\ar@{-}[lld]\ar@{-}[ddrr]\txt{a+g}%
&&\ar@{-}[lld]\ar@{-}[dd]\txt{n+g}\cr
\ar@{-}[d]\ar@/_10pt/@{-}[ddrrrr]\txt{a+g-n}%
&&\ar@{-}[ddrr]\ar@{-}[d]\txt{n+a-g}\cr
\ar@{-}[ddrr]\txt{a}&&%
\ar@{-}[drr]\txt{n}&&%
\ar@{-}[d]\txt{g}\cr
&&&&\ar@{-}[dll]\ar@{-}[d]\txt{a-g+n-g}\cr
&&\ar@{-}[d]\txt{a-g}&&\ar@{-}[dll]\txt{n-g}\cr
&&{\txt{a-n-g}}\cr}\hfil}
\lend

This is a sublattice of (\refn{natnphier}) in which \type{a-n} and all
coordinations involving \type{a-n} have been removed.

The constraint that relates the \feat{case} value of a coordination to
the \feat{case} value of its conjuncts can now be stated. Since the
conjuncts, being phrases, are linguistic objects, each has a pure
\feat{case} value. Let the \feat{case} values of the conjuncts be $x$
and $y$, and let the corresponding non-pure types be $x'$ and $y'$.
Finally, let the \feat{case} value of the coordination be $z$ with
corresponding non-pure type $z'$. Then it must be the case that $z'$
is the lowest type such that $z'$ is identical to or a supertype of
$x'$ and $y'$\footnote{In formal terms, $z'$ is constrained to be the
least upper bound of $x'$ and $y'$ with respect to the subtype
relation.}. The practical effect of this is that a coordination is at
most as valent as its least-valent component. For example, if $x$ is
neutral between cases A, B, and C, while $y$ is neutral between B, C,
and D, then the coordination of $x$ and $y$ is only neutral between B
and C.

This principle allows the analysis of all of the phenomena presented
so far. Envision a hierarchy similar to (\refn{natnphier}) in which
all the \type{n}s have been changed to \type{d}s and take this as an
approximation of German. Then the result of coordinating \type{p-acc}
and \type{p-acc-dat} is \type{p-acc\nocorr}. To see this, take $x
=\type{p-acc}$ and $y = \type{p-acc-dat}$. Then $x'=\acc$ and
$y'=\type{acc-dat}$. Find \type{acc} and \type{acc-dat} in
(\refn{natnphier}) and notice that \type{acc} is a supertype of
\type{acc-dat}. Thus $z'=\acc$ and $z=\type{p-acc}$. Therefore, the
coordination of accusative \ger{M\"anner} and syncretic \ger{Frauen}
is assigned \savm{case}{\type{p-acc}}. As such, this coordination can
occur anywhere a simple accusative NP can occur but nowhere that
requires a dative NP.

Similarly, as neither \type{acc} nor \type{dat} are supertypes of the
other, the coordination of accusative \ger{M\"anner} and dative
\ger{Kindern} receives \savm{case}{\type{p-acc+dat}}. Here, $x =
\type{p-acc}$ and $y=\type{p-dat}$, so $x'=\type{acc}$ and
$y'=\type{dat}$. Then $z'=\type{acc+dat}$ and $z=\type{p-acc+dat}$.
This type cannot satisfy either of the constraints \savm{case}{\acc}
or \savm{case}{\dat}, as desired.

We can now return to the Russian data in (\refn{ru-1}) (repeated
below), which illustrated selectional neutrality.

\lbegin
\item{(\refn{ru-1})}\vtop{\offinterlineskip\halign{\strut#\hfil&& # \hfil\cr
\pt V\v cera & ves' & den' & on & o\v zidal & svoju & podrugu\cr
\pt yesterday & all & day & he & expected & self's.\Acc & girlfriend.\Acc\cr
\noalign{\vskip2pt}
\pt Irinu & i & zvonka & ot & svoego & brata & Grigorija\cr
\pt Irina.\Acc & and & call.\Gen & from & self's.\Gen & brother.\Gen &
Gregory.\Gen\cr
\noalign{\vskip2pt}
\multispan{8}\strut`Yesterday he waited all day [for his girlfriend
Irina] and\hfil\cr
\multispan{8}\strut\pt[for a call from his brother Gregory].'\hfil\cr
}}
\lend

Here, the coordination \ger{podrugu i zvonka} receives
\savm{case}{\type{p-gen+acc}}, and as such it can be selected by the
constraint \savm{case}{\type{gen+acc}} (which must therefore be part
of the valence specification of \ger{o\v zidal}).

With the contrasting case of selectional ambiguity (recall
(\refn{leh-3}), shown below), the verb \ger{lehren} must be analyzed
as having
\savm{comps}{$\left<\hbox{\savm{case}{$\acc\lor\dat$}}\right>$}
(rather than\hfil\break
\savm{comps}{$\left<\hbox{\savm{case}{\type{acc+dat}}}\right>$}). Thus
the coordination \ger{M\"anner und Kindern\nocorr}, with\hfil\break
\savm{case}{\type{acc+dat}}, is not an acceptable object for this
verb.

\lbegin
\item{(\refn{leh-3})}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& *Er & lehrt & M\"anner & und & Kindern.\cr
& \ps he & teaches & men.\Acc & and & children.\Dat\cr
}}
\lend

The acceptability of (\refn{cu-2}) (repeated below) can now be
explained.

\lbegin
\item{(\refn{cu-2})} He is [a republican] and [proud of it].
\lend

Assume that the features appropriate for a type \type{p-a+b} are
exactly those appropriate for both \type{a} and \type{b}. Since the
feature \feat{pred} is appropriate for both adjectives like \ger{proud
of it} and nouns like \ger{a republican\nocorr}, it is appropriate for
the coordination type \type{p-noun+adj}. Furthermore, since both
\ger{proud of it} and \ger{a republican} are \savm{pred}{$\mathord+$},
the coordination is also \savm{pred}{$\mathord+$}. The copula \ger{is}
merely constrains its argument to be \savm{pred}{$\mathord+$}, so the
sentence is licensed.

To take another example, the English verb \ger{become} is like
\ger{be} in that its arguments can be of varying categories; unlike
\ger{be\nocorr}, its arguments cannot be prepositional or verbal.
Under this system, \ger{become} would subcategorize for
\savm{head}{\type{noun+adj}}; just as with \ger{be\nocorr}, the
coordination \ger{a republican and proud of it} meets this constraint.

For any given feature, the relationship between its value for the
conjuncts and its value for the coordination depends on the feature in
question. As presented above, \feat{case} in English and German
illustrates one type of combination -- a join on the corresponding
non-pure types. For valence requirements, such as those from conjoined
verbs as in (\refn{first}), the value of the mother's feature is the
unification of the daughter features' values. Among other agreement
features, like \feat{person}, \feat{number}, and \feat{gender}, more
elaborate constraints might relate mother values to daughter values;
see \cite{sag85} for a discussion of these features in English
conjoined NPs and \cite{corbett83} for a cross-linguistic discussion
of such relationships.

\ssec{4D. Neutrality Across Features}

We now return to the last set of data presented in section 2A. As
given in section 4B, the analysis of feature neutralization only holds
when values of a single feature are being neutralized. The phenomenon
of neutralization across features must still be accounted for.

Recent proposals (e.g. Kathol 1999\nocite{kathol99}) represent
morphosyntactic agreement information in HPSG as a bundle of features
(\feat{case}, \feat{person}, \feat{number}, and \feat{gender}). If the
values appropriate for these features were augmented as above, adding
new types to represent neutralizations, there would still be no way to
replace a constraint like (\savm{case}{\type{$\neg$nom}} $\land$
\savm{num}{\type{sg}}) $\lor$ (\savm{num}{\type{pl}}) in the same way
that \savm{case}{\type{nom}} $\lor$ \savm{case}{\type{acc}} was
replaced with\hfil\break \savm{case}{\type{p-nom-acc}}.

For illustration, consider a variation on the Russian verb in
(\refn{ru-1}) that may take either \Nom.\Sg\ or \Acc.\Pl\ objects (but
not \Nom.\Pl\ or \Acc.\Sg). That verb cannot be selecting
\savm{case}{\type{p-nom-acc}}, as that would improperly exclude
non-neutral forms. Neither can it select for
\savm{case}{$\nom\lor\acc$}, as discussed in section 2A. There needs
to be a way to account for this interdependence.

In the mathematical tradition of reducing new problems to ones already
solved, multiple inheritance can reduce the problem of neutrality
across features to that of single feature neutrality. Just as phrases
are classified along dimensions of clausality and headedness in
\cite{sag97}, morphosyntactic information can be represented in terms
of one feature \feat{uniagr} and one type \type{uniagr} which is
cross-classified in terms of person, number, gender, and case.

\lin\lbegin\item{\eqdef{agrhier}}\lend{\hfil\psTree{\TR{\type{uniagr}}}
\psTree{\TR{\psframebox{\feat{gender}}}}\TR{\type{masc}}\TR{\type{fem}}
\TR{\type{neut}}\endpsTree
\psTree{\TR{\psframebox{\feat{person}}}}\TR{1}\TR{2}\TR{3}\endpsTree
\psTree{\TR{\psframebox{\feat{number}}}}\TR{\type{sg}}\TR{\type{pl}}\endpsTree
\psTree{\TR{\psframebox{\feat{case}}}}\TR{\type{nom}}\TR{\type{acc}}
\TR{\type{dat}}\TR{\type{gen}}\endpsTree\endpsTree\hfil}

Each value of \type{uniagr} is an element of the cross-product over
the possible values of each of the component features. (For example,
one such value would be \type{masc.3.sg.acc\nocorr}, corresponding to
the German pronoun \ger{ihn}).

Only those feature combinations actually attested on some lexical item
are part of the type hierarchy. Just as \type{nom} and \type{acc} form
the basis of the case hierarchy for English in (\refn{nahier}), so
could these values of \feat{uniagr} form the basis of a unified
agreement hierarchy for German.

Every constraint expressable in the old system has an equivalent
constraint in this system. The full hierarchy of these types is too
large to provide in full, so I will use some naming conventions: each
type component will consist of four fields separated by dots. Within
each field, the initial letter/digit of the analogous type in
(\refn{agrhier}) will indicate that dimension of the \feat{uniagr}
value. For example, the constraint (\savm{gend}{\type{masc}} $\land$
\savm{per}{\type{3rd}} $\land$ \savm{num}{\type{sg}} $\land$
\savm{case}{\type{dat}}) is equivalent to
\savm{uniagr}{\type{m.3.s.d}} under this system. I will omit the dots
whenever a field has just one member, so that the aforementioned type
would appear as \type{m3sd}.

For notating types that are neutral between several of these values, I
will put both letters in a single field: thus \type{m3s.da} is a type
neutral between \type{m3sd} and \type{m3sa\nocorr}. If more than one
field has multiple letters, then that type is neutral between the
cross-product of the variants: i.e. \type{mf.3.sp.n} is neutral
between the four types \type{m3sn, m3pn, f3sn\nocorr}, and
\type{f3pn\nocorr}.

In general, by removing any character (except the last in a field),
one moves from subtype to immediate supertype. Thus \type{mf.3.sp.n}
is an immediate subtype of \type{m3.sp.n\nocorr},
\type{f3.sp.n\nocorr}, \type{mf.3sn\nocorr}, and \type{mf.3pn\nocorr}.

For neutralizations where such a full product is not appropriate, I
will continue to use the dash notation: \type{m3sd-f3sa} is a type
neutral between \type{m3sd} and \type{f3sa} that (unlike
\type{mf.3s.da}) excludes \type{f3sd} and \type{m3sa\nocorr}. As
before, removing a dashed component yields an immediate supertype of
the type in question: thus \type{m3sd} is an immediate supertype of
\type{m3sd-f3sa\nocorr}.

Finally, the omission of a field abbreviates the disjunction of all
possible values for that field. So \type{msn} abbreviates (\type{m1sn}
$\lor$ \type{m2sn} $\lor$ \type{m3sn}). This is different from
\type{m.123.sn}, which is neutral between all three persons.

These rules form the names of the non-pure types; the corresponding
pure typename is again formed by prefixing with \type{p-\nocorr}.

The acceptability of (\refn{3-a}), repeated below, can now be
accounted for.

\lbegin
\item{(\refn{3-a})}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
&\pt der & Antrag & des & oder & der & Dozenten\cr
&\pt the & petition & of-the.\Gen.\Sg & or & of-the.\Gen.\Pl &
docent.\Mas.\Gen.(\Sg/\Pl)\hfil\cr
&\multispan{6}`the petition of the docent(s)'\hfil\cr
}}
\lend

Using the naming conventions just described, we can write the lexical
entries in (\refn{le1}) -- (\refn{le3}).

\lbegin
\item{\eqdef{le1}}\avm\[\feat{phon} & der \cr \feat{uniagr} &
\type{p-m.123.s.n-f.123.s.dg-mfn.123.p.g} \cr \feat{val} &
\<\[\feat{uniagr} & \type{msn} $\lor$ \type{fsd} $\lor$ \type{fsg}
$\lor$ \type{pg}\]\>\]\endavm
\item{\eqdef{le2}}\avm\[\feat{phon} & des \cr \feat{uniagr} &
\type{p-mn.123.s.g} \cr \feat{val} & \<\[\feat{uniagr} & \type{msg}
$\lor$ \type{nsg}\]\>\]\endavm
\item{\eqdef{le3}}\avm\[\feat{phon} & Dozenten \cr \feat{uniagr} &
\type{p-mfn.123.s.adg-mfn.123.p.nadg}\]\endavm
\lend

This encodes the fact that the German article \ger{der} is neutral
between \Mas.\Nom.\Sg,\hfil\break \Fem.\Dat.\Sg, \Fem.\Gen.\Sg, and
\Gen.\Pl; the article \ger{des}, between \Mas.\Gen.\Sg{} and
\Neut.\Gen.\Sg; and the noun \ger{Dozenten}, between \Mas.\Gen,
\Mas.\Acc, \Mas.\Dat, and \Mas.\Nom.\Pl.

Then if we assume as before that coordination involves the unification
of the individual conjuncts' agreement constraints, the coordination
\ger{des oder der} will be looking for a noun consistent with
\savm{uniagr}{(\type{msg} $\lor$ \type{nsg}) $\land$ (\type{msn}
$\lor$ \type{fsd} $\lor$ \type{fsg} $\lor$ \type{pg})}.

The type \type{p-mfn.123.s.adg-mfn.123.p.nadg} is a subtype of
\type{msg\nocorr}, so the first conjunct is satisfied, and it is also
a subtype of \type{fsd\nocorr}, so the second conjunct is satisfied.
Hence \ger{Dozenten} is compatible with the selectional requirements
of \ger{des oder der} and (\refn{3-a}) is acceptable.

One side effect of this approach is that it becomes less
straightforward to account for phenomena in which elements are
constrained to agree in one aspect of \feat{uniagr} but not the
others. For example, in German there are examples where two phrases
must have the same case but may vary in person, number, and/or gender
(see \cite{mueller01} for one example of this). Since it is not
possible to structure-share part of a type, such a relationship cannot
be directly notated.

Given the existence of relational constraints, however, one could
define a \rel{same-case} relation such that
\rel{same-case}(\avmbox{1}, \avmbox{2}) holds exactly when \avmbox{1}
and \avmbox{2} are of types whose \feat{case} dimensions are the same.
Similar relations could be defined as needed for \feat{number},
\feat{gender}, and \feat{person}. This may have an intuitive feel of
``one step forward, two steps back'' (as relations are now needed to
provide what once came ``for free'') but it does account for a wider
range of the data than any standard theory of agreement. At any rate,
more work is certainly needed in this area.

\sec{5. Levy 2001}

Having developed a theory of feature neutrality and unlike
coordination for HPSG, it is now possible to compare it to the other
extant HPSG account of these phenomena, namely \cite{levy01}.

As mentioned above, Levy uses sets of sets to model neutrality and
coordination; the internal sets represent coordination and the
external set represents neutrality. In particular, a neutral form like
\ger{Frauen} is assigned \savm{case}{$\{\{\acc\},\{\dat\}\}$}, while
the coordination of an accusative NP and a dative NP would be given
\savm{case}{$\{\{\acc, \dat\}\}$}.

Like \cite{dalrymple00}, verbs impose a lower-bound constraint of the
form $\hbox{\savm{case}{\avmbox1}} \land \hbox{\avmbox1}
\trianglerighteq \{\{\dat\}\}$ (where the $\mathord\trianglerighteq$
symbol can be thought of as ``at least'').

The central difference, then, is that Levy does not modify the type
hierarchy in any way other than to change the appropriateness
conditions on \feat{case}: instead of taking values of type
\type{case}, it now takes values of type \type{set(set(B))}, where $B$
is the set of basic cases for the language. Levy thus avoids having
both pure and non-pure types. Then, since \feat{case} values are no
longer ordered with respect to the type hierarchy, the bounded nature
of subcategorization must be made explicit with the additional
$\mathord\trianglerighteq$ constraint. (In the proposal given in
section 4, subcategorization is effected directly through supertypes,
which implicitly represent the disjunction of all maximally-specific
types they dominate.)

When given a fully-neutralizing language, Levy's double-set lattice
and the type hierarchy proposed in section 4D are isomorphic; this is
shown in \cite{levy-pollard02}. For a partially-neutralizing language,
however, the analysis in section 4 can model this partiality directly,
as exemplified by (\refn{napnphier}) as compared to
(\refn{natnphier}); Levy's analysis must treat all non-neutralizing
combinations of values as accidental gaps.

\sec{6. Conclusion}

The constraints that relate a mother's feature values to those of its
daughters are quite complex, and this paper only begins to explore the
nature of these relationships. By examining \feat{case} as both a
valence feature (as is relevant to the analysis of feature neutrality)
and as an inherent morphosyntactic property (as relevant to the
analysis of unlike coordination), I hope to have made some progress in
this area.

In general, Ingria's assessment of unification-based theories of
grammar does not apply to constraint-based theories like HPSG: the
type hierarchy can directly represent indeterminate feature values as
well as coordinations of unlike categories, resulting in a theory of
feature neutralization and unlike coordination that does not need to
add anything new to the HPSG framework.

\sec{Works Cited}
\bibliography{hpsg}
\bibliographystyle{mwd2}
\bye