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\newcommand{\soa}[1]{$\langle\!\langle${#1}$\rangle\!\rangle$}
\title{Most Salient Referents To Express Causality Relations}
\author{Hiroshi Nakagawa}
\date{Dept. of Electronics and Computer Engineering,\\
Yokohama National University, Japan}
\maketitle
\section{Introduction}

The target of this work is semantics of a certain type of complex
sentences that express causality relations.
Roughly speaking, the general schema of causality is that one event E1
causes another event E2. But looking more closely, in cases that E2
describes a human activity, there has to be a certain person who is so
influenced by E1 that s/he acts as described by E2. We show an example.

\enumsentence{\label{ex1}
\begin{tabular}{lllll}
$[\phi_{experi}$ & atama ga & itai] & node, \\
              & head-NOM & feel pain ] & because, \\
$\phi_{agent}$ & kusuri o & nom-da.\\
             & medicine-ACC & drink-PAST\\
\end{tabular}\\
`$\phi_{agent}$ took a medicine because $\phi_{experi}$ had a headache.'}
%
Henceforth $\phi_{agent}$, $\phi_{experi}$, and $\phi_{patient}$
mean zero agent, zero experiencer, and zero patient, respectively.

In (\ref{ex1}) our intuitive reading is that $\phi_{experi}$ had so
influenced by her headache that she took a medicine. As a result the
main subject $\phi_{agent}$ corefers with $\phi_{experi}$. Thus, to
identify a person who is heavily influenced by the event described by
the subordinate clause helps identify the referent of the agent of main
clause.  In sum, the most important part of semantics of causality is to
identify this influenced person. In the rest of this draft we mainly
analyze Japanese complex sentences to know who comes to be this
influenced person by what kind of mechanism.

\section{Examples and Intuitions}

Let's look at a clause which has only a proposition part like the following.

\enumsentence{\label{ex2}
\begin{tabular}{lll}
$\phi_{experi}$ & atama ga & itai.\\
                     & head-NOM & feel pain\\
\end{tabular}\\
`$\phi_{experi}$ have a headache.'\\}
%
It is well known that $\phi_{experi}$ only refers to the first person,
namely the speaker when (\ref{ex2}) is assertive.  The reason of this
lies on the semantics of Japanese adjective {\it itai}(feel pain). 
Basically in Japanese language this kind of internal feeling is to be
known only by the experiencer herself.  Note that the situation of
$\phi_{experi}$'s headache is described from the speaker's viewpoint. 
Therefore $\phi_{experi}$ refers to the speaker. This gives us the
reason why we have the intuitive reading of (\ref{ex1}).  In (\ref{ex1})
whole the sentence is described from the viewpoint of subject of main
clause. Therefore the referent of the subject of main clause is the only
person who can say about her internal feeling like having a headache. As
a result $\phi_{agent}$ corefers with $\phi_{experi}$.

On the other hand, we have many Japanese predicates that does not comply
with this restriction. For example in

\enumsentence{\label{ex3}
\begin{tabular}{ll}
$\phi_{agent}$ & hasir-ta.\\
               & run-PAST\\
\end{tabular}\\
`$\phi_{agent}$ ran.'\\}
%
$\phi_{agent}$ can be any person including third person. This contrast
comes from {\it observability} of event described by the predicate. {\it
Hasir}(run) is for physical action of running which is easily observed 
by outsiders. In contrast, {\it itai} used in (\ref{ex2}) does not have
observability as you know from example (\ref{ex1}) and (\ref{ex2}).

Of course there are many predicates located inbetween {\it hasir} and
{\it itai} according to their observabilities. For example, {\it
odorku}(be surprised) means an experiencer's internal mental state, but
it also has a certain degree of observability from outside. Look at the
following sentence.

\enumsentence{\label{ex4}
\begin{tabular}{lllll}
$[$ Itumo & kuuruna & Taroo ga & odoroi-ta]& node,\\
$[$ usually & cool & Taroo-NOM & be surprised-PAST ] & because\\
 $\phi_{experi}$ & bikkuri & -sita.\\
                      & be astonished & -PAST\\
\end{tabular}\\
`$\phi_{experi}$ was astonished because Taroo who is usually cool was surprised.'}
%
The zero subject of main clause, $\phi_{experi}$, intuitively, does not
refer to Taroo. Therefore $\phi_{experi}$ should observe the situation
of Taroo's surprising. This is the evidence that {\it odorku} (be
surprised) certainly has some degree of observability.

Teramura classifies Japanese predicates including both verbs and
adjectives into several classes according to their observability
\cite{teramura}. Since there are many works for observabilities other
than Teramura's work, we know much about it, but they are yet to be
formalized.

Now we know the clue to identify the person who is enough influenced by
the event of subordinate clause to be a player of event of main clause.
If a predicate of subordinate clause does not have any observability,
the influenced person is an experiencer of that predicate. If a
predicate of subordinate clause does have a certain degree of
observability, the influenced person can not only be a semantic role
posed by the predicate, like an agent, experiencer and so forth, but
also be an observer. This results in ambiguity about the referent of the
enough influenced person.

Another factor which contributes to identify an influenced person in an
event described by subordinate clause is the structure of clause.  A
clause generally has a multi-layer structure. For instance, a
proposition part is embedded by a modality part. As for a modality part,
a speaker's attitude towards the proposition is embedded by a speaker's
attitude towards hearers \cite{palmer,sawada}.
This kind of multi-layer structure is formally
treated by JPSG \cite{gunji}, HPSG \cite{sag}, and so on.  Each layer
may introduce a new semantic role like {\it affectee} in intransitive
passivization, or a discourse role like {\it observer} whose
definitionis given below.

\enumsentence{\label{obs} Definition: The role {\it observer} of the
event or state refers to a person who observes that event or state from
outside. \footnote{By this definition {\it observer} refers  neither to
the experiencer of state nor to the agent of the event. }} 
%
Taking into account this muti-layer structure, the main question is from
which layer of subordinate clause a role corresponding to the most
strongly influenced person comes.  As the answer for this question, we
claim that a role introduced by the outermost layer of subordinate
clause becomes referring to the most strongly influenced person.  This
person turns out to be the most salient person in the succeeding part
that corresponds to the main clause.  Therefore we call this role ``most
salient referent'' or {\it msr} in short hereafter. Of course the notion
of {\it msr} corresponds to the strongly influenced person by the event
described by the subordinate clause.

\enumsentence{\label{outm} Claim: A role introduced by the
outermost layer of subordinate clause becomes the most salient
referent: {\it msr} in the main clause.}
%
This claim couldn't be proven logically, however the outermost layer is
regarded as the head of clause at least syntactically and at most
linguistically. If we take the outermost layer as a semantic head, the
role introduced by that layer is the most valid candidate of {\it msr}. 
Therefore Claim (\ref{outm}) naturally follows. We will show several
examples to ensure Claim (\ref{outm}).

\enumsentence{\label{ex5}
\begin{tabular}{lll}
$[ \phi_{experi}$ & kowakat-ta] & node,\\
                       & feel danger -PAST & because\\
 $\phi_{agent}$ & mou & ika-nai.\\
                & any more & go-NEG\\
\end{tabular}\\
`$\phi_{agent}$ will never go there because $\phi_{experi}$ felt
danger there.'\\ } 
%
In (\ref{ex5}) {\it msr} of subordinate clause corresponds to
$\phi_{experi}$ because {\it kowai}(feel danger) has no observability. 
Then the zero subject $\phi_{agent}$ of the main clause corefers with
$\phi_{experi}$ who corresponds to {\it msr}. This reading coincides
with natives' intuition. But in the following (\ref{ex6}) things are
different.

\enumsentence{\label{ex6}
\begin{tabular}{llll}
$[[ \phi_{experi}$ & kowa ] & -gat-ta ] & node,\\
                        & be scared & gar-PAST & because \\
 $\phi_{agent}$  & mou  & ika-nai.\\
                 & any more & go-NEG\\
\end{tabular}\\
`$\phi_{agent}$ will never go there because $\phi_{experi}$ behaved like
feeling danger there.'\\ \footnote{Henceforth, in example sentences [ ]
shows a multi-layer structure. For instance, [[A]B] means A is embedded
by B.} } 
%
In the intuitive reading of (\ref{ex6}) $\phi_{agent}$ does not corefer
with $\phi_{experi}$. This is because {\it gat} which is a past form of
{\it gar} is used as verbal suffix of {\it kowai}. {\it Gar} means
``behave like ..ing'' and introduces an observer of that behavior
\cite{nakagawa 94}. By the above mentioned intuitive reading, the {\it
msr} comes to be the observer introduced by {\it gat} which is the
outermost layer of subordinate clause, because there is no other
explicit role other than $\phi_{experi}$ and {\it observer} in the
subordinate clause.

Especially in Japanese language Claim (\ref{outm}) always holds. On the
contrary, in English this claim is a good default rule to interpret
complex sentences, but, of course, it has some exceptions. An example
for Claim (\ref{outm}) is the following.

\enumsentence{\label{ex7}
? Bill took a medicine because he looked like to have a headache.}
%
Since ``look like'' introduces an observer, the subject of main clause
can only be interpreted as the observer. Then ``he'' of the
subordinate clause should not refer to Bill. However the commonsense
that a person taking a medicine must be the person who has a headache,
contradicts the expected reading of the previous lines.  Thus the
awkwardness of (\ref{ex7}) is accounted for.

Auxiliary verbs make mulitiple embedded structure like ``might have
been'' or ``-rare-ta-rasii''(passive-past-seem). In this multiple
embedded structure, at least in Japanese, still Claim (\ref{outm})
holds. Look at the following example.

\enumsentence{\label{ex9}
\begin{tabular}{llllllll}
$[[[[ \phi_{experi}$ & kane & o & hosi $]_1$ & -gar $]_2$ & -are-ta $]_3$ & rasii $]_4$ \\
                         & money & ACC & want &               & -PASS-PAST & seem \\
\end{tabular}\\
\begin{tabular}{llllllll}
node, &  $\phi_{agent}$  & $\phi_{goal}$ & yar-ta.\\
because &                  &               & give-PAST\\
\end{tabular} \\
`$\phi_{agent}$ gave $\phi_{goal}$ money because $\phi_{goal}$ looked like to be asked money by $\phi_{experi}$.'\\}
%
The situation described by this Japanese sentence is this. 1)
$\phi_{experi}$ showed a sign that $\phi_{experi}$ needs some money. 
This is expressed by $[ ... ]_2$ part. 2) This sign is intensionally
intended to a certain person corresponding to $\phi_{goal}$. This is
expressed by $ -are-ta ]_3$. 3) Then $\phi_{agent}$ somehow came to know
the situation of 2) by {\it rasii}(seem)$]_4$. Note that the referent of
$\phi_{agent}$ has not been introduced till $[ ... ]_3$ finished. 
Actually the referent of $\phi_{agent}$ is introduced by the auxiliary
verb {\it rasii}. Then $\phi_{agent}$ gave $\phi_{goal}$ money. The
referent of $\phi_{agent}$ is to be {\it msr} of subordinate clause. As
you know from the intuitive reading of (\ref{ex9}), {\it msr} is the
referent introduced by the outermost layer of subordinate clause in this
case, too. This is exactly what (\ref{outm}) expects.

\section{Formal Definition of {\it msr}}

In this section we formalize the idea shown in the previous section. 
However the contents we propose here are minimal in formalism. That
means that {\it msr} and its related constraints can be used as a
semantic feature of feature structure\cite{nakagawa 94}, a part of DRS in
DRT\cite{kamp}, an infon of situation semantics, or whatever.

We start with the notation for the meaning of proposition part.

\enumsentence{\label{nota1} $P(role_1\! : \! X_1 , role_2\! : \! X_2, ... \; )$ is used
as a meaning of proposition part. $P$ means a predicate. $role\! : \! X$ means
that $role$ is a usual semantic role or pragmatic role {\it observer}
required by the predicate $P$ and $X$ is the referent corresponding to the
$role$.}
%
Then an {\it msr} of the proposition is given as (\ref{p-role}).

\enumsentence{\label{p-role}
$msr(P(role_1\! : \! X_1 , role_2\! : \! X_2 , ...)) = X_1$ if $role_1 > role_2 > .. $ in their saliency. }
%
The problem here is the definition of saliency order $>$ in
(\ref{p-role}).  As said in the previous section, saliency among roles
is determined by two factors. One is observability. If a predicate $P$
has high observability, role {\it observer} has the highest saliency. If
a predicate $P$ has no observability like {\it itai}(feel pain), $P$
doesn't have role {\it observer}. If a predicate $P$ has a certain level
of observability, we have two most salient roles including {\it
observer}. In this case, {\it msr} is ambiguous. As stated before,
observability of each predicate is determined respectively. Therefore it
should be written as one of the property of lexical description of each
predicate.  The other factor is a corresponding grammatical role. In
English a semantic role which corresponds to grammatical subject has the
highest saliency. For instance, if a predicate is a verb of volitional
action, then an agent which is a grammatical subject is the highest in
saliency.  The highest saliency of grammatical subject also holds in a
passive voice verb. For instance, if a predicate $P$ which has an agent
and a patient is used in passive voice, the patient becomes the most
salient role.  
%
\enumsentence{\label{pass} For a passive clause whose active counterpart's
meaning is $P(agent\! : \! X , patient\! : \! Y , ...)$, 
$msr(pass(P(agent\! : \! X , patient\! : \! Y , ...))) = Y$, where
$pass$ means a schema of passivization.}
%
Japanese intransitive passive sentences are very
different because intransitive passivization introduces a new role
called {\it affectee}. Actually an intransitive passive sentence has a
sort of feeling of adversity. And an {\it affectee} refers to a person
who gets a certain adversity from the event described by the predicate. 
As for {\it msr}, we have the following.

\enumsentence{\label{ipass} For intransitive passive clause,
$msr(ipass(P, affectee\! : \! X)) = X$ where a two place predicate $ipass$
means intransitive passivization. The first argument $P$ is the meaning
of the part which is passivized by $ipass$.  The
second argument is a new role $affectee$ which is introduced by
intransitive passivization.}
%
If a passivized part is a propostion, $P$ is a form of (\ref{nota1}).
As an example of (\ref{ipass}), look at the following sentence.

\enumsentence{\label{ex10}
\begin{tabular}{llllll}
$[ \phi_{affectee}$ & [ Tuma & ni & sin ] & -are-ta] & node,\\
                     & wife & DATIVE & die & PASS-PAST & because\\
 $\phi_{experi}$ & kanasii.\\
                      & be sad\\
\end{tabular}\\
`$\phi_{experi}$ is sad because $\phi_{affectee}$ 's wife died.'}
%
In the intuitive interpretation of (\ref{ex10}) $\phi_{affectee}$
corefers with $\phi_{experi}$. Intuitively $\phi_{affectee}$ refers to
the husband of the dead wife. This reading is accounted for as follows. 
By (\ref{ipass}) {\it msr} of the subordinate clause, namely
$msr(ipass(died(wife)),$ $ affectee\! : \! X)$ is $X$ who is the referent
of $\phi_{affectee}$. Then this {\it msr} comes to be the referent of
the subject of main clause. However matching of {\it msr} and main
subject will be formalized later.

Next we deal with clauses where an auxiliary verb, Japanese verbal
suffix {\it gar}, and so on, are attached to the verb phrase to express
modalities. There are two cases for this type of clause. Case 1 is the
case where no new role is introduced. For instance, in English {\it can}
that just means an ability is this case. Case 2 is the case where a
modality part introduces a new role like {\it observer}. Examples are
Japanese {\it gar} added to verb phrase shown in (\ref{ex6}) and English
epistemic auxiliary verbs like {\it may}.  Now we introduce a predicate
schema $modal$ to describe the meaning of any modality part. However as
said before, we have to have two types of $modal$ corresponding to case 1
and 2. For case 1 $modal$ is 1-place predicate whose argument is the
meaning of clause without the modality part. For case 2 $modal$ is
2-place predicate where the first argument is the same as case 1, and
the second argument is a newly introduced role. Then by Claim
(\ref{outm}), $msr$ of clause with auxiliary verb is given in the
following.

\enumsentence{\label{modal} Case 1. $msr(modal(P)) = msr(P)$\\ Case 2. 
$msr(modal(P , role\! : \! X)) = X$ where $role$ is a newly introduced role like
{\it observer}.}
%
Then think of Claim (\ref{outm}). It turns out to say that (\ref{modal})
applies recursively from inner layer to outer layer, because
$msr(P)$ is the most salient referent introduced by the outermost layer
of $P$. More formally as follows.

\enumsentence{\label{recurse} $msr(modal(P, role\! : \! X)) = X$ , for any $P$,
even though $P$ is the form of $modal(Q, role\! : \! Y)$.}
%
Next we think of the meaning of conjunctive particle like {\it
node}(because) in terms of $msr$. Claim (\ref{outm}) also holds for
conjunctive particle. However we have two types of conjunctive particles
in Japanese. Case 1 is conjunctive particles, like {\it node}(because),
that do not introduce a new role by itself. Case 2 is conjunctive
particles, like {\it nara}(if), that introduce a new role. The situation
is very similar with modality part case. As same as we did in modaliy
part, we introduce a predicate schema $conj$ to describe the meaning of
conjunctive particle. Then for case 1 $conj$ is a 1-place predicate. For
case 2 $conj$ is a 2-place predicate. $Msr$ of a clause attached with a
conjunctive particle is given in the following.

\enumsentence{\label{conj-1} For 1-place $conj$, $msr(conj(P)) = msr(P)$.}
%
\enumsentence{\label{conj-2} For 2-place $conj$, $msr(conj(P, role\! : \! X)) =
X$ where $role$ is a newly introduced role by the conjunctive particle.}
%
An example for (\ref{conj-2}) is the following.
\enumsentence{\label{ex29}
\begin{tabular}{llll}
$ [ \phi_{experi}$ & itai ] & nara,\\
                        & feel pain & if \\
 $\phi_{agent}$ & kusuri & o & dasi-masu.\\
                & medicine & ACC & priscribe-POLITE\\
\end{tabular}\\
`If $\phi_{experi}$ feels pain, $\phi_{agent}$ prescribes.'\\
}
%
In intuitive interpretation, $\phi_{agent}$ does not corefer with
$\phi_{experi}$.  The situation we can imagine from (\ref{ex29}) is, for
instance, that a physiscian talks to the patient who may feel pain.
Actually this interpretation contradicts the interpretation based on
{\it msr} stated as follows. Firstly {\it msr} of subordinate clause is
to be $\phi_{experiencer}$ because {\it itai}(feel pain) is about an
experiencer's internal feeling. Therefore $\phi_{agent}$ should corefer
with $\phi_{experi}$, and ends up with contradiction against the
intuitive interpretation. The key point to solve this problem is the
semantics of conjuntive particle {\it nara}(if), which is, unlike {\it
node}(because), a 2-place predicate. One of the arguments is, of course,
the content of subordinate clause. The other argument is referring to
the person who hypthesizes the situation described by the subordinate
clause. By (\ref{conj-2}) we know that {\it msr} of {\it nara} conjoined
subordinate clause is the second argument of {\it nara}. Then in
(\ref{ex29}) $\phi_{agent}$ refers to the person who hypothesizes the
$\phi_{experi}$'s feelings. This is exactly what we want to have. Note
that, as you just saw, the most basic claim (\ref{outm}), actually
(\ref{conj-2}) derived by (\ref{outm}), correctly predicts the intuitive
interpretation.

\section{Localization}

The problem yet to be solved is which role of a main clause predicate
refers to {\it msr} that comes from the subordinate clause. At the
first glance the referent of grammatical subject coincides with {\it
msr}. However there are counter examples such as the following.

\enumsentence{\label{ex21}
\begin{tabular}{lllllllll}
$[[ \phi_{experi}$ & gakkou & e & iku & no & o & iya ] & -gat-ta] \\
                        & school & GOAL & go & NOM & ACC & hate & gar-PAST \\
node, &  $\phi_{patient}$ & okor & -are & -ta.\\
because &                   & scold & -PASS & -PAST\\
\end{tabular}\\
`$\phi_{patient}$ was scolded because $\phi_{experi}$ was very reluctant to go to school.'\\}
%
Intuitively $\phi_{experi}$ corefers with $\phi_{patient}$ that is a
grammatical subject of the main clause. However {\it msr} of subordinate
clause is an {observer} introduced by {\it gar} due to (\ref{outm}). 
This trouble can be solved if we think of the active voice counterpart
of the main clause. The subject of active voice counterpart is the
scolder whose semantic role is an agent who turns out to refer to {\it
msr}. From this type of example, we come to the conclusion that we have
to deal with the problem not by grammatical roles but by semantic roles. 
Then according to the meaning category of main clause, namely, action or
state, we have two observations stated in the following.

\enumsentence{\label{m-active} If a main clause describes an action
$P_{main}(agent\! : \! X,..)$ in either active or passive voice, then $X =
msr(P_{sub})$ where $P_{sub}$ is either $conj(P)$ of (\ref{conj-1}) or
$conj(P, role\! : \! X)$ of (\ref{conj-2}).  }
%
\enumsentence{\label{m-stative} If the predicate of a main clause
describes a state $P_{main}(experi\! : \! X,..)$ in either active or
passive voice, then $X = msr(P_{sub})$ where $P_{sub}$ is the same as
stated in (\ref{m-active}).}
%
All the examples stated in the previous sections comply either
(\ref{m-active}) or (\ref{m-stative}). The important conclusion
(\ref{p-role}), (\ref{ipass}), (\ref{modal}), (\ref{recurse}),
(\ref{conj-1}), (\ref{conj-2}),(\ref{m-active}) and (\ref{m-stative})
derive is that semantics of causality is determined locally by using the
notion of {\it msr}. Namely {\it msr} of subordinate clause is
determined within the subordinate clause, and which semantic role {\it
msr} refers to is also determined within the main clause. This
locality is important because when you implement a natural language
understanding system, this locality makes the system very modular one.

Unfortunately , however, we have exceptional cases against this locality
even though they are minority. In the rest of this section we focus on
exceptional cases. We focus on is the case in which a
special role of main clause predicate comes to be an observer of the
subordinate clause even though there is no observer explicitly
introduced in the subordinate clause. One of the examples is the
following.

\enumsentence{\label{ex22}
\begin{tabular}{llllll}
$[$ Amari & hairu & hito & ga & ooi ] & node,\\
    very & enter & people & NOM & many & because\\
  $\phi_{experi}$ & odoroi & -ta.\\
                       & be surprised & -PAST\\
\end{tabular}\\
`$\phi_{experi}$ was surprised because very many people enter into there.'}
%
In this example, the subordinate clause does not explicitly introduce
{\it msr} other than the grammatical subject {\it hairu hito}(people who
enter). However the subject of main clause $\phi_{experi}$ is clearly
the person influenced by the event described by the subordinate clause. 
Actually the reason why $\phi_{experi}$ is surprised is that she saw the
event of very many people entered. Therefore $\phi_{experi}$ is the
observer of subordinate clause. However this observer is not explicitly
introduced solely by the expression of subordinate clause, but becomes
explicit by the main clause predicate. We regard this situation as
follows. The observer exists in the event described by the subordinate
clause, but very implicitly because the event of subordinate clause is a
property of physical action which is highly observable. Then this
implicit observer becomes explicit as {\it msr} by the predicate of main
clause. The question raised by this example is what kind of predicate
digs up an implicit {\it observer}. Firstly predicates that describe a
change of mental state are the answer for this question. For examples,
{\it odorku}(be surprised), {\it bikkuri suru}(be astonished), and so
forth. Secondly actions that are the result of mental state change are
the answer, for instance, {\it nigedasu}(flee). Look at the following.

\enumsentence{\label{ex23}
\begin{tabular}{lllllll}
$[$ Amari & ookuno & teki & ga & kuru] & node,\\
    very  & many   & enemy &  NOM & come & because\\
 $\phi_{agent}$ & nigedasi & -ta.\\
                & flee     & -PAST\\
\end{tabular}\\
`$\phi_{agent}$ fled because so many enemies came.'}
%
The reason why $\phi_{agent}$ fled is that he saw unexpectedly large
number of enemies coming. In other words, $\phi_{agent}$ is an {\it
observer} of the event described by the subordinate clause.
But to deal with this second type, we have to derive a presupposition
from the action explicitly described by the main clause. This is another
topic in pragmatics, but we will not pursue it further.


\section{Conclusion}

We analyze semantics of complex sentence by newly introduced notions as
most salient referent: $msr$ and observabilities of predicate, and Claim
(\ref{outm}). Then we propose the minimal formalization for them. We
have already implemented this formalization on unification grammar based
Japanses language understanding systems \cite{nishizawa}.

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\end{document}
