From: AAAI-86 Proceedings. Copyright ©1986, AAAI (www.aaai.org). All rights reserved.
MULTIPLE
FuAULTS
Johan
de Klcer
Intelligent
Systems
Laboratory
XEROX
Palo Alto
R.esenrch
Center
3333
Palo
Coyote
Alto,
Hill
Road
California
94304
and
Brian
M.I.T.
C.
Artilicial
Intelligence
545
Cambridge,
between
require
of an
determining
artifact
nnd
differences
between
and th,e predicted
the manifested
behuvior
of the
for
between
the
diflerences
diagnostic
inferring
edge
procedure
the behavior
oj the
nents
comprising
This
the
and
the
research
artifact
and
eficient
are
oj
diagnostic
Finally,
und behavior
procedure)
The
(GDE
novel
due
its
The
Sec-
and manipulated
in
assumptions,
resulting
reflecting
Third,
the
the
iterative
of
a clear separation
is drawn
between
diprediction,
resulting
in a domain
(and
independent
diagnostic
procedure.
Introduction
Engineers
stand
the
and
lllodels.
electrical
circuits
to
sively
refine
a model
process
of
theory
sense reasoning
tasks
models
and reality.
132 / SCIENCE
constantly
between
troubleshoot
find broken
based
on
formation.
involve
strive
physical
systems
mechanical
parts.
empirical
Many
finding
under-
and their
syst,cms
or
Scientists
succesdata
during
the
everyday
the
to
differcuce
commonbetween
If
the
the
is presumed
assigning
on
observed
task
is
differences
model.
Usually
circuits,
actual
does
Thus,
The first,
model-artifact
troubleshooting
determine
why
under
and
modeling
to
strategy
circuits,
a correctly
to
until
physical
diagnosis
employed
the
diagnostic
designed
piece
is at variance
is also
to
derive
task
is to
of cqltipmcnt
is
as it was intended;
the explanation
being
that
the particular
piece
consideration
tests
general,
encompassing
and analog
and digi-
approach
of the inference
from
observations.
the
mentioned
diifer-
differences.
is very
devices
Our
If
re-
evidence
difference.
programs,
systems.
independent
predictions
For
the
of diagnosis
mechanical
debugging
and
indicate
the
model-artifact
reflect
trou-
to be correct
indicate
part malfunctions.
then the artifact
is presumed
requires
two phases.
the set of possible
accurately
ment
scientists
differences
Engineers
observed.
model
of
based
The
second
proposes
evidence-gathering
the set of possible
model-artifact
differences
not functioning
faulty
behavior
1.
a means
model
all model-artifact
a unique
This
view
troubleshooting
tal
of the
differences
formation,
in
or biological
diagnostic
nature
admit
ences.
reline
they
First,
faults.
the
and
changes
diagnostic
task
above,
identifies
General
contributions:
t,hen
to be correct
not
requires
parts
discrepancies
quired
compo-
to multiple
represented
violated
model.
to
all model-artifact
the task is theory
and tested
on exdigital
circuits.
procedure.
is incremental,
itself
bleshooting,
individual
system
several
differences
paper is model-based,
device
from
knourl-
of the
The
failures
ond, j&lure
candidates
terms
of minimal
sets
diagnosis.
agnosis
injerence
artifact
reasoning
or blame
behavioral
behavior
of the artifact
model
guide
the setsrch
function
makes
diagnoses
procedure
the
in this
composite
device.
the
Engine)
has been implemented
the domain
of troubleshooting
system
in an
the
presented
of the
structure
Dirtgnostic
amples
in
02139
Diagnostic
credit
tasks
a model
Laboratory
Technology
Square
Massachusetts,
ABSTRACT
Diagnostic
Williams
in
some
for the
of equipway
with
its design
(e.g.,
a set of components
is not
rectly
or a set of connections
is broken).
To
working
cortroubleshoot
a system,
be proposed,
a sequence
executed
and
ance,
or fault.
consisting
adders,
A,
U = 3, and
then
For
of three
of measurements
analyzed
example,
multipliers,
must
to localize
this point
of variconsider
the circuit
in Fig.
1,
Ml,
Mz,
and
Ma,
and
two
and A,.
The inputs
are A = 3, D -x 2, C =-I 2,
E I= 3, and the outputs
are measured
showing
that
F
10 and
=
is possible
of components
didate
and
[AJZ,
the
MS].
12.’
that
useful
that
can
singleton
[A2,M2],
differentiate
to
is the
two
highly
faults.
nents,
addition,
probable
one
I
I
Al
-
M2
G
A2
each
only
-
and
on
diagnosis
and
failures
produced
Wh en one entertains
concentrated
faults,
tially
the
with
work
specifically
method
for
simultaneous
The
if none
paper
which,
component
using
paper
to
describes
when
an
due
is
the
guide
to
efficient
the
with
a powerful
with
multiple
the approach
faults.
in the
propagation
as the
the
fault
causes
the use
measurement
framework
diagnostic
for
procedure
inference
We
and
domain
presume
(as
The
ture
model
of the
obey
Ihe
of the
device
constituent
simple
forth,
Model-artifact
we
behavioral
without
predictions
being
concerued
presume
artifact
in terms
obeys
certain
describes
of its
behavior
I This
Systclns.
Law,
of
cirruit
consists
Xirchoff’s
<and so on. In
the
is ;dso
artifact
differs
1rwt1 by b3t.h
physical
constituents.
behavioral
electrical
circuit
where
wires
obey
Ohm’s
the
Each
rules.
of wires,
Current
tliaguosis,
frown
[z] nntl
For
type
of
csample,
a
generally,
inference
its
tions
[8] in cxpl:.il!ir!;;
Qualitative
It
is
In
“J’
C
(i.e.,
the
is observed
a symptom
proccdurc,
(inl’erred
of these
from
its
An
impor-
from
is that
-
in terms
of
=
short
circuits;
a common-
as persistence,
defaults
case)
that
be
inferred
section
for this
circuit.
makes
assumptions
details.
between
and
E
observa-
the
=
procedure),
a pre-
an
Given
D = 3, and
a genfor the
which
difference
example
from
present
but
procedure
procedure
inference
modelInstead,
indirectly
8 we
purpose,
observations
and
about
the procedure’s
is any
the
observable.2
inference
2,
any
in
the
inference
from
our
2,
of
directly
A x C + R x D = 12. However,
Thus
<are manifested,
hypothesis;
must
an
the
Consider
calculation
resistors
and so
Law,
resistors
it is given
that
model.
by
A = 3, B =
struc-
A conmodel
its
Symptoms
not
a symptom
made
a
which
characterizing
apply.
absence
such
violations
moment
tion.
produces
differences
is usually
for
Differences
the
are
Intuitively,
2.
models
needed.
of
all assumption
diction
on
longer
a faulty
Detection
differences
es-
is very general.
For example,
in elecmight
be the correct
functioning
behavioral
observations.
eral inference
architecture
engine.
no
model-artifact
di-
also demonelectronics,
and
differences
<are not
about
component
artifact
itlference
In addition
it
domain
of digital
models
3.
pro-
(2)
assumptions
hold.
If any
then
the artifact
deviates
may
of
which
model-artifact
is based
associated
model
In
a set
is a set of differences
sense domain
an assumption
or Occam’s
Razor.
of
of
it
as assumption
violations.
to behave
according
to
viol&ons
assumptions
of analyzing
a predictive
predictive
of
inference.
with
of possible
of which
A
compo-
differences
a set
phys-
of this
approach
([1,2:3,6,8,11])
specify
correct
models
for constituents
in a scientific
gen-
number
in a logical
associated
approach
of its
thus,
of each
exponenThis
any
process
a general
coupled
provides
dealing
strates
grows
consideration.
developing
failures
information
This
agnosis
the
including
a set of measurements,
constituent’s
are false,
assumption
tronics
the
faulty
comof multiple
of measurements
to identify
potential
discussion
on
(see [3] f or an extensive
variance
probabilistic
cess).
at
diagnosing
faults.
of this
focus
results
a single
possibility
space
of potential
candidates
the number
of faults
under
is aimed
eral
by
steps
(3)
(4)
Reasoning
primarily
concept,
model-artifact
diagnostic
explicit
circuit.
has
diagnosing
ponent.
the
1: A familiar
in
these
is a description
of its
each of its constituents.
has
constituent,
model,
Fig.
what
grain
size of the diagnosis.
takes
(1) the physical
structure,
tant
ramification
WC need
only
work
even
constituent
possible
i.e., all the
assumptions
Earlier
to determine
general
model-artifact
differences
stituent
is guaranteed
-I’
D
1
or more
Our
C
2-
a very
set of candidates,
each
explains
the observations.
F
B
2
the artifact
models
for
each
differences
Ml
for
plus
is
tablishes
the
Diagnosis
for
diagnostician
processes
measure-
[Ml].
of the
are.
constituent
1
3
task
The model
structure,
ical
produce
the
only
the
differences
as a canor
isolating
it
and
r
A
is likely
between
[Al]
candidates:
[M,],
then
sets
to
X
because
it
following
[A,],
in further
is optimal
measurements
of the
is referred
mea>uring
information
X
these
one
(each
set
by [...I):
Furthermore,
most
From
at least
is faulty
is designated
Intuitively,
ment
G =
to deduce
inputs,
3,
by
simple
F =
X
x 1’ =
F is measured
to be
10.
to be 10, not 12”
.C u,ny inconsistency
1.
is a symptom.
detected
More
by the
and
ber.wecn
prcdic-
distinct
way
occur
oleasureiuents)
two
as well
as n
thei!
Reasoning
and
Diagnosis:
AUTOMATED
REASONING
/
133
measurement
and
a prediction
(inferred
from
some
other
5.
measurements).
Candidates
A cnndidate
4.
The
Each
Conflicts
diagnostic
procedure
symptom
that
tual artifact
of diagnosis
are
tells
possibly
faulty).
us
violated
Intuitively,
all
(e.g.,
“F
is a set
with
symptoms.
A
candidate
assumptions
(indicated
the
more
components
correctly.
is observed
lation
that
E’ =
Ml,
M2 and Al,
functioning,
then
by
or
consistent
that
nmy
to
Consider
be
be
of assumptions
sup-
and thus leads to an inconsistency.
might
be a set of components
be functioning
sylllptonl
one
a conflict
porting
a symptom,
electronics,
a conflict
cannot
is guided
about
10,
not
our
12.”
In
which
Our
perset
of
(Ml,
set
Mz,
value
E
=
E =
rise
on
MS
that
correctly
first
(Al,
Al,
To
be
far.
by
a set
assumption
As
every
(i.e.,
its
have
a non-empty
of
assumptions
mentioned
candidate
conflicts),
each
in
must
set
the
explain
representing
intersection
a
with
every
of
teed
electronics,
where
(any
to
be
a candidate
components
working.
Before
taken
we know
nothing
initial
candidate
space
any
about
measurements
the
grows
ber of components.
Any
faulty,
thus the candidate
of 2” = 32 candidates.
is a set of failed
mentioned
a.re
not
circuit.
The
exponentially
component
space for
compoguaran-
have
been
size
of the
with
the
num-
could
be working
or
Fig.
1 initially
consists
suno
all
[MI.MZ.MJ.Al)
reduce
a conflict.
if it has
This
observation
of our diagnostic
tion is to identify
but
minimal
no
calculate
even
G
always,
conflict.
proper
is central
each
[AL421
it
Fig.
a conflict
symptom
2 Initial
combinatorics
of
set must
also
be a
be represented
conconIlicts,
where
a
subset
which
is also
to the
performance
corresponds
to a
as well.
Notice
property
that
didate
candidate
that
any
the
candidates
l;~tlicf:
working
empty
set,
2.
the
space
can
rccoguition
of t,he
have
must
represented
the
is the
the
the
single
root
the
sll )sct,-snI)cl.,~ct
tltcn
of the
flcfitie
is a
might
be
is the
at the
bottom
is constructed
candidate
observations
a
up
candidate
lattice
and
construct
minimal
Idie
minimal
the
a can-
is to idcnThe space of
boundary
below
is not.
every
component
fro~il
set of candidates
to
of a
camflitl~~lcs
recognition
uses
device
be
consistent
by
in tcrri1s
tnirliurnl
thus
conflict
ConIlict
concisely
candidates
of all candidates
be
t.hat f~vcrytling
;vhilc:
everything
measurements
[], which
a model
ic
‘1‘1
summarize,
stages:
example.
of a candidate
be vislinlixed
correctly,
of Fig.
circuit
goal of candidate
generation
set of niinimnl
candidates.
2).
bonritli~ry
suc!i
vnlifl
candidate,
Given
no
for
be represented
conflicts,
superset
Thus
can
(Fig.
To
like
observations
candidates.
The
tify
the complctc
space
candidates
that,
as well.
with
two
/ SCIENCE
IMU9
&i%All
=
though
procedure.
The goal of conflict
recognithe complete
set of minimal
conIlicts.3
not
PfMwI
[Mull
of conflicts
be repreIf a set of components
the set of conflicts
can
identifying
the minimal
is minimal
D = 3,
correctly
It is essential
the
of that
every
and
For
symptom
can give
the set of all com-
superset
then
12,
single
including
is a conflict,
134
must
nents,
MS).
set
‘JJyJ>ically,
symptom
candidate
thus
starting
produces
that
the
concisely.
Thus
by only
are
However,
it still
any
A2
we
to
ponents
in the circuit.
diagnosis
it is essential
sented
and manipulated
single
hold.
ac-
A = 3, C = 2,
AZ, Ml, and MS, (i.e.,
AZ, Ml,
For complex
domains
to a large
set of comlicts,
conflict
to
the
inputs
functioning
prediction,
second:
and
12.
G to be
10, the
=
G is measured
the
the
M2,
assuming
arc
when
with
conflict.
cisely
other
agree
with
one prediction
resulting
in a symptom.
inputs
B = 2, C = 2,
assuming
3, and
Thus,
based
might
another,
with
the
3, <and
1W2)
agrees
any
fail
Every
how
[MI.M2.Ml.Al.A2)
we calculate
observation
F
ignoring
10.
and
every
[...I).
for
Ultimately,
the goal
the set of candidates
at F.
funct,ioning
with
the
and
AZ),
Al)
A measurement
yet disagree
with
example,
starting
and
M’2, Ai,
must
observations
is represented
by
For
calcu-
are conflicts
as well;
however,
M;!, Al)
are necessarily
confticts
since
in the conflict
were necessary
to constrain
subsets
of (Ml,
the components
the
(Ml,
the
hypothesis
the model.
and refine,
conflict.
12 depends
on the correct
operation
of
i.e., if Ml,
A42, and A, were
correctly
F = 12. Since
F is not 12, at least one
the
set
example
of Ml,
M2 and Al is faulted.
Thus
the set (Mi,M2,Ai)
(conIlicts
are indicated
by (...))
is a conflict
for the synlptom.
Because
the inference
is monotonic
with
the set
assumptions,
is a particular
differs
from
is to identify,
made
a complete
in
generation.
along
set
with
of min-
imal
conflicts.
minimal
candidates.
Next,
candidate
conflicts
to
Candidate
section,
While
generation
conflict
recognition
[&fz];
the
of minimal
of the next
imal.
Ijowever,
in Section
[W,
the
uses
construct
a complete
generation
is the
the
set
topic
is discussed
set
of
we must
7.
0.
Candidate
Diagnosis
is an
incremental
measurements
process;
takes
didate
ments.
space
and then
uses this
Within
a single
diagnostic
candidates
must
to having
the
through
decrease
the
the total
corresponds
set of conflicts
to having
tonically
down
the conflict
generated
old
to generate
The set of candidates
lows.
Whenever
a new
minimal
flict
are
candidate
is replaced
by one
minimal
based
on
complished
minimal
which
by
intersection
the
up
along
the
new
Eliminated
from
added
to the
thus
explains
all
single
those
=
10
Mz).
This rules
its immediate
and
[AZ]
are
and
[A,]
explain
examined.
the
superset
the three
candidates
minimal
does
not
explain
ate
superset
candidates
the
new
new
and
minimal
thus
12”
the
old
When
are
any
which
candidates
are
new
already
All
are
implicitly
set
that
one
minimal
[Mz],
candidate
[MS],
[Al],
are
their
[AZ, MS]
discovered
[Mz],
recorded;
immediate
are supersets
above.
[AZ,
however,
of the
its
three
represented.
consists
the
conflict
[MI],
thus
of
supersets
candidate
seen
candidates
conflict,
are
no conflicts,
working)
produces
and
not.
for
there
are
everything
single
[Ml],
of the
do
except
candidates
the
have
not
conflict
[MS]
candidates
We
out the
supersets
Each
and
which
is ac-
non-empty.
remaining
Initially
[] (i.e.,
observations.
[AZ]
is
of
MS]
immediminimal
Therefore,
of [Ml],
[Mz],
and
[AI].
1%
The
second
(4,
A2,
Ml,
conflict
MA
(infcrrcd
only
eliminates
from
observation
minimal
[p/f2,
M3],
howcvcr,
resulting
[Ml],
[AZ, Mz],
Candjdate
of [Mz]:
of these
[A,,MzJ
in
the
and [Mz,
generation
remain
and
surements
never
minimal
once
eliminated
accumulate
Second,
decrease.
[A2,
M21
[MI],
[A2,
candidate
candidate
(and
thus
assumption
that
there
is necessarily
is only
a single
never
model-based
troubleshooting
every
false.
fault
SU-
n/iz],
and
set:
[Al],
proper-
increase
however,
or
a
AS mea-
reappear.
minimal
candidates
appears
in every
candidate),
then
Third,
the
(exploited
that
presupposition
in all
strategies),
assuming
all candidates
set of candidates
can
are
respec-
interesting
the sizes of the
if an assumption
n/r,],
explains
[n/r,,
ad
are
several
can
min-
candidates
[Al, Mz],
candidates
Il;inimal
Mz].
has
[ tll]
of minimal
ties:
First,
the set of minimal
candidates
may
decrease
in size as a result
of a measurement;
G ==
Catldidid!
Qualitative
7.
con-
candidates.
(A,, Ml,
[I. Thus,
however,
new
from
recorded
the
conflict,
aud
set
previous
is equivalent
are singletons.
be obtained
by
In this
intersecting
to
case,
all
the
the
conflicts.
the
lattice
the
as folprevious
with
more
than
one parent
be found
along
each branch.
example.
candidate
“F
care
the
first
candidate
reached
i.e., when
the candidate’s
candidates
set of new
symptom
towards
modified
any
explain
the
the
or duplicated;
Consider
our
the minimal
lattice
candidate(s).
conflict
past
a candidate
candidate
must
subsumed
This
mono-
or more
superset
candidates
this
new information.
This
moving
up
a consistent
are
new
not
recording
new conflict;
with
candi-
Similarly,
empty
set. Candidates
the new conflict(s)
and
does
moving
candidate,
explains
the
the
[Ml],
complete
of the minimal
candidates
[Al]
Thus
the new minimal
candidates
candidate,
up
monotonically.
conflicts
move
is incrementally
conflict
is discovered,
which
of
corresponds
towards
superset
by the
using
measuretotal
set
components.
a conflict
represented
incrementally,
candidate(s)
of all
must
increase
the minimal
through
new
can-
monotonically
lattice
set
amgnosthe
This
move
superset
by
as the
relines
to guide
further
session
the
candidates
candidate
represented
continually
monotonically.
minimal
the
date
he
candidntcs
to
consider
the supersets
Each
an d [M2, M3].
M2],
persets
tjvely.
Generation
tician
unaffected
Recognition
tion
we first
This
approach
A conflict
sumptions,
they
are
then
the
quires
present
a simple
to
an inference
ENV,
In
example,
approach
made
thus
whether
the
after
is refined
Refinement
of
to
the
At
each
I:
minimal
minimal
vironment,
recognition.
lo},
and
given
the
combination
F =
{M~,M2,A,})
the conflict
the
cnvironis consis-
10,
and
(Ml,
before
(leaving
M2, Al).
as follows:
Exploiting
minimality.
To
environments
we begin
up along
pattern
environment
strategy.
a set of as-
which
far,
measuring
inconsistent
conflicts),
moving
search
of conflict
C(OBS,ENV)
OBS
measuring
G = 12, C({F
=
off the inputs)
is false indicating
This
constructIn this sec-
as an environment,
and testing
if
with
the observations.4
If they
are,
environment
is a conflict.
This
re-
determines
our
model
strategy
of observations
tent.
incrementally
generation.
is then refined
into an efficient
can be identified
by selecting
referred
inconsistent
inconsistent
merit
set
Strategy
The remaining
task involves
the conflicts
used by candidate
ing
set
Conflict
our
its
used
search
parents.
during
we apply
identify
(and
at
the
This
candidate
the
thus
the
empty
enis sinlilar
generation.
C(OBS,ENV)
to dcterrnine
4 An environment
should not be confused
with n calldidnte.
An
environment
is n set of assumptions
all of which
are assnrned
to
be true (e.g., A41 alld M2 WC CSSIII~~CI
to bc working
correctly),
a
cnndidntc
is a set of assumptions
all of which arc assumed
to be
false (e.g., colllpollents
Ml and A42 are liot fuuctionillg
correctly).
at least one of which is f&c.
A conflict
is n, set of ;lssun~~~l.iolls,
Intuitivrly
an rnvironmtmt
is t,bc% set of assulllptions
tlmt defijl:? il
"contc!ut"
in a deductive
infc~rcrtcc
engin(B, in this cnx: t,llc engilM2
i:; IISCX~ for
particular
Reasoning
pdict.iotr
n~otlcl-artifact
and
Diagnosis:
and
t.ho
assurnpt,iom
;IIC
;hout
the
1:lck
of
dilfcrctlccs.
AUTOMATED
REASONING
/
13 j
whether
or not
ment
ENV
is explored,
is a conflict.
all other
of the new environment
ronment
is inconsistent
supersets
are
been
explored
run
on the
We
must
then
environment
presume
hypothetical
For example,
Mz})
produces
OBS
are
=
the
circuits
8.
ceding
for
plementation
made).
which
To
vnri-
modified
ENV.
be implemented
in terms
of P.
Refinement
2:
puts
our
are kept
knowledge
constant,
of the
cally.
Given
a new
a superset
the
of every
values
only
of
infer
Refinement
ically
with
from
tion
an
when
the
incremental
each
{Al,Ml,
= 6, Y =
a datum
is completely
If P com-
the
simply
measurement
for
environment.
If a set
Analomonoton-
on
every
possible
Inferences.
environment.
and
over
can
the same
antecedents.
by utilizing
ideas
the
same
rule
we
will
Refinement
an
cessful.
ignore
enviromnent
inferences
ronment
absent
in every
a new
be faced
bcr
of potential
practice,
with
this
empirical
only
assumption
136
I SCIENCE
are
over
and
of this
overlap
Maintenance
as a dependency
[ 71.
This
previous
doesn’t
one
of its
unique
a computation
exponential
are
weakly
connected.
property.
For
of interest
weakly
Our
example,
will
G
two
supporting
Any set
the
strategy
depends
If
the
in electronics
of components
are
performed
inference
For
proce-
example,
forms
prediction,
many
of resolution
V,
it follows
call this
the
set of envi-
(i.e., ENVS(V)
set the support-
Exploiting
the
agenda
the
IllClJi,,
B
correctly.
Thus,
{Mz}.
Second,
Y
=
F
=
=
6
X
x 15) =
6 assuming
one of its supporting
G - 2 = G - (C
working.
Therefore
inference
x
the
are
for
enviroamcnl
on
;dwnys
oho
lhat
in their
property
that
whenever
a datum
first.
Whenever
is marked
or:‘* -iron nlcut.
dctlucetl
dcsircd
this.
are
A
simple
a symptom
a conflict
Using
this
nlinilual
th,at
created
effect
of
computational
producing
is performed
srlIfices
lJlCChc?~JiSlll
any
one
done
changes,
consequents
such
the
is ever
a fact
dcpcndencies
achieves
the
IJrixCSS
posslhle,
environment
the
the
l’his
first, run.
without
incurring
the
stops
of
of its
by tracing
was
rule
smaller
no inference
environment
environments
are
facts
calculate
Y := 6 are {{Mz}{A:!,
MS}).
to derive
Y = G is a superset
m dependencies
supporting
control
;Lcllicving
can
=
,‘l13 nre
min-
measurements
we
Y
monothe
two.
rule
the
inf::ro~icing
schr~lle
First,
supporting
is rccoguizcd,
the
case
of
used
is
controlled
that
the in-
framework.
after
112 and
inFerenccs
in the
the
ways.
in
propagation,
demon
qualitative
simulations,
which
We
this
automatically
Wc
two
in-
In
exploitin,
updated
envi-
connected,
example
of these
By
overhead,
in
our
environments
of assumptions
interesting
However,
be con-
dependencies.
Al
prediction.
12.
I;-‘) == 6 assl~ming
when
the
rerunning
num-
=
n/r, is functioning
environnlents
is
then
we would
every
from
env)}).
of the
different
strategy
to
its name)
in the
be sets
and
twice.
If every
then
differences,
components
sets
subsets.
inference,
with
can
be ext.ernally
we presume
many
general
main-
processing,
whenever
permissible,
that
Most
and
this
ENVS(V),
E P(OBS,
Consider
10
of one
care suc-
some
associate
these
criteria.
systems,
be
truth
or disbelief
inferences
general
fit
environments
and
is primarily
refinements
contain
model-artifact
as the
rules
be executed
four
refinements
allow
the
extent
of not even generating
which
run
set
locality.
the
contained
still
ferences
Exploiting
of why
The
first
(i.e., to the
any
on
5:
observation
be
a large
All
Truth
these
order
can
Finally,
can
tonicity
property,
it is only necessary
to represent
imal
(under
subset)
supportiug
environments.
in
need
of
such that every
inference
is recorded
no inference
is ever performed
twice
very
P must
Thus,
of data-bases,
again
on
be avoided
of P(OBS,ENV)
been analyzed.
We
ing
follow
computation
have already
Redundant
by
is monotonic.
four
deduction
ronments,
E {envlV
ENV.
simple
4:
procedure
these
belief
that,
during
is simultaneously
itn-
(or
utilizing
(2)
pre-
t, Ihe
meels
justification)
and
determined
ference
of
typ-
in the
augmcn
P
for
(i.e.,
in which
theorem-proving
then
the addition
of any assumponly
expands
this set. Therefore
P(OBS,E)
for every
subset
E of
Refinement
criteria
inference,
and that
this
our architecture).
meet
that
natural
environment,
to that
environment
contains
P(OBS,ENV)
This
makes
the
if all its subsets
presume
basic
irrelevant
(i.e., by
dures
colllporlent
discussed
and
cache
set
of predictions
order
ideas
moclify
ENV)
the
grows
two
the
to
we presume
one inference
actual
interact
SO that
Architecture
expert
rule-based
systems,
constraint
invocation,
taxonomic
reasoning,
is made
assumptions.
set of predictions
We
A dependency
If in-
to
of P.
(1)
if we
addition
need
for
P(OBSU{M},
a new
exploit
we
structed
cumulative
and
grows
monotoni-
Thus
Monotonicity
2, the
the
M,
P(OBS,ENV).
P,
3:
to refinement
are
completely
tenance:
more
signals
designed
Procedure
the
of measurements.
measurements
circuit’s
structure
measurement
is always
we need
predictions.
Monotonicity
(or
Inference
In addition,
more than
whose
limited.
section
Let
follow
12).
now
explicitly
to)
assumptions
two distinct
values
for a quantity
z and - TC), then
ENV
is a conflict.
and
are
are
entirely
values
connected
interactions
explored.
3,B
= 2,C
= 2,D
= 3},
3, B = 2, C == 2,D
= 3,X
=
are
ically
not
observations
predictions
given
which
a subset
operates
(e.g.,
given
the
behavioral
environ-
has already
then
C is not
strategy
predictions
P({A
{A
C can
gous
are
first.
If the enviconflict
and its
its supersets
inference
environments
P(OBS,ENV)
b e all
from
the observations
putes
both
be explored
it is a minimal
and
the
in
6, F =
a new
which
not explored.
If an environment
or is a superset
of a conflict
by inferring
ables
Before
environments
only
and all
control
environminimal
conflicts
(i.e.,
In this
usually
inconsistent
environments)
architecture
is).
The
P can
only
fewer
conflicts
will
will be eliminated
mistakenly
arc
geueratcd.
be incomplete
consequence
trigger
(in praclice
of incolnplcteness
be detected
and thus
than
the ideal - no
it
is that
fewer
candidates
candidate
will
be
taken.
far
we
Thus
have
handling
domain
the
P.
During
the
the
power
of this
function
demonstrate
the
problem
For our
of circuit
example
suppositions.
only
we
in terms
of each
type
thus
some
values
value
the
model
must
be
every
are
terminal
from
other
values
points,
using
the
values.
The application
assumption
that
working
correctly.
If two
values
quantity
its
in different
ways,
then
component
of each
corresponding
are
component
deduced
a coincidence
differ
then the coincidence
consists
of every
component
throng11
from
the
measurement
cidence
(i.e.,
the
sympt,om
used
points
implies
to deduce
the
two
the
has
occurred.
point
at least
values
same
C
to
constraint
cells:
con-
some
unas-
of insufficient
it can also =arise
in the
of each
For
tcrmi-
cells
propa-
component
example,
in analya-
are
are
circuits,
0 and
t, and
model
A,
for
and
are
the
cells
the
constraints
the
repre-
circuit
of Fig.
D, E, X, Y, 2, F, and
the observed
values:
A = 3,
B,
C,
provided
= 2, D = 3 and E = 3.
There
are three
and two
adders
each of which
is modeled
by
MI
CXE,
following
constraint
process
and
behavior
In digital
values
constraint:
: 2 =
by
used
the cells represent
circuit
voltages
are numbers,
and the constraints
the
of which
a single
MS
values
inconsistency
incompleteness
the
ten
AI
: X = A x C, M, : Y = I3 x D,
and A2 : G = Y+Z.
The
: F = X+Y,
is a list of cleductions
propagator
generates
(component
and dependencies
(a dependency
that
the
is indicated
: antecedents):
is a symptom.
propagated
to the
that,
is
for
are
B = 2,
lnultipliers
to deis based
in
a parhave
different
propagation
domain,
equations.
There
G, five
the
recognized
from
the
models
model
If the two values
The conflict
then
components
and
Intuitively,
symptoms
are
locally
through
components
can
cells
out
inputs
are
unused
of logical
circuits
the values
Consider
1.
Instead,
two
dependencies
constraints
sent logic levels,
the
are boolean
equations.
expensive,
is known.
trace
the
usually
arises
as a consequence
about
device
inputs.
However,
mathematical
Fi-
values
to other
a logical
as a set of constraints.
ing analog
currents,
is whether
when
constraints
which
inputs
(i.e.,
constraint
some
circuit
is modeled
correctly.
of measurements
the
cell
event
consequence
In the
pre-
from
same
the
leaving
as the
gator.
of a circuit
considered
is working
in terlns
inferred
WC
it to
Thus,
along
conflict.
signed.
This
informatiou
plus a behavioral
Second,
that
the
Measurements
at
component
models.
by propagating
out
on
the
the
In this
the
nates
deduced.
is manifcstcd
for
Sometimes
paper,
applying
of simplifying
difference
component
are made
terminals.
every
measurement
duce new
that
this
by
locally
,i synlptom
diagnos-
whose
applicathe selection
of
of
approach,
assume
of model-artifact
not
remainder
of a circuit
topology
of its components.
or not a particular
nally,
all observations
at a component’s
general
faults:
only on
diagnosis.
we make
a number
First,
is described
description
a very
multiple
depends
to be
of conduits
The dependencies
recorded
through
the constraints
that
deduced
struct
descrihcd
tic strategy
for
tion to a specific
out
is identified).
Diagnosis
values
as a set
the system.
ticular
path
are
Circuit
more
be viewed
be propagated
eliminated.
9.
and
may
X=6(MI:A=3,C=2)
of coinone
Y=6(M2:B=2,D=3)
of the
is inconsistent,).
Z=6
(M3:C=2,E=3)
F=12(Al:X=6,Y=6)
10.
Constraint
Constraint
ues,
and
propagation
constraints.
as voltages,
Propagation
Cells
represent
state
constraint
isfies
propagation
the
that
viously
unknown
values
v = 2 and
to calculate
records
the
If’s
newly
The
allows
variables
cell.
i =
value
a set
each
such
basic
For
1, then
R =
a value
inference
step
on
value
a value
example,
it rises
2. In
if it
the
cnusc
the
the
when
measuring
conflict(s)
symptom
(A,,
has
some
important
necessary
for
the
find
to
be inputs
v = iR
1~ -z ill.
conslrnints
Qualitative
to
at, any
or outputs
point
in the
taken.
tions
Scconcl,
about
Ilie
ncnts.
Tn most
inputs
to
constructed
Reasoning
and
it is not
direction
digital
outputs.
by
Diagnosis:
where
detcrnlincd
AUTOMATED
Each
the
properties.
circuit.
First,
of these
A path
can
only
a subtracI.or
xi
input
begin
has
lo make
any
flow tliroiigh
a signal
paths
may
a measurement
cxa~l~plc,
reversing
12).
example
in this
points
necessary
that sigllnls
circuits
For
sinlply
starting
of the
circuit
are
MI, Mz)),
a conflict
is to
propa.gnt,or
(e.g.,
indicates
is not
discovered
values
F to be 10 not
approach
it
a pre-
two
This
sat-
constraitit
other
is indicated
same cell (e.g.,
leads to new
that
for
has
A symptom
for the
symptom
values,
constraint
addition,
21, i and
~lrny
of initial
cell
it to determine
depclltloricy
recorded
Given
assigns
constraints.
a constraint
The
R.
G=12(AZ:Y=6,Z=6)
val-
example,
among
V, i, and
flows.
cells,
lates
a condition
that
the cells must
satisfy.
For
Ohm’s
law, ZI = iR, is represented
as a constraint
cells
or fluid
on
stipu-
three
levels,
operates
A constraint
the
logic
[12,13]
been
assumyconipoflow
from
cannot
,and
REASONING
the
bc
output
/
137
of an adder
since
However,
the
irrelevant
to our
a constraint
be
any
mation
diagnostic
direction.
function
values
desired.
flow
directionality
of signal
technique:
the
way
can
the
of a component’s
between
used
infer
it violates
directionality
along
a path
terminals
its
inputs
must
places
can
which
discrepancies,
infor-
through
a component
in any
have
subtractor
its outputs
D=
E=
F=
is
detect
For example,
although
the
in reverse,
when
we observe
what
flow
a component
of its
To
flow.
signal
does
we
3,0
390
lO,{}
G=
12,{}
X
=
4, (AI,
j&&G,
Ad&)
ww
not
can
Y I=
{Al,
4,
M,}
%{M2}{Az,M3)
been.
Z =
8, {&,~MI)
6,{M3}{A2,M2)
11. Generalized
Each
step
tecedent
of constraint
values
a constraint
which
and
each step
crementally
our
We
are
first.
ensure
This
assertion
x with
any
the
its
associated
measurements
the
inputs,
[B = 2, {}],
[[C =
Observe
that
when
nent,
the assumption
dependency,
the
and
thereby
supporting
propagated
place,
to
the supporting
Propagating
value.
= 6, {Ml}].
gations
produce:
12, {AI,
wafdn,
[[Y = 6, w2)n,
uz = 6, w3n
and [G = 12, (A2, M2, it&}].
This
adds
measure
F to be 10.
Suppose
10, {}I
we
to
t,he
(starting
4, {Al,M2}~,
between
[[F
ognized
Thns
tion
smaller
in
the
Next,
tom
“G
MS).
The
A=
B=
c=
=
Ml,
Mz}
goes one more step:
are no more
inferences
=
MIIII,
12 not
final
we
measure
6, {A2,M3}],
and [X = 4,
10”
produces
data-base
state
G
as
Given
measurements
further
and
its
be
12.
approach
structs
Truth
Maintenance
[IF
=
straint
module,
=
the
and
propagasupersets.
AZ, MI,
Propaga-
agenda
approach
are
structures
base
state
uate
hypothetical
[Y = 6, {&,~I~}],
12 =
{A 1, A2, &}].
The sympthe conflict
(Al,A,,
Ml,
all minimal
is:5
ure
/ SCIENCE
within
The
first
and
conmini-
the
the
third
con-
is a general
two modules.
incrementally
minimal
the
model-based
measurements
and
con-
The last
constructs
conflicts.
paradigm,
our
potential
model-
are given.
In [3] we exploit
the framein two ways
to generate
measurements
optimal.
constructed
of Section
11)
by our
make
environments,
strategy
it easy
measurements.
(e.g.,
the
data
and
eval-
as we construct
and
to compare
information
First,
the
to consider
Second,
conflicts,
relatively
straight
forward
ments
(using
probabilistic
candidates,
it
is
potential
measureof component
fail-
rates).
The
wards
work
Ihe
remains
order
candi-
implemented
implementation
maintains
information-theoretically
goal
much
1) incorpornling
138
from
work
differences
of this paper
data
propagathe
for each prediction
and
It is based on Assumption-Based
of [5].
presumes
which
completely
on the
generator,
candidates
As all the
artifact
work
been
architectures
language
based
the candidate
minimal
the
until
[4]. Tl le second
controls
the inference
conflicts
are discovered
first and records
of inferences.
It is based
on the consumer
such that minimal
the dependencies
=
6 uses the two minthe set of mini-
continues
constrained
examples.
Our
modules.
The first
environments
conflicts.
minimal
effort
Research
has
mal supporting
3,0
2,{)
2,o
has
generation
cycle
been sufficiently
tested
on numerous
sists of four basic
up
[[X
[G = 10, {Al,
to be made.
to
candidates.
new
is
conflicts.
mal
Our
follows
propagation
in section
construct
12. Connected
propa-
first):
during
non-minimal
discussed
incrementally
given
NOW the symptom
{Al, Ml,M2}~
is recconflict:
(Al, MI, M2).
prevents
{Al,
environment
[I2
A2,
sets
minimal
architecture
suppose
gives:
8, (4,
a new
inference
proceeds
assumption
= 4, {Al,Ml}j.
and [TF = 12,
and [Y
= 10, {}I
indicating
the
Analysis
base.
the
The propagation
MS}].
There
tion
data
with
remaining
point
The algorithm
conflicts
to
[A = 3, {}I,
environment(s)
and C through
A
The
no
imal
environments.
take
of:
[[X
we
and
the
at
in constructing
tion/candidate
date space
2, {>],
[[D = 3, -OD, and UE = 3, Onpropagating
values
through
a compofor the component
is added
to the
thus
that
wasted
guar-
obtain:
Ml
Note
to infor
propagations
first,
or propagations
data
base consists
conflicts:
(AI, 4, Mdf3)
guides
that
the resulting
supporting
environments
arc minimal.
We use 15, el, e2, . ..I to represent
Before
minimal
built
manner
candidates
that
performed
in two
architecture
in an efficient
conflicts
and
example.
results
a set of anWe have
inference
environments
environments
anteeing
conflicts
of
our
during
propagation
construct
minimal
in subset
takes
a consequent.
within
minimal
multiple
faults.
Consider
Propagation
propagation
computes
propagator
explores
only
Constraint
This
to
diagnosis
presented
here
of automatecl
to
be
the
done.
represents
diagnosis,
Plans
predictive
systcn~s
for
cnginc
with
<another
step
nevcrthcless
the
future
cliscussed
time-varying
tothere
include:
in
signals
[14]
in
and
state,
and
2) controlling
ences
being
considered.
the
set
of
model-artifact
differ-
10. Mitchell,
T.,
learning,
78-711,
13. Related
R.,
Artificial
This
research
fits
within
the
model-based
paradigm:
propose
[1,2,3,6,8,
9,111. However,
a general
method
of diagnostic
effic.ient,
incremental,
extended
has
to
been
include
these
account
of many
recognition
and
faults,
and
strategies.
ideas
Reiter
independently
of our
and
“intuitive”
candidate
is easily
(111
(University
12. Steele,
AI
of
generation.
Ramesh
cially
Patil,
thank
Ray
productive
Randy
Halasz,
provided
Reiter
for
Davis,
Walter
useful
his
“Doing
G.L.,
Time:
Penn.,
and
Diagnosis:
(August,
first
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Also:
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595,
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language
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