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\rightline{\vbox{\offinterlineskip\halign{\strut#\hfill\cr
Michael W. Daniels \cr Synners \cr September 28, 2000 \cr}}}

\lin\centerline{\bigrm On Syntactic Concord and Morphological
Ambiguity}

\item{\eqdef{a}} Factored coordination: material involved in all
conjuncts of a coordination appears once, typically at the edge of the
coordination.

\lin\slbegin
\itemitem{(A)} He has gone to the store and bought a loaf of bread.
\itemitem{(B)} He washed, and I dried, the china we received on
our wedding day.
\itemitem{(C)} John and Mary left the party at midnight.
\slend

\item{\eqdef{b}} Languages with agreement differ on how agreement is
maintained in the presence of factored coordination; see
\cite{corbett83}. I am concerned with languages where the conjunct
must agree with each of the conjuncts.

\item{\eqdef{c}} These agreement relations may be independent; in
particular, when the factor is morphologically ambiguous between two
or more feature values, it may agree in one value with the first
conjunct and in other values with others. This pattern is illustrated
in the following sentences (data from \cite{eisenberg73},
\cite{zaenen84}), \cite{pullum86}).

\lin\slbegin
\itemitem{(D)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \pt\ps weil & Franz & das & Haus & kauft.\cr
& \pt\ps because & Franz & the & house & buys.3SG\cr
& \multispan5\ps`because Franz is buying the house.' \hfil\cr}}
\itemitem{(E)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \pt\ps weil & ich & den & Garten & kaufe.\cr
& \pt\ps because & I & the & garden & buy.1SG\cr
& \multispan5\ps`because I am buying the garden.' \hfil\cr}}
\itemitem{(F)}\pt*weil Franz das Haus und ich den Garten kaufe/kauft.
\itemitem{}\ps`because Franz is buying the house and I am buying the
garden.'
\lin
\itemitem{(G)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt weil & Franz & das & Haus & kaufen & kann.\cr
& \ps\pt because & Franz & the & house & buy & can.(1,3)SG\cr
& \multispan6\ps`because Franz can buy the house.' \hfil\cr}}
\itemitem{(H)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt weil & ich & den & Garten & kaufen & kann.\cr
& \ps\pt because & I & the & garden & buy & can.(1,3)SG\cr
& \multispan6\ps`because I can buy the garden.' \hfil\cr}}
\itemitem{(I)}\pt\ps weil Franz das Haus und ich den Garten kaufen
kann.
\itemitem{}\ps`because Franz can buy the house and I can buy the
garden.'
\lin
\itemitem{(J)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt der & Antrag & des & Dozenten\cr
& \ps\pt the & petition & of-the.GEN.SG & docent.GEN.SG\cr
}}
\itemitem{(K)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt der & Antrag & der & Dozenten\cr
& \ps\pt the & petition & of-the.GEN.PL & docents.GEN.PL\cr
}}
\itemitem{(L)} \ps\pt der Antrag des oder der Dozenten
\itemitem{} \ps `the petition of the docent(s)'
\lin
\itemitem{(M)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt Er & findet & Frauen.\cr
& \ps\pt he.NOM & finds & women.ACC\cr
}}
\itemitem{(N)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt Er & hilft & Frauen.\cr
& \ps\pt he.NOM & helps & women.DAT\cr
}}
\itemitem{(O)} \ps\pt Er findet und hilft Frauen.
\itemitem{} \ps `He finds and helps women.'
\slend

\item{\eqdef{d}} Mere phonological identity is not sufficient to
license this kind of factoring.

\lin\slbegin
\itemitem{(P)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt Sie & singt.\cr
& \ps\pt she & sings.3SG\cr
}}
\itemitem{(Q)}\vtop{\offinterlineskip\halign{\strut\hfil#&& # \hfil\cr
& \ps\pt Sie & singen.\cr
& \ps\pt they & sing.3PL\cr
}}
\itemitem{(R)} \pt *Sie singt und singen.
\slend

\item{\eqdef{e}} Morphosyntactic ambiguity has traditionally been
represented in terms of underspecification, i.e. [CASE {\it nom\/}
$\lor$ {\it acc\/}] or [CASE $\neg${\it gen\/}]. When these lexical
constraints are combined with the selectional constraints that
implement agreement, the disjunction is resolved to a base type, as
HPSG requires.

\item{\eqdef{f}} One extension to this account of agreement to handle
factored coordination constructions could involve a version of the
factor which agrees with the first conjunct being unified with a
version that agrees with the second. Indeed, \cite{kathol95} presents
such an analysis for factored coordination. His Distributive Factor
Constraint (pg. 331) essentially states that a domain object appearing
on the same edge of each conjunct may only appear once (at the same
edge) of the cooordinate phrase. But domain objects (in this version
of the theory, at least) contain the morphosyntactic properties of
their corresponding signs. Hence this theory cannot account the data
presented above.

\item{\eqdef{g}} A similar problem is encountered by \cite{levineTA}.
In their account of parasitic gaps, a single object is used to
represent the local properties of both the normal and parasitic gaps.
When different case requirements are imposed on the two gaps, the
resulting sentence is only acceptable when the filler is
case-ambiguous.

\lin\slbegin
\itemitem{(S)} *whom even friends of \_ believe \_ should be
closely watched.
\itemitem{(T)} \ps who even friends of \_ believe \_ should be
closely watched.
\slend

\item{\eqdef{h}} Their solution is to augment the type hierarchy with
three new types:\break an `overspecified' type {\it nom-acc} and two
`pure' subtypes {\it nom} and {\it acc}.

\lin\slbegin
\itemitem{(U)}\xymatrix@-1pc{
&&\ar@{-}[dl]\ar@{-}[dr]\txt{\it case}\cr
&\ar@{-}[dl]\ar@{-}[dr]\txt{\it acc}&&\ar@{-}[dl]\ar@{-}[dr]\txt{\it
nom}\cr
{\txt{\it acc}}&&{\txt{\it nom-acc}}&&{\txt{\it nom}}\cr}
\slend

\item{\eqdef{i}} Case-ambiguous pronouns like {\it who}, as well as
common and proper nouns, are listed in the lexicon as [CASE {\it
nom-acc\/}], while case-specific pronouns like {\it he\/} or {\it
whom\/} are listed as [CASE {\it nom\/}] or [CASE {\it acc\/}], as
appropriate.

\item{\eqdef{j}} Verbs by default will select complements with [CASE
{\it sacc\/}] and subjects with [CASE {\it snom\/}]. Then, as a
description like [CASE {\it sacc\/}] is actually an abbreviation for
the disjunction ([CASE {\it acc\/}] $\lor$ [CASE {\it nom-acc\/}]),
the result of unifying [CASE {\it sacc\/}] and [CASE {\it snom\/}] (as
found in (T), for example) is no longer a failure, but instead [CASE
{\it nom-acc\/}].

\vfill\eject

\item{\eqdef{l}} Given a hierarchy $T$ of input types, an algorithm
for the construction of the corresponding augmented type hierarchy can
be given.

\itemitem{$\bullet$} For every base member $t$ of $T$, create the type
$pure-t$ such that $pure-t$ ISA $t$. 
\itemitem{$\bullet$} For every distinct (non-pure) $s$, $t$ in $T$
such that $s$ $\neg$ISA $t$ and $t$ $\neg$ISA $s$, create the type
$s-t$ such that $s-t$ ISA $s$ and $s-t$ ISA $t$. Then create
$pure-s-t$ such that $pure-s-t$ ISA $s-t$.

\item{\eqdef{k}} Matters are more complex with the German data
presented above, due to the conflation of person, tense, and number
that the various morphological forms represent. For example, the {\it
-en\/} suffix in {\it Dozenten\/} can signify a genitive singular
form, or any plural form. Similarly, the determiner {\it der\/} can
represent MASC.NOM.SG, FEM.DAT.SG, FEM.GEN.SG, or GEN.PL.

\item{\eqdef{l}} Thus augmenting a system of agreement features (CASE,
PERSON, NUMBER, and GENDER)\footnote{See \cite{kathol99} for complete
details of such a system.} as above, adding new types like {\it
pure-gen\/} and {\it sg-pl}, will not be enough -- there will still be
no way to replace a constraint like ([CASE {\it gen\/}] $\land$ [NUM
{\it sg\/}]) $\lor$ ([NUM {\it pl\/}]) in the same way that [CASE {\it
acc\/}] $\lor$ [CASE {\it nom\/}] was replaced with [CASE {\it
nom-acc\/}].

\item{\eqdef{m}} Thus to account for factored agreement using this
strategy, it will be necessary to use a multi-inheritance hierarchy to
represent the structure of morphosyntactic information. Just as
\cite{sag97} cross-classifies {\it phrase\/}s in terms of their
clausality and headedness, I propose to represent morphosyntactic
information in terms of one feature AGR and one type {\it agr\/} which
is cross-classified in terms of person, number, gender, and case.

\lin\slbegin\itemitem{(V)}\slend

\psTree{\TR{\it agr}}
\psTree{\TR{\psframebox{GENDER}}}\TR{\it masc}\TR{\it fem}\TR{\it
neut}\endpsTree
\psTree{\TR{\psframebox{PERSON}}}\TR{1}\TR{2}\TR{3}\endpsTree
\psTree{\TR{\psframebox{NUMBER}}}\TR{\it sg}\TR{\it pl}\endpsTree
\psTree{\TR{\psframebox{CASE}}}\TR{\it nom}\TR{\it acc}\TR{\it
dat}\TR{\it gen}\endpsTree
\endpsTree

\item{\eqdef{n}} Applying the algorithm in (\refn{l}) to the
seventy-two fully-qualified base types of this hierarchy will then
form the appropriate type hierarchy. In other words, each of these
base types will have for subtypes a pure form (like {\it nom\/} and
{\it acc\/} in (U) as well as all conjoined forms that include it. For
example, {\it masc.3rd.sg.dat\/} will have a subtype {\it
pure-masc.3rd.sg.dat-neut.3rd.sg.dat\/} for pronouns like {\it ihm\/}
which are ambiguous between 3SG.MASC.DAT and 3SG.NEUT.DAT.

\item{\eqdef{o}} It is important to note that this is in some sense
just a technical trick -- there is no more information being stored in
a constraint like [AGR {\it masc.3rd.sg.dat}] than is in the
constraint ([CASE {\it dat\/}] $\land$ [NUM {\it sg\/}] $\land$ [PER
{\it 3rd\/}] $\land$ [GEN {\it masc\/}]). Similarly, the various
interacting constraints that account for agreement will remain almost
unchanged. Verbs that select dative complements will now select for
[AGR {\it dat\/}] instead of [CASE {\it dat\/}], for instance.

\item{\eqdef{p}} Recall that under a system where {\it Frauen\/} was
described by [CASE {\it acc\/} $\lor$ {\it dat\/} $\lor$ {\it gen\/}]
(or [CASE $\neg${\it nom\/}]), it was impossible to provide an
explanation for the acceptability of (O). This is now straightforward.
Let {\it Frauen\/} be described by [AGR {\it
pure-fem.gen.sg-fem.pl\/}], a subtype of {\it fem.gen.sg\/} and {\it
fem.pl}. The definite article {\it der\/} is [AGR {\it
pure-masc.nom.sg-fem.dat.sg-fem.gen.sg-gen.pl\/}] and {\it des\/} is
[AGR {\it pure-masc.gen.sg-neut.gen.sg\/}].

\item{\eqdef{q}} Under the normal noun-determiner mutual-selection
model, each of these words will select for the disjunctive equivalent
of their own agreement features. Thus {\it der\/} will be selecting
for [AGR {\it masc.nom.sg\/} $\lor$ {\it fem.dat.sg\/} $\lor$ {\it
fem.gen.sg \/} $\lor$ {\it gen.pl\/}] and {\it des\/} for [AGR {\it
masc.gen.sg\/} $\lor$ {\it neut.gen.sg\/}].

\item{\eqdef{r}} Then if we assume as before that factored
coordination involves the unification of the individual conjuncts'
agreement constraints, the coordination {\it des oder der\/} will be
looking for a noun with [AGR {\it masc.nom.sg\/} $\lor$ {\it
fem.dat.sg\/} $\lor$ {\it fem.gen.sg \/} $\lor$ {\it gen.pl\/}]
$\land$ [AGR {\it masc.gen.sg\/} $\lor$ {\it neut.gen.sg\/}]. The type
{\it pure-masc.gen.sg-neut.gen.sg\/} is such a type and hence (O) is
acceptable.

\item{\eqdef{s}} As noted above, many languages only allow some
agreement features to take part in factored agreement or restrict the
environment in which factored agreement can involve a feature; recall
the unacceptability of (R). This can be analyzed by having two lexical
items with phonology {\it sie\/} in the lexicon -- one purely singular
and one purely plural -- rather than a single form with [AGR {\it
sg-pl}]. Then neither form will make (R) acceptable. In languages
where certain features never take part in factored agreement, no
subtypes will exist conjoining those features with others.

\vfill\eject
\sec{Works Cited}
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