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\title{A Situation-Theoretic Analysis of Stylized Documents}

\author{Keith Devlin\\Saint Mary's College of California\\Moraga, California, USA\\ and\\
CSLI, Stanford University\\Stanford, California, USA \and
Duska Rosenberg\\Department of Computer Science\\Brunel University\\Uxbridge,
Middlesex, UK}

\date{EXTENDED ABSTRACT}

\begin{document}

\maketitle

\begin{abstract}
We summarize the investigation reported in our papers \cite{devros1}, \cite{devros2}, 
\cite{devros3}, and \cite{devros4}, and describe the hitherto unpublished conclusion to the
project. In particular, we outline the analytic technique we developed---Layered Formalism
and Zooming---and apply it to the analysis of a class of stylized documents. We also
describe and use a new kind of grammar, interpretive grammar, based upon the interpretive
stategies that a reader must use to extract information from a stylized document.
\end{abstract}

\section{Introduction}

In our first paper, {\it Situation Theory and Cooperative Action\/} \cite{devros1}, we
examined a classic analysis in ethnomethodology, namely Sacks' analysis of a child's story,
in which he investigates the role played by social information in understanding language. 
We used Sacks' analysis as the basis for developing a more precise and rigorous analytical 
framework than the purely descriptive one used by Sacks himself, to provide a formal
account of the social and interactive phenomena he had observed.

In the second paper, {\it Networked Information Flow via Stylized Documents\/}
\cite{devros2}, we described an application of this framework in the analysis of Problem
Report Forms ({\small PRF}s). These are documents that contain information about
cooperative activities centered on computer maintenance, in particular on reports of fault
repairs. We discussed the effectiveness of the tools we developed within our framework in
providing an account of the role of context in the interpretation of real language data as
encountered in the forms. We examined the information flow captured by a network of
constraints that linked different object types, and used our tools to specify the
contextual background which plays a part in establishing referential identities. 

In the third paper, {\it Layered Formalism and Zooming\/} \cite{devros3}, we continued
the analysis of the {\small PRF}s begun in \cite{devros2}. We provided an overview of the
analytic method that we had developed in order to examine the Sacks data and the {\small
PRF}s. We called this method ``layered formalism and zooming'' (LFZ). We believe it has
potentially wide application in the analysis of information flow in various contexts. In
particular, we suggested how our methods and techniques may be of benefit  in informing the
design of interactive information systems.

In the fourth paper, {\it Interpretive Grammar and Stylized Documents\/} \cite{devros4}, we
formulated a grammar that captures the essential informational structure of the {\small
PRF}s. 

In a fifth paper, currently under preparation, we shall complete our analysis.


\section{The PRF}

A sample {\small PRF} is shown in Figure~\ref{prf1}.

\medskip

\begin{figure}[bhtp]
\hrule {\tt
\begin{verbatim}
Site No: 23024     Cust. Name: XXXX                   System: JN1700
Call No: B04053   Call rcvd: 11/08/88   Call clrd: 11/08/88  Visits:1
Type/bar No: 006234/01      Serial No: 001165       Unit type: FP1500
Call text: LP02 TRACTOR SLIPPING
Clearance text: RESET TRACTORS TO ORIG POSITIONS Parts used:
\end{verbatim} }
\hrule
\caption{A typical PRF.}
\label{prf1}
\end{figure}

In our analysis of these documents, our starting point is that a document mediates
communication by virtue of certain `formal features' that the document exhibits, features
that are recognized (not necessarily consciously) by the producer and the recipient of the
document. In reading  a document that describes some scene or event, the reader does not
normally need direct access to that scene or event, or to the objects constituent to that
scene or event, in order to understand the document; the document itself is enough.
Moreover, any number of different persons may read the same document, describing a scene or
event to which they have no direct access, and achieve very nearly the same understanding.

In order for the document to convey information in this way, the text must have {\it
formal features\/} that associate with it an {\it abstract structure\/} that the writer
(or the writer plus the document designer in the case of an `official form') imparts to
the document and the reader may recognize or utilize. Part of our analysis consists of
providing a mathematical description of---or, if you prefer, model of---that abstract
structure.

We assume that it is the combined effect of all parts and expressions in a {\small PRF}
that characterizes, or maybe even enables, interpretation of the {\small PRF}. One of the
more intriguing aspects of the {\small PRF} is that it contains both a highly stylized
`attribute--value' presentation of information as well as two `natural language'
descriptions (the call and clearance texts). The interplay between these two very
different presentations of information is not only fascinating, it presents a
considerable challenge when it comes to trying to describe the grammatical stucture of
the document. Though clearly in the domain of `natural language', the call and clearance
texts are nothing like the stuff that linguists normally study. They are almost never
sentences. Indeed, they seem to be so unstructured in terms of the normal syntactic
features that it seems unlikely any kind of {\it syntactic structure\/} theory could
capture the features of these texts that enable them to convey the appropriate information.
Accordingly, we have developed a new approach to grammar, based not only on the syntactic
structure but also on the interpretive stategy that must be used to recover the appropriate
information from the document. We refer to this kind of grammar as an {\it interpretive
grammar}. In situation-theoretic terminology, the grammar assigns types not only to classes
of words (the more familiar notion of a `grammar') but also to uses of words.

We identify three different kinds of interpretive mechanisms (collections of constraints)
that readers of the form must utilize in order to extract the information they require from
a particular {\small PRF}, depending on the way it is completed. The three interpretive
mechanisms involve three different collections of constraints. First, there are linguistic
constraints: readers correct some errors in the form, such as information entered in the
incorrect location, by means of linguistic constraints that govern the completion of the
form. Second, interpretation of the form often requires domain-specific, technical
knowledge. Finally, some form entries can only be understood relative to knowledge of the
social constraints that obtain in the organization. The interpretation of some forms
requires a combination of all three kinds  of knowledge.


\section{Scenes, stories, and explanations}

Interpretation of the {\small PRF} involves different kinds of mechanisms, depending on the
way the document has been completed. Using the principles of LFZ analysis (Layered
Formalism and Zooming) outlined in \cite{devros3}, we adopt the minimal formalism necessary
to capture the interpretation of a scene, a story and an explanation.

Suppose $s$ is the situation being described by some description.

The description of $s$ is called a {\it scene\/} if it consists of a largely
unstructured list of isolated facts. For example:
\begin{quote}
{\it There are some people. A man is wearing a black robe. Some men are carrying a long, 
wooden box. Some people are walking.}
\end{quote}
Such a scene provides information about $s$ as a proposition where the descriptive content
consists of a collection of infons, with  constituents related minimally to one another,
thus: $$s \models \sigma$$ where
$$\begin{array}{rcl}
\sigma &=& \ll \mbox{\rm wear}, \para{m}, \para{b}, \para{t}_{now}, 1 \gg \wedge\\
       && \ll \mbox{\rm carry}, \para{m}_1, \ldots, \para{m}_6, \para{c},
              \para{t}_{now}, 1 \gg \wedge\\
       && \ll \mbox{\rm walk}, \para{p}_1, \para{t}_{now}, 1 \gg \wedge \ldots\ \wedge
          \ll \mbox{\rm walk}, \para{p}_n, \para{t}_{now}, 1 \gg. \end{array}$$
Here, \para{m}, $\para{m}_1$, \ldots, $\para{m}_6$ are parameters for men, \para{b} is a
parameter for a black robe, \para{c} is a parameter for a wooden box, and $\para{p}_1$,
\ldots, $\para{p}_n$ are parameters for people.

In the case of a {\it story}, the description has an internal structure, linking the
various components. For example:
\begin{quote}
{\it There are some people. Some of the people, all men, are carrying a long wooden box. A
man wearing a black robe walks in front of them. The remaining people all walk behind the
box.}
\end{quote}
This description provides information about $s$ as a proposition where the descriptive
content consists of a collection of infons having strutural connections, captured by means
of parameters, like this:
$$s \models \sigma \wedge \tau$$ where
$$\begin{array}{rcl}
\tau &=& \ll \mbox{\rm in-front-of}, \para{m}, \para{m}_1, \para{t}_{now}, 1 \gg \wedge
             \ldots \wedge \ll \mbox{\rm in-front-of}, \para{m}, \para{m}_6,
             \para{t}_{now}, 1 \gg \wedge \\
     && \ll \mbox{\rm in-front-of}, \para{c}, \para{p}_1, \para{t}_{now}, 1 \gg \wedge
             \ldots \wedge \ll \mbox{\rm in-front-of}, \para{c}, \para{p}_n,
             \para{t}_{now}, 1 \gg .
\end{array}$$
This proposition makes explicit how the different groups of people are related: the man in
a black robe is walking in front of the box, the other people are walking behind the box,
etc. In other words, there are connections that link the constituents of the descriptive
content.

An {\it explanation\/} has a still deeper structure, in that it does what its name
suggests, namely it provides an explanation of the events described. For example:
\begin{quote}
{\it A funeral is taking place. The priest, wearing a black robe, walks at the head of the
procession. The pallbearers carry the coffin. The mourners follow on behind.}
\end{quote}
Such an explanation classifies the event and places it in a social/cultural context (in
this  case a funeral), so that functional relationships between the constituents of the
described situation are specified. The description provides information about $s$ in the
form of a proposition of the form
$$w \models \ll \mbox{\rm of-type}, s, T_{\mbox{\scriptsize\it funeral}}, 1 \gg$$
where $w$ is the world of social practices and customs and \ $T_{\mbox{\scriptsize\it
funeral}}$ \ is the type of funerals.

It is in the nature of the type \ $T_{\mbox{\scriptsize\it funeral}}$ \ that
$$w \models T_{\mbox{\scriptsize\it funeral}} \Rightarrow [\para{s} \mid
    \para{s} \models \sigma \wedge \tau].$$
This indicates how the above explanation does in fact {\it explain\/} the events described
by the scene proposition \ $s \models \sigma \wedge \tau$.

Notice that an explanation for a situation $s$ provides an object type that applies to $s$
in an appropriate (external) context, whereas scenes and stories classify $s$ `internally'
as a situation type. In terms of situation theory, the provision of an {\it explanation\/}
for a scene \ $s \models \rho$ \ comprises a determination of an appropriate supporting
situation $w$ and an object type $T$ having $w$ as the grounding situation, such that:
$$\begin{array}{rl}
1. & w \models \ll \mbox{\rm of-type}, s, T, 1 \gg \\[.1in]
2. & w \models T \Rightarrow [\para{s} \mid \para{s} \models \rho].
\end{array}$$


\section{A situation-theoretic account of fault repair}

The call and clearance texts are intended to provide descriptions of the fault in the system
and the corrective action taken by the field engineer. Since the grammar we  develop is
based on the interpretive strategy the reader of the {\small PRF} must adopt in order to
recover from the various entries an understanding of what happened, we need to have
available a sufficiently formal account of the activity of fault repair.

Consider what happens in the field. Let $s$ be the repair situation; this has the field
engineer, $e$, and the faulty computer system, ${\cal S}$, as constituents, it supports the
various constraints that constitute $e$'s technical expertise, and it includes, as a
subsituation, the site visit, which starts at a time $t_{v_1}$ and ends at a time $t_{v_2}$,
where $t_r < t_{v_1} < t_{v_2} < t_c$.

The following two aspects of the engineer's expertise are particularly relevant to us here:
\begin{enumerate}
\item the engineer can locate a fault and recognize the type, $F$, of a particular
      fault;
\item the engineer can associate with the fault-type, $F$, an appropriate action-type,
      $A$, designed to correct the fault.
\end{enumerate} We shall denote by ${\cal E}$ the map that takes the fault-type $F$ to the
corresponding action-type $A$, $A = {\cal E}(F)$.

Let Perf$(e,f,A,t)$ be the relation that, at time $t$, the individual $e$ has completed
(performed) an action of type $A$ to the object $f$.

At the outset of the repair, we have, for some component $f$:

\medskip

(1) \hfill $s \models \ll$faulty$, f, t_{v_1}, 1 \gg$ \hfill \phantom{(1)12345}

\medskip

\noindent and the task facing $e$ is to determine $f$. Moreover, $e$ seeks to determine a
type $F$ such that:

\medskip

(2) \hfill $s \models \ll$fault-type$, f, F, t_{v_1}, 1 \gg$ \hfill
\phantom{(2)12345}

\medskip

Given $F$, $e$ performs an action of type $A = {\cal E}(F)$ so that:

\medskip

(3) \hfill $s \models \ll$Perf$, e, f, A, t_{v_2}, 1 \gg$ \hfill \phantom{(3)12345}

\medskip

(4) \hfill $s \models \ll$faulty$, f, t_{v_2}, 0 \gg$ \hfill \phantom{(4)12345}

\medskip

In carrying out the repair, the engineer is following the constraints:

\medskip

(5) \hfill $[\para{s} \mid \para{s} \models \ll$faulty$, \para{f}, \para{t_r}, 1\gg]
\Rightarrow [\para{s} \mid \para{s} \models \ll$faulty$, \para{f},
\para{t_c}, 0\gg]$ \hfill \phantom{(5)12345}

\medskip

(6) \hfill $[\para{s} \mid \para{s} \models \ll$fault-type$, \para{f}, \para{F},
\para{t}_{v_1}, 1\gg] \Rightarrow [\para{s} \mid \para{s} \models \ll$Perf$,
\para{e}, \para{f}, \para{{\cal E}}(\para{F}), \para{t}_{v_2}, 1\gg]$ \hfill
\phantom{(6)12345}

\medskip

\noindent The first of these is the general repair constraint ``If something is faulty, then
fix it.'' Constraint (6) expresses the repair procedure the engineer follows, namely to act
in accordance with the function ${\cal E}$. Both of these constraints will hold saliently in
$s$. The engineer will be successful providing the following constraint is also valid in $s$:

\medskip

(7) \hfill $[\para{s} \mid \para{s} \models \ll$Perf$, e, f, A, t_{v_2}, 1\gg]
\Rightarrow [\para{s} \mid \para{s} \models \ll$faulty$, f, t_{v_2}, 0\gg]$ \hfill
\phantom{(7)12345}

\medskip

A person reading the {\small PRF} is intended to come to learn of the events that take place
in $s$ by virtue of the facts:

\medskip

(8) \hfill $u \models \ll$describes$, \theta_1, F, 1\gg$ \hfill \phantom{(8)12345}

\medskip

(9) \hfill $u \models \ll$describes$, \theta_2, A, 1\gg$ \hfill \phantom{(9)12345}

\medskip

\noindent where $u$ is the situation that comprises the constraints involved in completing a
{\small PRF}, including writing the call text and clearance text to record what happened.
Note that $u$ is a subsituation of both ${\cal C}$, where the {\small PRF} is completed, and
${\cal P}$, where it is read.

In reading a completed {\small PRF}, what does the reader need to know---indeed, what {\em
can} the reader know---in order to construct an understanding of what happened? In answering
this question, we shall first of all ignore the issue of the mechanisms used to interpret
the call text and the clearance text, that is to say, the features of these texts that,
under normal circumstances, enable the reader to come to know what the fault was and what
the corrective action was. We shall concentrate instead on how the reader comes to the
appropriate understanding of the events in the field, assuming these texts are correctly
comprehended. In particular, we are interested in the different interpretive strategies that
are required in order to understand each of our three different {\small PRF} examples.

Certainly, a typical reader has no direct access to any of the facts (1), (2), (3), (4), and
(7), since each of these are actual events in the field. But, in order to understand the
{\small PRF}, the reader surely needs to be aware of the constraints (5) and (6) (which are
both parametric, and not specific to $s$) and of the validity in $s$ of the parameterized
version of (7), namely:

\medskip

(7)$'$ \hfill $[\para{s} \mid \para{s} \models \ll$Perf$, \para{e}, \para{f}, A,
\para{t}_{v_2}, 1\gg] \Rightarrow [\para{s} \mid \para{s} \models \ll$faulty$,
\para{f}, \para{t}_{v_2}, 0\gg]$ \hfill \phantom{(7)$'$12345}

\medskip

\noindent (Note that $A$ is not parameterized. The reader knows $A$ by virtue of (9).)

\medskip

In other words, the reader needs to have an understanding of the general principles of fault
repair. In particular, the reader needs to assume the {\it existence\/} of a fault-repair
strategy, ${\cal E}$, though knowledge of the details of this strategy are neither necessary
nor, in general, available.


\section{Grammatical structure of the PRF}

Our grammar is concerned with the `rules' that enable particular {\small PRF} entries
both to satisfy the style constraints of the document and to enable the completed form to
be used as medium of communication.

We assume that the formal features of the {\small PRF}, in addition to directing or 
prescribing how the form should be filled in correctly, serve the functional purpose of 
integrating the formal structure of the document with patterns of its use. The two 
aspects of the {\small PRF}, as a stylized document and as a medium of communication,
are described and formalized in terms of interactive linguistic processes, meaning
that the {\small PRF} can be properly understood only if both its form and its 
function  fit together. Our grammar is therefore intended to explain this fit as
precisely and  systematically as possible. 

Our analysis differs from most linguistic studies with respect to the data for which we are
attempting to write a grammar. Even a superficial glance at a {\small PRF} illustrates that
the language forms are unusual. Most linguistic grammars do not concern themselves with
codes and abbreviations, which appear in the first part of the {\small PRF}, or with
ungrammatical strings of the kind found in the call and clearance texts.

Focusing on the language data in the call and clearance texts, we make the following 
observations:
\begin{itemize}
\item the strings are often ungrammatical or elliptical;
\item the informational value of strings in not dependent on their grammaticality or other
       kind  of correctness, but on contextual background that provides any missing
       information;
\item interpretation strategies do not rely on any pre-established sequence of information 
      coming in or becoming available to the interpreter.
\end{itemize}

On the basis of this, we make the following assumptions about the nature of a grammar
suitable for our purposes:
\begin{enumerate}
\item the grammar should be based on informational structure, not just syntactic structure;
\item the contextual information in the document intension compensates for any lack of
      explicit information in the call or clearance text;
\item links between call and clearance texts enable non-sequential retrieval of
      information.
\end{enumerate}

It should be emphasized that, in approaching the {\small PRF} as a carrier of information,
we are not concerned with syntactic correctness; a completed {\small PRF} will be `good' if
the desired information can be extracted from it. Though the call and clearance texts are
often `ungrammatical', they are generally predictable---they are, ofter all, about fault
identification and repair.

We are not aware of any existing grammar that can serve our purposes.

The grammar we introduce has two distinct but related components, reflecting the two
distinct parts of the documents: the identification part and the fault/repair
descriptions.

We assume that among the types individuated by the expert reading the {\small PRF} are
the following:
\begin{quote}
{\it site, customer, system, owns, visit, faulty, site-no, customer-name, system-type,
part-of, date-call-received, date-fault-corrected, no-of-visits, type/bar-no, serial-no,
unit-type, fault-reported, fault-cleared, call-text, clearance-text, parts-used,
refers-to.}
\end{quote}
Moreover, the expert knows the role these types play in the {\small PRF} world: for
instance, a {\it customer} is a person or an organization that {\it owns} a particular
computer {\it system}, a {\it site-number} is an integer the company uses to {\it
refer-to} a particular {\it site}, etc.

These types are constituents of the {\it intension} of the {\small PRF}. In order to
give the formal definition of the intension, we need the following restricted parameters
(given here with their type-restrictions):
$$\begin{array}{rclrcl}
\para{S} &:& \mbox{\rm a computer system} &
     \para{N} &:& \mbox{\rm a site number}\\
\para{p} &:& \mbox{\rm a customer} &
     \para{M} &:& \mbox{\rm a customer name}\\
\para{l} &:& \mbox{\rm a location} &
     \para{T} &:& \mbox{\rm a system type}\\
\para{U} &:& \mbox{\rm a unit type} &
     \para{b} &:& \mbox{\rm a type/bar number}\\
\para{k} &:& \mbox{\rm a serial number} &
     \para{f} &:& \mbox{\rm a component in a computer system}\\
\para{t}_a &:& \mbox{\rm a time-interval} &
     \para{t}_r, \para{t}_c &:& \mbox{\rm times}
\end{array}$$
where $\para{t}_r$ and $\para{t}_c$ are within the interval $\para{t}_a$, and
$\para{t}_r$ precedes $\para{t}_c$.

Given a {\small PRF} $D$, with call text $\theta_1$ and clearance text $\theta_2$, the {\it
intension} of $D$, denoted by ${\cal I}(D)$, is defined to be the following compound
infon:

$$\begin{array}{lclc}
{\cal C}(D) = & & & \\[.1in]
\llangle \mbox{\it site-no}, \para{S}, \para{N}, \para{t}_a, 1 \rrangle &\wedge&
\llangle \mbox{\it type-of}, \para{S}, \para{T}, \para{t}_a, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it owns}, \para{p}, \para{S}, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it name-of}, \para{p}, \para{M}, \para{t}_a, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it located-at}, \para{S}, \para{l}, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it system-type}, \para{S}, \para{T}, \para{t}_a, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it part-of}, \para{f}, \para{S}, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it type-of}, \para{f}, \para{U}, \para{t}_a, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it type/bar-no}, \para{f}, \para{b}, \para{t}_a, 1 \rrangle &\wedge&
\llangle \mbox{\it serial-no}, \para{f}, \para{k}, \para{t}_a, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it faulty}, \para{f}, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it operational}, \para{S}, \para{t}_c, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it fault-reported}, \para{S}, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it fault-cleared}, \para{S}, \para{t}_c, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it call-text}, \theta_1, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it clearance-text}, \theta_2, \para{t}_c, 1 \rrangle &\wedge
\\[.01in]
\llangle \mbox{\it refers-to}, \theta_1, \para{f}, \para{t}_r, 1 \rrangle &\wedge&
\llangle \mbox{\it refers-to}, \theta_2, \para{f}, \para{t}_c, 1 \rrangle &
\end{array}$$

\medskip

By an {\it infomorphism} from $D$ to ${\cal C}$ we mean an anchor, $\sigma$, for all the
parameters in ${\cal I}(D)$ to objects in ${\cal C}$, such that $${\cal C} \models {\cal
I}(D) [\sigma].$$ In the case such an infomorphism $\sigma$ exists, the object
$\sigma(\para{x})$ to which a particular parameter \para{x} in $D$ is anchored is called
the {\it referent\/} of \para{x}.

\medskip

When an infomorphism $\sigma$ exists, the compound infon ${\cal I}(D) [\sigma]$ serves
to identify the system reported faulty, the faulty unit, the date the fault was
reported, the date the fault was declared corrected, the various reference names and
numbers associated with the faulty system, and the two texts, the call text and the
clearance text. It also provides the relevant informational links between these items,
in particular, the fact that they all refer to the same system, $\sigma(\para{S})$.

The {\small PRF} is designed so that, if every slot in the form is correctly filled-in,
then there will be an infomorphism, and the {\small PRF} will refer, via that
infomorphism, to real objects and real events in the world.

The second part of the grammar associates structure with the call and clearance text.

First, we observe that an expert reading a completed {\small PRF}, having read the initial,
identificational part of the form, approaches the task of understanding the call text and
the clearance text under the guidance, in general implicit, of various {\it genre
maxims}, which we describe in \cite{devros4}. In addition to the genre maxims, we formulate a
number of other rules and maxims that govern the completion and/or interpretation of the
forms. These are also listed in \cite{devros4}.

Let \ $T_{\mbox{\scriptsize\it call}}$ \ denote the fault type specified by the call text
and let \ $T_{\mbox{\scriptsize\it fault}}$ \ be the type of the actual fault. Let
\ $T_{\mbox{\scriptsize\it clear}}$ \ be the action type specified by the clearance
text and let \ $T_{\mbox{\scriptsize\it action}}$ \ be the type of the actual corrective
action taken at the site. Relating this to the discussion of the previous section, we
have  \ $T_{\mbox{\scriptsize\it fault}} = F$ \ and \ $T_{\mbox{\scriptsize\it action}} =
A$.

Specifically, let
$$\begin{array}{ll}
T_{\mbox{\scriptsize\it call}} = [\para{r} \mid \para{r} \models &
  \ll \mbox{\rm call text}, \para{\theta}, d, 1 \gg \wedge\\
& \ll \mbox{\rm contains term}, \para{\theta}, \para{\tau}_c, 1 \gg \wedge\\
& \ll \mbox{\rm referent type}, \para{\tau}_c, T_{\mbox{\scriptsize\it component}}, 1 \gg 
     \wedge\\
& \ll \mbox{\rm containsterm}, \para{\theta}, \para{\tau}_f, 1 \gg \wedge\\
& \ll \mbox{\rm referent type}, \para{\tau}\!_f, T_{\mbox{\scriptsize\it fault}}, 1 \gg 
     \wedge\\
& \ll \mbox{\rm appropriate for}, \para{\tau}\!_f, \para{\tau}_c, 1 \gg \wedge\\
& \ll \mbox{\rm refers-to}, \para{\tau}_c, \para{f}, 1 \gg \wedge\\
& \ll \mbox{\rm refers-to}, \para{\tau}\!_f, \para{F}, 1 \gg ]
\end{array}$$
where $\para{r}$ is a parameter for the situation comprising the reading and interpretation
of the {\small PRF} $d$, and where $\para{f}$ and $\para{F}$ are as in the previous
section.

Intuitively, to say that a situation $r$ is of type $T_{\mbox{\scriptsize\it call}}$ is to
say that in the document $d$ that forms the focus of the reading in $r$, the call text
$\para{\theta}$ contains a term $\para{\tau}_c$ that refers to a component $f$ (to which
the paramter \para{f} is anchored) and a term $\para{\tau}_f$ that refers to a fault-type
$F$ (to which the parameter \para{F} is anchored), and moreover, the fault referred to is
appropriate for the component referred to.

Again,
$$\begin{array}{ll}
T_{\mbox{\scriptsize\it fault}} = [\para{s} \mid \para{s} \models &
     \ll \mbox{\rm faulty}, \para{f}, \para{t}_{v_1}, 1 \gg \wedge\\
& \ll \mbox{\rm fault-type}, \para{f}, \para{F}, \para{t}_{v_1}, 1 \gg]
\end{array}$$
where $\para{s}$ is a parameter for the computer system situation.

The formal definitions of the types $T_{\mbox{\scriptsize\it clear}}$ and
$T_{\mbox{\scriptsize\it action}}$ are similar.

Let $FC$ (`fault constraint') denote the constraint
$$T_{\mbox{\scriptsize\it call}} \Rightarrow T_{\mbox{\scriptsize\it fault}}$$ that links
the call text with the fault and let $RC$ (`repair constraint') denote the constraint 
$$T_{\mbox{\scriptsize\it clear}} \Rightarrow T_{\mbox{\scriptsize\it action}}$$ that
links the clearance text with the repair action. Further, let $EC$ denote the engineer's
constraint
$$T_{\mbox{\scriptsize\it fault}} \Rightarrow T_{\mbox{\scriptsize\it action}}$$ that
connects the fault to the action taken to repair the fault. ($EC$ was discussed in the
previous section.)

In a perfect fault-repair world where the {\small PRF} is accurately and informatively
filled in, the following neat and comforting picture obtains:
$$\begin{array}{rcccl}
 & T_{\mbox{\scriptsize\it call}} & & T_{\mbox{\scriptsize\it clear}} & \\[.1in]
\mbox{\small\it FC} & \Downarrow & & \Downarrow & \mbox{\small\it RC}\\[.1in]
 & T_{\mbox{\scriptsize\it fault}} & \Longrightarrow & T_{\mbox{\scriptsize\it action}} &
\\
          &  & \mbox{\small\it EC} &  &
\end{array}$$

In the ideal situation, the reader is familiar with
the constraints
$FC$, $RC$, and $EC$, all of which are supported by the `fault reporting/repair
situation', and the reader's task is to determine \ $T_{\mbox{\scriptsize\it fault}}$
\ and \ $T_{\mbox{\scriptsize\it action}}$ \ to fit the above diagram, given
\ $T_{\mbox{\scriptsize\it call}}$ \ and \ $T_{\mbox{\scriptsize\it clear}}$.

The reader faced with a {\small PRF} in which the entries are not sufficiently precise to
allow use of one or both of the constraints $FC$, $RC$ has to search for additional
information to compensate.

On the face of it, there are four possibilities:
\begin{enumerate}
\item $FC$ obtains, $RC$ obtains;
\item $FC$ fails, $RC$ obtains;
\item $FC$ obtains, $RC$ fails;
\item $FC$ fails, $RC$ fails.
\end{enumerate}
(The engineer's constraint, $EC$, concerns the activity in the field, not its reporting on
the {\small PRF}, so it does not figure in this interpretation taxonomy.)

The first of the four cases listed above is straightforward; it corresponds to what we have
been calling a `scene'.

In the second case, the information obtained from $RC$ (i.e.  $T_{\mbox{\scriptsize\it
clear}}$) has to be used to compensate for the lack of $FC$. There are two possiblities. In
the first case, which corresponds to our notions of a `story', $T_{\mbox{\scriptsize\it
fault}}$ can be deduced from \ $T_{\mbox{\scriptsize\it clear}}$ \ and $EC$ as `reverse
information'. This is the strategy known as Rose's gloss. On the other hand,
if \ $T_{\mbox{\scriptsize\it clear}}$ \ does not correspond to $EC$, that is to say, if
$EC$ is not sufficient to yield \ $T_{\mbox{\scriptsize\it fault}}$ \ from
\ $T_{\mbox{\scriptsize\it clear}}$, then the reader has to look for a constraint other
than (or in addition to) $EC$ that will enable $T_{\mbox{\scriptsize\it fault}}$ to be
deduced from \ $T_{\mbox{\scriptsize\it clear}}$. If successful, this is the case we 
refer to as an `explanation'.

The third case in the above list is ruled out by the {\small PRF} maxims.

If the fourth possibility arises, it is not possible to reconstruct events from the
document. (For example, the `band errors--band errors' case mentioned above.)

These possible strategies for understanding a completed {\small PRF} may be displayed on a
`parse' tree, though for our grammar the tree is a tree of interpretive strategies, not
syntatic structure. 

The {\it grammatical structure\/} of a given {\small PRF} ${\cal D}$ is defined to be a
pair
$${\cal G(D)} = \langle {\cal I(D)}, {\cal S(D)} \rangle$$
consisting of the document intension ${\cal I(D)}$ and a finite sequence
$${\cal S(D)} = \langle \pm FC, \pm RC, \pm EC, \pm \mbox{\it ?}C \rangle$$
where, for each entry in the finite sequence, at most one sign is chosen, and where the
resulting sequence has to represent a path through the tree. (If no sign is chosen for an
entry in the sequence, that entry does not appear.) The second component of the grammatical
structure, the finite sequence ${\cal S(D)}$, is called the {\it interpretive strategy\/} of
the document.

{\small PRF}s having the interpretive strategy \ $\langle +FC, +RC \rangle$ \ are said to
be in the category {\it scene}. {\small PRF}s having the interpretive strategy \ $\langle
-FC, +RC, +EC \rangle$ \ are said to be in the category {\it story}. {\small PRF}s having
the interpretive strategy \ $\langle -FC, +RC, -EC, +\mbox{\it ?}C \rangle$ \ are said to
be in the category {\it explanation}. A {\small PRF} having any other interpretive
strategy is said to be (informationally) {\it bad}.

By analyzing the tree, we are able to prove the following theorem.

\medskip

\noindent{\bf Theorem}. {\it There are exactly three basic interpretive strategies that can
lead from a completed {\small PRF} to an understanding of what happened in the field.}

\medskip

This theorem tells us that our previous taxonomy of interpretive strategies (scenes,
stories, and explanations) is exhaustive. In terms of the tree, the theorem corresponds to
the fact that there are exactly three paths through the tree that lead to an informative
interpretation of the document.


One question that remains to be answered is this. Having recognized the string in the call
text slot as of type $T_{\mbox{\scriptsize\it call}}$, how does the expert determine
whether the situation $+FC$ or $-FC$ obtains, and then similarly for the clearance text?

The most natural assumption is that the expert can judge the situation to be $+FC$ if the
text itself is sufficiently informative.

The {\small PRF} is effective in conveying information, and we explain this effectiveness in
terms of the wealth of referential information provided by:
\begin{enumerate}
\item the linguistic context of the form captured by the document intension;
\item the contextual background information concerning the nature and purpose of the
forms, as captured by the genre maxims;
\item the communicative aim of the call and clearance texts, captured by the constraints
concerning general principles of fault repair.
\end{enumerate}
When all of these have made their contributions to the referential information, the expert
can decide whether or not there is sufficient information to proceed.



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\end{document}


char 11 reqs adj as keeps moving to the right.



