# Paper on consensus knowledge acquisition

davis@ai.mit.edu (Randall Davis)
From: davis@ai.mit.edu (Randall Davis)
Date: Wed, 3 Apr 91 20:52:00 est
Message-id: <9104040152.AA17727@hatcher.ai.mit.edu>
To: srkb@isi.edu
Subject: Paper on consensus knowledge acquisition


Below is a paper describing the work on consensus knowledge that I discussed
at the Workshop.

R.

+++++++++++++++++++++

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\begin{document}
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\begin{center}
{\Large
Consensus Knowledge Acquisition\footnote{\noindent This report
describes research done at the Artificial Intelligence Laboratory of the
Massachusetts Institute of Technology.  Support for the laboratory's artificial
intelligence research is provided in part by the Advanced Research Projects
Agency of the Department of Defence under Office of Naval Research contract
N00014-85-K-0124.  Additional support for this research was provided by the
International Financial Services Research Center of the MIT School of
Management, Digital Equipment Corporation, McDonnell Douglas Space Systems,
General Dynamics Corp, and the Faculty of Commerce at the University of British Columbia.}

\skipl{1}
}
Andrew Trice\\
(Andrew\_Trice@mtsg.ubc.ca)\\
Faculty of Commerce\\
2053 Main Mall\\
University of British Columbia

\skipl{1}
Randall Davis\\
(davis@ai.mit.edu)\\
MIT Artificial Intelligence Lab\\
545 Technology Sq.,  Room 801\\
Cambridge, MA 02139\\
(617) 253-5879
\end{center}

\skipl{2}

\centerline{\bf Abstract}

We have developed a method and prototype program, called {\sc carter}, that
assists two experts in agreeing on what knowledge should go into a single,
consensus knowledge base, i.e., a knowledge base that reflects the best
judgment of each of them.  We show that consensus building can be effectively
facilitated by a debugging approach that identifies, explains, and resolves
differences in the knowledge of the two experts.  {\sc carter}'s expertise is
in the task of consensus building; its knowledge base is a collection of some
35 entries, each made up of a discrepancy detection procedure and a
corresponding resolution procedure.  Examples of the use of this knowledge are
illustrated with descriptions of the program in operation, assisting with the
reconciliation of two independently developed knowledge based systems.

A significant part the program's task lies in finding the places where the two
knowledge bases match (e.g., two concepts that may be labeled differently but
actually mean the same thing), where they differ, and where they overlap.  The
program displays an interesting degree of success in using circumstantial
evidence in the knowledge bases themselves to help infer the degree of overlap
in the intended meaning of concepts.  We also show that the same fundamental
technique is necessary for matching any two independently constructed
representations, and that the richer the set of primitives provided by the
representation in use, the more confidence we can place in the circumstantial
evidence that is available.

\newpage\section{INTRODUCTION}
\setcounter{page}{1}

There is a curious contradiction in the current state of practice of knowledge
acquisition: At a time when the view is widely shared that valuable knowledge
is often distributed among multiple experts, common practice in knowledge
acquisition still focuses on acquiring the knowledge of a single individual.
At best, system builders may work with multiple experts by appointing one of
them as knowledge czar'' and giving him the final word in any dispute, or
they may simply require the experts to achieve consensus on their own, without
providing any substantive assistance.

Multi-expert acquisition techniques that have been proposed to date have
significant shortcomings.  Work based on mathematical formulations [6] tends
to be very restrictive; adaptations of established group decision-making
techniques [9] offer little insight on the issue of consensus; methods like
[2,18] focus on simply using knowledge from multiple sources rather than
finding and resolving the inconsistencies; while methods like [7] provide only
very basic assistance in detecting potential inconsistencies.

Our research is focused on developing ideas and tools to facilitate the
process by which multiple experts construct a single, consensus knowledge
base, the process of consensus knowledge acquisition (CKA).  We have developed
a system called {\sc carter} that is capable of aiding pairs of experts in
this process, by systematically finding, explaining, and suggesting
resolutions for discrepancies in their knowledge.

\section{HOW CAN WE HANDLE MULTIPLE EXPERTS?}

The problem of reconciling multiple points of view has been an issue of study
for some time in a number of different areas.  Unlike previous work that has
focused either on combining decision outcomes [15,1] or supporting the process
of logical argumentation [5,13,21,23], our concentration is on getting agreement
on the knowledge itself.

We do not want to focus on outcome alone, because we believe that the
fundamental task is to reach consensus on the knowledge itself: differences in
outcome may simply be symptoms of a disagreement about what to know.  We
choose not to focus on argumentation in the belief that the knowledge
representation in use provides an appropriate framework for structuring the
discussion.  Instead we seek to assist the experts in detecting, deliberating
over and reconciling discrepancies in their knowledge.  Our approach is
normative and focused on the underlying knowledge used by each expert: we want
to understand how experts ought to come to agreement and we want that
agreement to be about the thing we consider to be fundamental to this
undertaking---the knowledge used to make the decisions.

\section{BOUNDING THE PROBLEM}

Several assumptions help bound the task.  First, we assume the expertise to be
reconciled is homogeneous in the sense that both experts are capable of
solving the entire problem.  This enables us to focus on resolving
discrepancies rather than combining knowledge from disparate fields.

Second, we assume the experts have constructed individual knowledge bases
(KBs) prior to the start of the process.  This ensures that the experts can
explain the reasoning they used to arrive at their answers and that that
reasoning can be adequately captured by a known reasoning process.  This in
turn allows us to focus on knowledge debugging rather than knowledge
acquisition.

This assumption presents some limits: knowledge bases are difficult enough to
build that duplicates are infrequently encountered.  They do, however, occur,
hence the assumption is plausible.  The assumption also gives us a place to
start work on a fundamentally difficult problem.  In addition, as we have
speculated [22] and other work has demonstrated [14], the process of knowledge
acquisition with a single expert can itself be viewed as establishing
consensus: in this case consensus between the expert's view of the domain and
the view currently embodied in the knowledge base.

Third, we assume that the experts already have some shared frame of reference,
some basic set of terms and assumptions in common.  Without that, determining
where they agree and disagree would be difficult, not only for our system, but
for any human attempting the task.  Note, however, that we do not know in
advance which terms those are; we presume only that there is some overlap, up
to us to discover.  Note, too, that the only information available to our
system about the meaning of a term is to be found in the knowledge bases
themselves; the system must use that information to infer whether two terms
were intended to mean the same thing.

Finally, a hypothesis fundamental to our approach is that a consensus KB can
perform better than an individual expert's KB.  Our belief is that unearthing
and resolving differences between two experts will be fundamentally
synergistic, removing limitations and defects in both of their knowledge.
This is plausible but of course not guaranteed: some consensus knowledge bases
may not be as good as either of the originals.

\markright{CARTER}\section{CARTER$^{1}$}\markright{CARTER}
\footnotetext{Conflict AnalyzeR for Targeted Expert Resolution}

Our prototype system plays the role of a non-binding arbitrator mediating
between two experts, each of whom has constructed a knowledge base.  {\sc
carter} examines each knowledge base, looking for matches and discrepancies
between them, decides which discrepancy to try to resolve, and suggests
possible resolutions.  The two experts discuss the suggested resolutions and
can choose to update their individual KBs as suggested, update them in some
other manner, or not update them at all.\footnote{That is, we allow them to
agree to disagree.''} The individual KBs are then analyzed anew, until no
new discrepancies can be found.

As one of its first tests, we used the program to assist two statisticians
(Bruce and John) in reconciling two knowledge-based application systems they
designed to assist novice statisticians in detecting and repairing problems in
applying linear regression models.\footnote{Linear regressions model the
relation between two variables as a linear function and indicate how well the
model fits the (possibly noisy) data.} While the modeling process involves
straightforward arithmetic formulae, there is considerable expertise in
knowing the conditions on use of those formulae, determining when the data do
not satisfy those conditions, and selecting possible corrective actions.  The
statistician's assistant system built by each expert captured some part of
this expertise.  The systems test for validity of the assumptions of linear
regressions (e.g., the independent variables are not correlated) to prevent
spurious interpretations of data, and they suggest alternatives for improving
the model (e.g., model transforms, removing an outlying point from the
dataset).

Bruce's knowledge base contained 54 rules, John's 32.  The rule language was
essentially identical to {\sc mycin}, with rules constructed from attribute,
object, value triples (e.g., if the {\tt Defect} of the {\tt Model} is {\tt
Multicollinearity} \ldots), plus a degree of certainty.  The attributes,
objects, and values are the primitive vocabulary of each system; Bruce's
knowledge base had a total of 108 such terms, John's had 70.

As a {\sc mycin} equivalent, the rule language was of the complexity used to
build many real-world application systems and was sufficiently complex to
provide an interesting challenge when attempting to match concepts.  With a
few dozen rules, the knowledge bases were of modest size, but each was
the underlying application systems were modest but real examples of knowledge
based systems.

Rule based systems were chosen as a testbed for several reasons.  First, the
wide use of rules meant that real examples of knowledge bases were available,
providing realistic data about the kinds of discrepancies that
arise.\footnote{John's knowledge base had been built as an MS thesis in 1986;
we provided Bruce with a high level description of the problem solved by
John's system and asked Bruce to independently create a knowledge base on the
same topic.}  Second, wide use of rules also means that the specific techniques
developed in this work could be widely applicable.  Finally, since (as we
demonstrate below) the fundamental issue of matching representations arises
everywhere, all of the difficult problems arise in working with rules, even
though they are a relatively modest representation mechanism.

In analyzing the two knowledge bases {\sc carter} was able to identify 49 out
of the total of 76 of discrepancies that existed between them.  When working
with the experts to help them reach agreement, {\sc carter} was able to assist
them in repairing 15 of these discrepancies; this lower figure was determined
primarily by the time available from the experts.  We illustrate the system's
knowledge and performance with examples drawn from this application,
simplified slightly for the sake of presentation.

{\sc carter}'s fundamental task is to determine how and where the knowledge
bases match and where they differ.  While the knowledge bases may be
meaningful to the experts, to {\sc carter} of course they are simply elaborate
directed graphs.  The system's task is interesting precisely because a purely
syntactic match of the graphs is of relatively little value, hence this is not
a standard graph matching problem.  To provide useful assistance {\sc carter}
must be able to infer that two concepts that happen to be named differently in
the two KBs might in fact mean the same thing, or infer that two concepts that
happened to be named identically are actually being used differently in the
two knowledge bases.

Strictly speaking, the task is impossible for {\sc carter} to accomplish
alone, because only the experts themselves can know for sure what they actually
meant.  The best {\sc carter} can hope to do is make educated and informed
guesses.  The system approaches the task with this mindset, trying to find
places of most plausible match and most likely discrepancy, then presenting
the human experts with its findings and asking for confirmation.  The system's
utility is thus in asking a small set of well chosen questions, presenting the
two experts with the right agenda of things to discuss (possible discrepancies
and potential repairs), then making it easy to effect those repairs.  The
system's effectiveness is determined by how well it can focus that discussion
down from the complete space (the crossproduct of concepts from the two KBs)

To do this {\sc carter} relies on three forms of knowledge: a knowledge base
about the kinds of discrepancies that can arise, a strategy for attacking
those discrepancies in a particular order, and a body of circumstantial
evidence it accumulates to infer whether two apparently different concepts in
fact mean the same thing.

{\sc carter}'s knowledge is organized in a catalog currently containing 35
entries, each of which in turn consists of a discrepancy detection procedure
and a corresponding resolution procedure.  This simple detection-resolution
organization of the catalog facilitates adding new entries as we gain more

Among the types of discrepancies that {\sc carter} can recognize and repair
are:
\skipl{-.3}
\begin{enumerate}
\item  Differences in the {\em character of the result}: one system is content
to classify the problem (e.g., specify the nature of a defect in the data,
like {\tt Heteroscedasticity}), while the other both classifies the problem
and then goes on to suggest what to do about it (e.g., do a {\tt
Log-Transform}).
\skipl{-.3}
\item  Differences in {\em vocabularies}: one expert refers to the {\tt
Defects} of a regression model, while the other refers to its {\tt Problems},
but they are referring to the same thing.  Other forms of vocabulary
discrepancy the system knows about include differences in representation
choice (e.g., one expert represents a concept as an attribute, while the other
represents it as a value) and missing terms (e.g., one KB contains values
missing from the other).
\skipl{-.3}
\item  Differences in {\em pattern of inference}: the experts agree on the
overall vocabulary, but interconnect the terms differently, as in the case
where one expert uses only an {\tt F-test} statistic to judge the quality of a
model, while the other relies on both an {\tt F-test} and a {\tt S-squared}
statistic.
\skipl{-.3}
\item  Differences in the {\em rules}: the experts agree on the vocabulary and
pattern of interconnection between terms, but write different rules.  For
example, one expert had a rule that an {\tt F-test} result below a specified
threshold indicated that the {\tt Quality} of the {\tt Model} is {\tt Poor},
while the other reasoned from the same evidence that the {\tt Quality} of the
{\tt model} is {\tt Fair}.  Both reason from the value of the {\tt F-test} to
the {\tt Quality} of the {\tt Model}, but they use different rules.
\end{enumerate}
\skipl{-.3}

\subsubsection{Ordering Strategy}

{\sc carter}'s overall strategy is to attack these in the order given,
beginning by trying to establish agreement on the nature of the outcome.  This
is motivated by both the computational and negotiation character of the task.
Since the computational task is one of matching two KBs that are directed
graphs, any useful guidance about where to start the matching process will
vastly improve the system's chances of making intelligent suggestions.
Expressed in these terms, we anchor the search at the end(s) of the graph,
trying first to match the outcomes, relying on the heuristic that two KBs
about the same topic are likely to have the same concept(s) as their
goal(s).\footnote{If the KBs have more than one outcome, there is an $n^{2}$
problem in matching the outcomes, but this $n$ involves only a very few of the
total set of concepts in the KBs.} This also makes sense from the negotiation
point of view: it is difficult to imagine an effective discussion about the
details if the two knowledge bases are trying to arrive at different kinds of
conclusions.

Establishing a discrepancy (or correspondence) in the nature of the outcome(s)
typically requires dealing with the second task, discrepancies in vocabulary,
because the experts may simply have named the goal(s) differently.

The process then works backward a level at a time, attempting to match the
nodes (the vocabulary) directly connected to the outcome.  Once this is
accomplished the system can focus on the patterns of inference that link these
nodes with the goal.  This in turn enables comparison of the specific rules
that establish the goal in each KB.

The process continues from there, moving back one level at a time through the
knowledge base, attempting to establish correspondence.  The system is also
opportunistic in the expected sense, working from any islands of agreement it
discovers.

This overall approach, working from goal node to vocabulary, to topology, to
specific rules, has proved to be a powerful way to focus the attention of both
our system and the human experts working with it, on a task that might
otherwise present an overwhelming amount of detail.

\subsection{An Example}

The examples below show {\sc carter}'s first few steps in finding and
resolving discrepancies in the two KBs, and illustrates 3 of the 35 types of
discrepancies it can detect and resolve.\footnote{The dialog {\sc carter}
presents is quite straightforward, constructed from simple text templates that
ask multiple choice questions, and is omitted here to save space.  A detailed
example can be found in [22].}

\subsubsection{Matching Vocabularies: Circumstantial Evidence of Semantic Match}

In the example at hand, {\sc carter} identifies the goal of Bruce's KB as {\tt
Solution} and John's as {\tt Defect}.  The concepts are named differently, but
perhaps the two experts meant the same thing and simply happened to choose
different names?  {\sc carter}'s most fundamental task is to determine whether
this is the case.  To do this it accumulates four kinds of circumstantial
evidence, available from the knowledge base itself:
\skipl{-.3}
\bitem	 Are the concept labels the same?  In this case they are not ({\tt
Solution \rm vs. \tt Defect}), but this can of course be an artifact of name
choice or (in other circumstances) variations in spelling or abbreviation.
Conversely, a match in labels is useful evidence but no guarantee of match in
meaning.
\skipl{-.3}
\item  In the case of attributes, are they associated with the same object?
The answer here is no, which is reasonably strong evidence of mismatch (a
positive answer is considered only weak evidence of match).
\skipl{-.3}
\item  In the case of attributes, are the values associated with them the
same?  Here the answer is no (e.g., \tt Solution \rm has as values terms like
\tt Log-transform, Deflate-by-x, \rm etc., while \tt Defect \rm has as values
terms like \tt Heteroscedasticity, Multicollinearity \rm etc.).
\skipl{-.3}
\item  Are they inferred from the same concepts and are they in turn used to
infer the same concepts?  That is, do the occupy similar places in the local
topology of the knowledge base?\footnote{Here local'' means exactly one step
away from the concept in either direction, both because of the weakness of the
evidence provided by more distant matches and the expense of complete graph
matching.}  Again in this case the answer is no, accumulating substantial
circumstantial evidence that {\tt Solution} and {\tt Defect} are labels for
genuinely distinct concepts.
\eitem
\skipl{-.3}
Weighing the evidence in the case at hand, {\sc carter} concludes (correctly)
that {\tt Solution} and {\tt Defect} are different concepts, hence there is a
difference in the character of the result provided by each system.  This
matching process is conceptually quite simple, but, as we argue below, an
unavoidable part of the task.  {\sc carter}'s expertise is in the 35 varieties
of discrepancies and repairs it knows, not the simple matching process that
accumulates evidence of the sort noted above.

The system next attempts to classify this discrepancy in more detail.  As
noted, {\sc carter} knows that one of the ways in which this discrepancy can
occur is if the reasoning chain in one system is longer than the other, as for
example if one system only classifies the problem, while the other both
classifies it and goes on to suggest a solution.  To determine whether this is
the case {\sc carter} searches along the reasoning chain in each KB to see
whether it can find the goal attribute of one KB on the route to the goal
attribute in the other KB.  That is, since the two endpoints in the graphs do
not match, perhaps the endpoint in one matches one of the intermediate points
(conclusions) in the other.

{\sc carter} tries to match {\tt Solution} (the endpoint of Bruce's KB) with
the intermediate conclusions in John's KB, using the same criteria of label,
value, and topological correspondence.  When this fails, {\sc carter} attempts
it the other way around, trying to match {\tt Defect} of John's KB with the
attributes on the route to {\tt Solution} in Bruce's KB.  This second version
succeeds when {\sc carter} finds evidence that {\tt Defect} seems to mean the
same thing as {\tt Problem} in Bruce's KB.  Although they are named
differently, they are attributes that happen to share two different values
({\tt Heteroscedasticity} and {\tt Multicollinearity}), and they are in turn
inferred from attributes that themselves appear to match ({\tt Determinant}
and {\tt IV-Determinant}).  This is substantial evidence that these two
differently named concepts---{\tt Problem} and {\tt Defect}---are in fact
identical.

This apparent match enables {\sc carter} to propose a specific diagnosis about
the discrepancy between the two KBs.  Since the goal attribute of John's KB
({\tt Defect}), seems to match a concept on the route to the goal of Bruce's
KB ({\tt Problem}), {\sc carter} concludes that {\tt Solution} is a concept
that reflects an additional inference that only Bruce's KB performs (indicated
schematically in Fig. 1).

\newpage{\tt\parindent 0in
\rule{\textwidth}{.005in}

John's\ \  Knowledge Base: ... $\Rightarrow$ ... $\Rightarrow$\ \ DEFECT

\skipl{.75}

Bruce's Knowledge Base: ... $\Rightarrow$ ... $\Rightarrow$\ \ PROBLEM \ $\Rightarrow$\ \ SOLUTION}

\skipl{1}
\noindent Fig. 1: Aligning the two KBs.\\
\noindent\rule{\textwidth}{.005in}

The generic problem now facing {\sc carter} is that one KB contains a term
missing from the other.  In response the system offers the experts the obvious
choice: either add the missing attribute to the first KB or delete the extra
attribute from the second.

The experts decide to add the missing attribute ({\tt Solution}) to John's KB.
{\sc carter} then indicates the additional work that is necessary: since {\tt
Defect} and {\tt Problem} are the same underlying concept, they must be
reconciled (e.g., a common name chosen).  John must also provide his version
of the rules that take the additional inference step, determining {\tt
Solution} from {\tt Defect}.  Finally, those rules must in turn be compared
with Bruce's and any discrepancy resolved.

\subsubsection{Matching Rules}

After reaching agreement on the ultimate goal for each KB, the system moves
one step back in the inference chain in each, to see which attributes are used
to determine the goal in each KB.  It then uses the techniques just
illustrated to get agreement on those attributes.

Once agreement on them is reached, the system begins to detect and remove
incompleteness and inconsistency in the rules that link them.  An example of
detecting two inconsistent rules arises in examining the rules that each
expert used to determine the {\tt Quality} of the model:

\skipl{-.7}
\bfig
BRUCE's KB                             JOHN's KB
IF F-TEST less-than THRESHOLD         IF F-TEST less-than THRESHOLD
THEN QUALITY of MODEL is POOR         THEN QUALITY of MODEL is FAIR
\end{verbatim}
\efig{Fig. 2:  Two inconsistent rules}
\skipl{-.75}
{\sc carter} knows six ways in which this sort of discrepancy---conflicting
rules---can arise:
\begin{enumerate}
\item  There is a misunderstanding about the vocabulary: {\tt Poor} and {\tt
Fair} could be synonyms, hence the rules are actually identical.  This is
ruled out here because the experts have already agreed on the vocabulary (in a
part of the interaction not shown).
\skipl{-.4}
\item  There is not really a mismatch because both rules should be in both
knowledge bases (each expert forgot one rule that the other
remembered).\footnote{If {\tt QUALITY} were known to be single-valued, this
too could be ruled out, but this version of {\sc carter} didn't have that
information.}
\skipl{-.4}
\item	One of the rules is incorrect and should be removed.
\skipl{-.4}
\item	There is not sufficient precision in the vocabulary terms to
differentiate between the two outcomes, e.g., perhaps we need more than a
single threshold.
\skipl{-.4}
\item	There is chain of inference between {\tt F-TEST} and {\tt QUALITY}
that has not been made explicit in the current KBs and the discrepancy lies
somewhere along that chain.
\skipl{-.4}
\item   Both rules are over-generalized as stated: they are both missing an
attribute whose value constitutes an important unstated assumption that the
experts know, but forgot to make explicit.
\end{enumerate}
\skipl{-.4}
After some discussion, the experts agree that the last possibility is correct,
and that they omitted information about the {\tt R-squared} statistic.  In
response they elaborate their rules to include this, and discovere that they
The two revised rules turn out to be acceptable to both experts.

\skipl{-1}
\bfig
BRUCE's KB                            JOHN's KB
IF F-TEST less-than CRITICAL-VALUE    IF F-TEST less-than CRITICAL-VALUE
& R-SQUARED is NOT-SIGNIFICANT        & R-SQUARED is SIGNIFICANT
THEN QUALITY is of MODEL is POOR      THEN QUALITY of MODEL is FAIR
\end{verbatim}
\efig{Fig. 3: The modified rules.}

\skipl{-1}
{\sc carter} then guides the experts in resolving remaining details about the
new attribute {\tt R-squared}, and continues to look for other places where
the two knowledge bases differ.  The techniques described above allowed {\sc
carter} to find roughly 65\% of the known discrepancies in the two KBs and
allowed it to guide the two experts to consensus on a subset of rules
concerned with the problem of multicollinearity.

\markright{MATCHING REPRESENTATIONS}
\section{Matching Representations: Circumstantial Evidence Is Inevitable}
\markright{MATCHING REPRESENTATIONS}

Rules provide a good way to express inferences, but are not specifically
designed to capture and represent meaning.  Hence {\sc carter} must attempt to
infer the overlap in meaning between two concepts by collecting circumstantial
evidence from the knowledge bases themselves, e.g., comparing how these
concepts are used in the rules and how they relate to other vocabulary terms.
The difficulty here is in using circumstantial evidence to infer whether two
concepts were intended to have the same or different meanings.

Why not then just have definitions for each concept in the knowledge base and
compare the definitions?  That is, build the original domain knowledge bases
so that they contain not only rules built from attribute-object-value triples,
but also have formal definitions for each concept (i.e., each attribute,
object, and value), perhaps definitions of the sort created with predicate
calculus, or other formal representation language (e.g., [3]).  Given formal
definitions of the concepts, it would appear that we could compare those
definitions directly and avoid the need for circumstantial evidence.

But the problem is unavoidable.  If the domain knowledge bases have formal
definitions for their terms, this immediately brings up the question of where
those definitions came from.  If they had already been agreed upon by the
experts, then we are dealing with a situation in which there is a consensus
vocabulary already established.  {\sc carter} would have to deal only with
rule differences, and a substantial part of the consensus task would already
have been done.

While this is a plausible situation, it is one in which most of the consensus
problem has been solved before we get there.

If, on the other hand, each knowledge base has definitions for its concepts,
but these were {\em created independently} (and have not yet been jointly
agreed on), the same fundamental problem arises: given two concepts
represented in independently developed KBs, the only grounds on which to
determine whether they are likely to be the same is the circumstantial evidence
arising from comparing their representations.

The key observation is that two experts working independently will construct
ontologies (ways of looking at the world) that differ in some respects simply
because they were constructed independently.  Given two independently
constructed ontologies, the only grounds on which to decide whether two
concepts are the same is the circumstantial evidence available from comparing
their representations.

A specific example from a common sense domain will help illustrate the point.
Assume our first expert defines the concept of a {\tt satisfied-parent} as a
parent with at least two children, all of whom are professionals.''  A {\sc
kl-one} style representation of this would look something like:

\noindent\rule{\textwidth}{.005in}
\begin{verbatim}
satisfied-parent    a-k-o         parent
role    children      (value-restriction professional)
(number-restriction >= 2)
\end{verbatim}\noindent\rule{\textwidth}{.005in}

\noindent
A parent would be further defined as {\tt a-k-o human}, etc.

The second expert, working independently, decides to define what we as
onlookers happen know is the same concept, but phrases it slightly
differently: a {\tt happy-parent} is a parent with at least two offspring,
all of whom have professional degrees:''

\noindent\rule{\textwidth}{.005in}
\begin{verbatim}
happy-parent    a-k-o          parent
role    offspring      (value-restriction professional-degreed)
(number-restriction >= 2)
\end{verbatim}\noindent\rule{\textwidth}{.005in}

Now suppose {\sc carter} attempted to match up {\tt satisfied-parent} in one
KB with {\tt happy-parent} in the other, in an effort to determine whether
they actually meant the same thing (i.e., the experts would agree that they
had the same concept in mind).  The only form of evidence available to the
machine is the circumstantial evidence arising from matches (and mismatches)
in the representation structure.

For example, both concepts are {\tt a-k-o parent}, lending some support to the
notion that they are the same, but certainly not proving so.  Note that even
this evidence is in turn dependent on believing that {\tt parent} is intended
to capture the same concept in both knowledge bases (likely, but not a foregone
conclusion).  The only way to determine that in turn would be by matching the
definition structures for {\tt parent}, etc., applying the same matching
process on up the {\tt a-k-o} chain.\footnote{Note the similarity to tracing
back along the inference chain when matching concepts in the rule-based
system.}

In matching the rest of the definition of these two terms, the machine would
discover that one of them has a role called {\tt children}, while the other
has a role called {\tt offspring}.  The process would once again have to
subgoal on gathering evidence about whether those two were in turn the same.

Hence the fundamental task involved in matching two independently constructed
representations is unavoidably one of gathering circumstantial evidence from
the representation structures themselves.

\subsection{The Utility of Formal Definitions}

While inferring meaning from syntactic evidence is inevitable, there is some
benefit in using a representation that provides a facility for definitions of
terms.  One obvious reason for this is that when we want to compare meanings,
the task is easier if we have a representation designed to capture meaning,
rather than one designed primarily to capture inference (i.e., rules)

A more subtle form of benefit arises because representation languages designed
to express formal definitions often provide a carefully chosen set of
representational primitives (e.g., {\tt a-k-o}, {\tt role}, {\tt
value-restriction}, {\tt number-restriction}).  To see how these can help,
consider two different reasons why two experts might construct two different
representations of the same concept.  First of course, they may think about
the world differently, perhaps creating different {\tt a-k-o} hierarchies.

Second and somewhat more subtly, they may each have a slightly {\em different
understanding} of what {\tt a-k-o} is supposed to mean.
That is, the consensus problem recurs here in a subtle way because the
experts might not have a shared understanding of {\em the representation
language itself}, and may write different representations of the same concept
even when their internal'' ontologies match.

A carefully chosen set of representation primitives can raise the likelihood
that the meanings of those primitives are themselves shared between the
experts, thereby reducing the chance for error in the translation from mental
construct to written representation structure.  This also means that a system
like {\sc carter} can justifiably put more emphasis on the overlaps that it
finds when working with those representations.

Hence using representations that provide formal definitions of meaning may
improve the system's ability to match concepts.  But the fundamental problem
is inescapable: when working with two independently created knowledge bases,
we inevitably have to compare meaning by matching representation structures
and accumulating circumstantial evidence, no matter what representation
language is used.

\section{RELATED WORK}

Several efforts share some similarity in general spirit with ours.  The Delphi
technique ([8], [9]) for instance, uses debugging to achieve consensus among a
group of experts on a specific issue.  While such methods can prove useful, we
believe it is premature to combine the results of two reasoning processes
before even attempting to achieve consensus on the underlying knowledge used
to arrive at those results.  Exploring that knowledge may reveal key
differences in reasoning, vocabulary, or problem assumptions which, once
reconciled, remove the outcome discrepancy entirely.

We have also drawn on the work of Brown [4] and Kuper [12] in conceiving of
the problem in terms of detecting bugs in knowledge and associating a repair
procedure with each bug.

Work in knowledge acquisition based on the repertory grid notion [2, 6, 18]
focuses on using knowledge of multiple experts, but offers only modest
guidance for reaching consensus, providing little knowledge about either
detection or repair.

Work by Reboh [19] suggests using the explanatory facilities of rule-based
systems to pinpoint areas of disagreement between two systems, but leaves it to
the user to decide which point of view to accept.  Work by Mittal [16] explores
the utility of interviewing multiple experts as a way of understanding a task
better, but does not deal with combining their knowledge.

Some of the work on the {\sc consul} system [14] addressed the issue of
finding good matches and discrepancies in concept definitions, and shared the
intuition that the system might determine whether two concepts were closely
related by comparing their representations.  In this case the discrepancy
problem typically arose when adding new concepts to the knowledge base, and
the two participants in the negotiation were the existing knowledge base and
the human expert who supplied the new concept.

A recent study [11] addresses the issue of resolving conflicting design
specifications.  Although their typology of conflicts is similar in some
respects to our discrepancy catalog, their primary focus is on reconciling the
designs themselves rather than design knowledge.

More distantly related is work on argumentation methods, aimed at assisting
the process of discussion by helping people specify the logical structure of
their positions.  As such they introduce an element of rigor into the
deliberation process, but offer little guidance in resolving differences
between the experts.} These ideas have recently been embodied in
computer-based tools (e.g., [13], [16], [20], [21]), but they are almost
entirely process oriented: they assist experts in the process of deliberating
and debating, but, importantly, do not suggest resolutions to inconsistencies.

\section{CONTRIBUTIONS}

One primary contribution of this work is the catalog of 35 varieties of
discrepancy, a store of detailed information we have codified for facilitating
CKA.  It represents a small but growing and relatively systematic expression
of knowledge about how to detect and resolve disagreements in knowledge.

A second contribution arises from the surprisingly effective degree of
bootstrapping displayed by {\sc carter}.  The system must make its best guess
about the meaning of a term from the way it is used in a knowledge base, it
can gather only circumstantial evidence of the sort reviewed above, and it
must, paradoxically, gather that evidence from the very same knowledge bases
it is attempting to modify to reach consensus.  It it thus quite interesting
how effective the system's heuristics are at guiding it.  {\sc carter} manages
to make plausible judgments about which concepts match, so that even when it
cannot be sure and has to ask the experts, the questions are for the most part
sensible and well chosen.

A third contribution is the extensibility of our discrepancy catalog,
illustrated during a session with the two statisticians that revealed the need
for a new category of entry: differences in problem solving strategy.  Where
one expert looked for all possible problems, then suggested a solution, the
other searched for and corrected one problem at a time.  This new kind of
discrepancy turns out to be detectable in terms of a difference in the
topology of the two KBs (specifically, a difference in the number of goals);
the detection/resolution organization of the catalog allowed us to add the
appropriate new entries with minimal effort.

A final contribution is the potential of our work as a general approach to
constructing systems that detect and resolve knowledge-level discrepancies.
While our current system removes discrepancies in knowledge expressed in rules
and attribute-object-value triples, we believe debugging and repair strategies
can equally well be organized around other kinds of knowledge representations.
The related work done using {\sc kl-one} [14] strongly suggests the
plausibility of this approach.  The fundamental process involves specifying
the components of the representation, developing a taxonomy of how the
representations can differ across these components, and prescribing possible
resolutions for each of these discrepancies.  We anticipate testing this on
other forms of representation.
\section{FUTURE WORK}

One of the most important areas for future research is the question of
discrepancy resolution strategy.  While our strategy of starting at the
outcome and working backward is useful, it is one of several possibilities.
One problem is that it may be a bit too myopic to be effective in a large
scale knowledge base.  The system in effect immediately dives into the details
and it needs a better sense of the larger picture.  Our next task is thus to
generate a number of strategies and evaluate them in terms of the efficiency
and effectiveness with which they increase the degree of consensus, and the
naturalness and coherence of the dialogues they produce.

Alternative strategies include working forward from inputs (because the two
KBs are likely to start reasoning from the same basic information) and
beginning at an intermediate point of agreement and expanding in both
directions (emphasizing what the experts already agree on and building from
there).
\section{CONCLUSION}

We have described a novel approach to and prototype system for facilitating
consensus knowledge acquisition.  The key contributions of this work include
the development of a detailed store of knowledge for detecting and resolving
discrepancies in rule-based systems, a general procedure for developing
similar systems for other representations, and the empirical result that
circumstantial evidence in the knowledge base itself can provide a useful
degree of power in determining concept meaning.  We expect the next advance in
this area to come from implementing improved discrepancy resolution
strategies.  This work will serve as the starting point for understanding more
generally how experts reach consensus and how we can best support them in
their efforts to do so.

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\parskip \baselineskip
\parindent 0pt

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