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\begin{document}
\begin{slide}
\begin{center}
\begin{large}
  On a Type-Based Analysis of Feature Neutrality and the
  Coordination of Unlikes
\end{large} \\
Mike Daniels \\
The Ohio State University\\
19 April 2002
\end{center}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Overview\end{large}\end{center}
\begin{itemize}
\item Two related problems:
\begin{itemize}
\item Feature Neutrality
\item Coordination of Unlikes
\end{itemize}
\item A common solution:
\begin{itemize}
\item Expand the set of possible values for a feature
\end{itemize}
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Neutrality\end{large}\end{center}
\begin{itemize}
\item Sometimes, the answer to the question \textit{A or B?} is
  \textit{Both!}
\begin{itemize}
\item Is the period in the following sentence an abbreviation-final
  period, or a sentence-final period?
\begin{examples}
\item Dukakis had been Governor of MA and Bentsen a Senator from Tex.
\end{examples}
\end{itemize}
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Case Neutrality\end{large}\end{center}
\begin{itemize}
\item What is the case of \textit{Frauen} in (2)?
  \begin{examples}
    \item{\begin{tabular}{lllll}
      \ps Er & findet & und & hilft & Frauen\\[-6pt]
      \ps he & finds & and & helps & women.ACC/DAT\\
    \end{tabular}}
    \item{\begin{tabular}{lllll}
      *Er & findet & und & hilft & M\"anner\\[-6pt]
      \ps he & finds & and & helps & men.ACC\\
    \end{tabular}}
  \end{examples}
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Neutrality vs. Ambiguity\end{large}\end{center}
\begin{itemize}
\item A word that appears to be compatible with multiple feature
  values can be either neutral or ambiguous with respect to that
  value.
\item \textbf{Ambiguity} describes a situation where the
  \textit{lexical entry} is compatible with both values; any
  individual token of a word with an ambiguous feature value may only
  act as though it has \textbf{one} of the possible values.
\item \textbf{Neutrality} describes a situation where the \textit{word
  tokens} themselves are compatible with both values; thus a word with
  a neutral feature value may act as though it simultaneously has
  \textbf{both} feature values.
\end{itemize}
\end{slide}

%\item Words with ambiguous feature values may be plausibly treated as
%  separate lexical entries. Words with neutral feature values may not.

\begin{slide}
\begin{center}\begin{large}Example of Feature Ambiguity\end{large}\end{center}
\begin{examples}
\item{\begin{tabular}{llll}
      *Sie & singt & und & singen.\\[-6pt]
      \ps She/they & sings.SING & and & sings.PL\\
      \end{tabular}}
\end{examples}
\begin{itemize}
\item The word \textit{Sie} is ambiguous between \avm\[NUM &
  pl\]\endavm\ and \avm\[NUM & sg\]\endavm; hence it cannot occur in a
  context where it must be both singular and plural.
\item The problem of predicting whether a given feature will take
  ambiguous or neutral values is still largely an open question; see
  \cite{zaenen84} and \cite{pullum86} for two attempts.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Underspecification?\end{large}\end{center}
\begin{itemize}
\item Neutrality cannot be represented by underspecification.
\item The form must act as if it had both feature values:
\begin{examples}
    \item{\begin{tabular}{lllll}
      *Er & findet & und & hilft & M\"anner.\\[-6pt]
      \ps He & finds & and & helps & men.ACC\\
    \end{tabular}}
    \item{\begin{tabular}{lllll}
      *Er & findet & und & hilft & Kindern.\\[-6pt]
      \ps He & finds & and & helps & children.DAT\\
    \end{tabular}}
\end{examples}
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}The Ingria Problem\end{large}\end{center}
\begin{itemize}
\item Ingria (1990) \nocite{ingria90} used this data to criticize one
  of the fundamental aspects of the treatment of concord in
  constraint-based frameworks: the idea that a single object should be
  shared between the two representations involved.
\item The lack of a treatment of this phenomenon has been seen as a
  critical drawback to HPSG.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}A Solution\end{large}\end{center}
\begin{itemize}
\item Levine et al. (2001) \nocite{levine01} presents an analysis of
  case consistency in English parasitic gap constructions that can be
  adapted to the general case of feature neutrality.
\item The general idea: augment the type hierarchy to explicitly
  contain neutral type values.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Example\end{large}\end{center}
$$\xymatrix@-1pc{
  &&\ar@{-}[dl]\ar@{-}[dr]\txt{\itshape case}\cr
  &\ar@{-}[dl]\ar@{-}[dr]\txt{\itshape%
    acc}&&\ar@{-}[dl]\ar@{-}[dr]\txt{\itshape dat}\cr
  {\txt{\itshape p-acc}}&&{\txt{\itshape%
      p-dat-acc}}&&{\txt{\itshape p-dat}}\cr}
$$
\begin{itemize}
\item Types for linguistic objects (words): \textit{p-dat},
  \textit{p-dat-acc}, \textit{p-acc}.
\item Other types (\textit{dat}, \textit{acc}, \textit{case}) are only
  appropriate for descriptions (selectional restrictions).
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Coordinate Constituent
    Structure\end{large}\end{center}
\begin{itemize}
\item Assume a variant of the phrase structure for coordinations
  originally proposed by \cite{sag85} for GPSG.
\item The valence features of the coordinate mother are
  structure-shared with the valence features of all daughters.
\item {\it coord-phrase\/} $\to$ \begin{avm}\[ VAL & \@2 \cr
DTRS & \<\[VAL & \@2\],\[VAL & \@2\]\>\]\end{avm}
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Example\end{large}\end{center}
\begin{itemize}
\item\avm\[PHON & \<findet\>\\ COMPS & \<[CASE acc]\>\\\]\endavm
\item\avm\[PHON & \<hilft\>\\ COMPS & \<[CASE dat]\>\\\]\endavm
\item\avm\[PHON & \<findet und hilft\>\\ COMPS & \<[CASE p-dat-acc]\>\\\]\endavm
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Example (Cont.)\end{large}\end{center}
$$\begin{psTree}
  {\TR{\avm\[PHON & \<findet und hilft Frauen\> \\ COMPS & \<\>\\\]\endavm}}
  {\TR{\avm\[PHON & \<findet und hilft\>\\ COMPS & \<[CASE p-dat-acc]\>\\\]\endavm}
   \TR{\avm\[PHON & \<Frauen\>\\ CASE & p-dat-acc\\\]\endavm}}
\end{psTree}$$
\end{slide}

\begin{slide}
\begin{center}\begin{large}The Coordination of Unlikes\end{large}\end{center}
\begin{itemize}
\item Earliest analyses of coordination dealt with \textbf{like}
  coordination: $XP \to XP\, and\, XP$
\item What about sentences like these? \cite{sag85}
\begin{examples}
\item He is a Republican and proud of it. [NP and AP]
\item She has become a banker and very conservative. [NP and AP]
\item He is healthy and of sound mind. [AP and PP]
\item I am both expecting to get the job and of the opinion that it is
  desirable. [VP and PP]
\item I consider that a rude remark and in very poor taste. [NP and PP]
\end{examples}
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Coordinate NP Case in German\end{large}\end{center}
\begin{itemize}
\item In German, the coordination of a dative and an accusative NP
  cannot be the complement of a dative or accusative verb. Complements
  which coincide or overlap in case, however, are allowed.
\end{itemize}
\begin{examples}
    \item{\begin{tabular}{lllll}
      *Er & findet & M\"anner & und & Kindern.\\[-6pt]
      \ps He & finds & men.ACC & and & children.DAT\\
    \end{tabular}}
    \item{\begin{tabular}{lllll}
      *Er & hilft & M\"anner & und & Kindern.\\[-6pt]
      \ps He & helps & men.ACC & and & children.DAT\\
    \end{tabular}}
    \item{\begin{tabular}{lllll}
      \ps Er & findet & M\"anner & und & Kinder.\\[-6pt]
      \ps He & finds & men.ACC & and & children.ACC\\
    \end{tabular}}
    \item{\begin{tabular}{lllll}
      \ps Er & hilft & M\"annern & und & Frauen.\\[-6pt]
      \ps He & helps & men.DAT & and & women.ACC/DAT\\
    \end{tabular}}
\end{examples}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Coordinate NP Case in Russian\end{large}\end{center}
\begin{itemize}
\item Under some circumstances, the coordination of a genitive and an
  accusative NP in Russian may be the complement of (among others) the
  verb `expect' (example from \cite{levy01}).
\end{itemize}
\begin{example}
\begin{tabular}{llllll}
V\v cera & ves' & den' & on & o\v zidal & svoju\\[-6pt]
yesterday & all & day & he & expected & self's.ACC\\
podrugu & Irinu & i & zvonka & ot & svoego\\[-6pt]
girlfriend.ACC & Irina.ACC & and & call.GEN & from & self's\\
brata & Grigorija\\[-6pt]
brother & Gregory\\
\end{tabular}
\end{example}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Adding Coordinate Types to the Type Hierarchy\end{large}\end{center}
\begin{itemize}
\item Both \textit{M\"anner und Kindern} and \textit{podrugu i
    zvonka}, being noun phrases, need to have CASE values.
\item For the latter NP, we need a subtype of \textit{case} that is
  not a subtype of \textit{acc} or \textit{gen}.
\end{itemize}
$$\xymatrix@-1pc{
&&\ar@{-}[dl]\ar@{-}[d]\ar@{-}[dr]\txt{\it acc+gen}\cr
&\ar@{-}[dl]\ar@{-}[dr]\txt{\it acc}&{\txt{\it p-acc+gen\/}}%
&\ar@{-}[dl]\ar@{-}[dr]\txt{\it gen}\cr
{\txt{\it p-acc}}&&{\txt{\it p-acc-gen}}&&{\txt{\it p-gen}}\cr}
$$
\end{slide}

\begin{slide}
\begin{center}\begin{large}Three Cases\end{large}\end{center}
{\hfil\xymatrix@-1pc{
&&\ar@{-}[lld]\ar@{-}[d]\ar@{-}[drr]\txt{a+d+g}\cr
\ar@{-}[d]\ar@{-}[drr]\txt{a+d}%
&&\ar@{-}[lld]\ar@{-}[drr]\txt{a+g}%
&&\ar@{-}[lld]\ar@{-}[d]\txt{d+g}\cr
\ar@{-}[d]\ar@{-}[drrrrr]\txt{a+g-d}%
&&\ar@{-}[drrr]\ar@{-}[d]\txt{d+a-g}%
&&\ar@{-}[d]\ar@{-}[dr]\txt{g+d-a}\cr \ar@{-}[d]\txt{a}&&%
\ar@{-}[d]\txt{d}&&%
\ar@{-}[d]\txt{g}&%
\ar@{-}[dlllll]\ar@{-}[dlll]\ar@{-}[dl]\txt{a-d+a-g+d-g}\cr
\ar@{-}[d]\ar@{-}[drr]\txt{a-d+a-g}%
&&\ar@{-}[dll]\ar@{-}[drr]\txt{a-d+d-g}%
&&\ar@{-}[dll]\ar@{-}[d]\txt{a-g+d-g}\cr
\ar@{-}[drr]\txt{a-d}&&\ar@{-}[d]\txt{a-g}&&\ar@{-}[dll]\txt{d-g}\cr
&&{\txt{a-d-g}}\cr}\hfil}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Illustration\end{large}\end{center}
\begin{itemize}
\item Core Idea: anything can coordinate, but only some coordinations
  are acceptable arguments in a given syntactic construction.
\item \avm\[CASE p-acc+gen\]\endavm\ can be selected by \avm\[CASE %
  case\]\endavm\ or \avm\[CASE p-acc+gen\]\endavm.
\item \avm\[CASE p-acc\]\endavm\ can be selected by \avm\[CASE %
  case\]\endavm, \avm\[CASE acc\]\endavm, or \avm\[CASE %
  p-acc\]\endavm.
\item \avm\[CASE p-acc-gen\]\endavm\ can be selected by \avm\[CASE %
  case\]\endavm, \avm\[CASE acc\]\endavm, \avm\[CASE gen\]\endavm, or
  \avm\[CASE p-acc-gen\]\endavm.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Illustration (Cont.)\end{large}\end{center}
\begin{itemize}
\item \avm\[CASE p-acc\]\endavm\ and \avm\[CASE p-acc\]\endavm\ conjoin
  to \avm\[CASE p-acc\]\endavm.
\item \avm\[CASE p-acc\]\endavm\ and \avm\[CASE p-acc-gen\]\endavm\
  conjoin to \avm\[CASE p-acc\]\endavm.
\item \avm\[CASE p-acc\]\endavm\ and \avm\[CASE p-gen\]\endavm\ conjoin
  to \avm\[CASE p-acc+gen\]\endavm.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}\textit{become}\end{large}\end{center}
\begin{itemize}
\item Having dealt with coordinations of unlike case, we can turn to
  coordinations of unlike parts of speech.
\item Recall that \textit{become} can take NPs and APs, but not PPs or
  VPs, as arguments.\cite{sag85}
\begin{examples}
\item Connie has become of the opinion that we should get out.
\item Tracy became awarded a prize.
\item Chris will became talking to colleagues.
\end{examples}
\item We can therefore conclude that \textit{become} selects for
  \textit{np+ap} complements.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}A Future Issue\end{large}\end{center}
\begin{itemize}
\item Neutrality across features: the German determiner \textit{der}
  is nominative singular or genitive plural (but not genitive singular
  or nominative plural).
\item One simple idea: just fold agreement features into one new
  feature.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Feature Folding\end{large}\end{center}
{\hfil\psTree{\TR{\textit{uniagr}}}
\psTree{\TR{\psframebox{GENDER}}}\TR{\textit{masc}}\TR{\textit{fem}}
\TR{\textit{neut}}\endpsTree
\psTree{\TR{\psframebox{PERSON}}}\TR{1}\TR{2}\TR{3}\endpsTree
\psTree{\TR{\psframebox{NUMBER}}}\TR{\textit{sg}}\TR{\textit{pl}}\endpsTree
\psTree{\TR{\psframebox{CASE}}}\TR{\textit{nom}}\TR{\textit{acc}}
\TR{\textit{dat}}\TR{\textit{gen}}\endpsTree\endpsTree\hfil}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Feature Folding (cont.)\end{large}\end{center}
\begin{itemize}
\item The result: seventy-two basic \textit{uniagr} types, ranging
  from masc.1.sg.nom to neut.3.pl.gen.
\item Each subset of these seventy-two types could represent a
  potential neutralization.
\item There are $2^{72}$, or $4.72 \times 10^{21}$ possible subsets of
  seventy-two elements.
\item Many people feel that this is an uncomfortably large number of
  types.
\end{itemize}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Conclusion\end{large}\end{center}
\begin{itemize}
\item The ``Ingria Problem'' is an illusion that has no impact on
  HPSG.
\item Adding types to directly represent neutral and coordinate
  items is all HPSG needs to account for unlike coordination and
  neutrality within a feature.
\item More work is needed to find the optimal way to handle more
  complex cases.
\end{itemize}
\end{slide}

\begin{slide}
\bibliography{hpsg}
\bibliographystyle{mwd2}
\end{slide}

\begin{slide}
\begin{center}\begin{large}Acknowledgements\end{large}\end{center}
This paper arose from and was greatly informed by an Autumn 2000 --
Winter 2001 seminar on coordination at The Ohio State University led
by Carl Pollard; participants were Peter Culicover, Wesley Davidson,
Anna Feldman, Soo-Young Kang, Arantxa Martin-Lozano, Vanessa Metcalf,
and Adam Przepiorkowski. Thanks also 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.
\end{slide}

\begin{slide}
\begin{center}\begin{large}Contact Information\end{large}\end{center}
\begin{itemize}
\item Michael W. Daniels \\ 222 Oxley Hall \\ 1712 Neil Avenue \\
  Columbus, OH 43210
\item daniels@ling.osu.edu
\item \path|http://ling.osu.edu/~daniels/drafts.html|
\end{itemize}
\end{slide}
\end{document}