DOCUMENT RESUME IR 001 805 Collins, Allan; And Others Reasoning from Incomplete ... - Eric

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DOCUMENT RESUME
IR 001 805
ED 104 401
Collins, Allan; And Others
AUTHOR
Reasoning from Incomplete Knowledge.
TITLE
Bolt, Beranek and Newman, Inc., Cambridge, Mass.
INSTITUTION
Advanced Research Projects Agency (DOD), Washington,
SPONS AGENCY
D.C.
BBN-R-3019
REPORT NO
Mar 75
PUB DATE
62p., For a related document see IR 001 803
NOTE
HC-$3.32 PLUS POSTAGE
MF-$0.76
EDRS PRICE
Artificial Intelligence; *Computer Assisted
DESCRIPTORS
Instruction; *Computer Programs; Geography;
Individualized Instruction; *Logic; Kan Machine
Systems; On Line Systems; Tutorial Programs
Inferential Reasoning; SCHOLAR; Socratic Method
IDENTIFIERS
ABSTRACT
People use a variety of plausible, but uncertain
inferences to answer questions about which their knowledge is
incomplete. Such inferential thinking and reasoning is being
incorporated into the SCHOLAR computer-assisted instruction (CAI)
such as SCHOLAR
system. Socratic tutorial techniques in CAI systems
application using the geography
are described, and examples of their
module in SCHCLAR are shown. (Author/DGC)
BOLT BERANEK AND NEWMAN
I N C
DEVEtOPMEN I
CONSULTING
RESE ARCH
BBN Report No. 3019
REASONING FROM INCOMPLETE KNOWLEDGE
Allan Collins
Eleanor H. Warnock
Nelleke Aiello
Mark L. Miller
March 1975
Sponsored by
Office of Naval Research and the
Advanced Research Projects Agency
Approved for public release; distribution unlimited.
Reproduction in whole or in part is permitted for
Government.
any purpose of the United States
8
2
SAN FRANCISCO
LOS ANGELES
WASHINGTON, D C
CHICAGO
HOUSTON
CAMBRIDGE
.'-1Mr====,
REASONING FROM INCOMPLETE KNOWLEDGE
Allan Collins
Eleanor H. Warnock
Nelleke Aie:lo
Mark L. Miller
Bolt Beranek and Newman Inc.
02138
Cambridge, Massachusetts
Contract No. N00014-71-C-0228, dated March 1, 1971
Amendment Modification No. P00002, dated January 1, 1973
Expiration Date, June 30, 1975
Total Amount of Contract $586,000
491-1850]
Principal Investigator, Allan M. Collins [(017)
Office of Naval Research
Sponsored by:
Contract Authority No. NR 154-330
Dr. Marshall Farr and
Scientific Officers:
Dr. Joseph Young
and
Advanced Research Projects Agency
ARPA Order No. 2284, dated August 30, 1973
Program Code No. 61101E
document are those
The views and conclusions contained in this
necessarily
of the authors and should not be interpreted as
implied,
representing the official policies, either expressed or
Office of Naval
of the Advanced Research Projects Agency, the
Research, or the U.S. Government.
Reproduc-
unlimited.
Approved for public release; distribution
of the
tion in whole lr in part is permitted for any purpose
United States Covernment.
UNCLASSIFIED
LIRIT Y I L A.S11- k w T ION OF TIN, PA E (When thud I litre)/)
iii. ,u 'Ns! HI ( !Inv,
REPORT DOCUMENTATION PAGE
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i MB ER
FIF
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Technical Report No.
4
TYPE OF REPORT h PERIOD COVE nl tl
TITL_E,.,1,0,,,,a,-,
5
Semi-Annual
REASONING FROM INCOMPLETE KNOWLEDGE
(1 Aug 74
- 31 Jan 75)
PERFOPMING ORG REPORT NUMBER
8
BBN Report No. 3019
AU THOR(SI
B. CONTRACT OR GRANT NUMBERS)
7
Allan Collins, Eleanor H. Warnock,
Nelleke Aiello, Mark L. Miller
No. N00014-71-0228
F ERFORMING ORGANIZATION N AMF AND ADDRESS
PROGR AM ELEMENT PROJECT TASK
10
AREA 6 WORK UNIT NUMBERS
Bolt Beranek and Newman Inc.
61153N
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RR042-06;PR042-06-01
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,,
,ONTROI LING OFFICE NAME AND ADORE SS
REPORT D ATE
12
Personnel and Training Research Programs
March 1975
Office of Naval Research (Code 458)
NUMBER OF °AGES
13
Arlington, VA 22217
50
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1. MONITORING AGENCY N AME 6 ADDRESS(t) ,ifft rrql from Controlling Offte e)
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Unclassified
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SCHEDULE
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Approved for public release; distribution unlimited.
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DISTPIBUTION ST Al EMENT (,.j the
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17
SUPPLEMENT AR,' NOTES
8
To appear in D. G. Bobrow
& A. M. Collins
(Eds.) Representation
Academic
and Understanding.
New York: Press, 1975.
by block
KEY WORDS (( onunue tnt reverse ,vde tf neces,ur, and tdenufy
'Lumber)
9
Education, CAI, Tutoring, Inference, Cognitive Psychology,
Analogy, Indu.Lion, Causality.
by block
ABSTR ACT (Cont.nue on reterse sole t) necessary and tderittfy
number)
20
The paper describes how people use a variety of plausible, but
uncertain inferences to answer questions, about which their
This kind of reasoning is described
knowledge is incomplete.
in terms of how it is being implemented in the SCHOLAR/CAI
The paper also shows how people can be taught to
syst.i:m.
reason in this way, using a Socratic tutorial method implemented
in a system like SCHOLAR.
FO3 EDITION OF 1 NOV 65 IS OBSOLETE
747
RM
1
DD
,
JAN
HNCLASSIFIED
3
nr)rt II
SECL ilTY CL ASSIFICATION OF THIS PAGE (When Data I
4
REASONING FROM INCOMPLETE KNOWLEDGE
Allan Collins
Eleanor LI. Warnock
Nelleke Aiello
Park L. Miller
Bolt Beranek and Newman Inc.
TABLE OF CONTENTS
INTRODUCTION
2
OPEN VERSUS CLOSED WORLDS
3
NEGATIVE INFERENCE.;
7
Match Processes
8
13
Contradictions and the Uniqueness Assumption
23
Lack-of-Knowledge Inferences
26
FUNCTIONAL INFERENCES
35
LEARNING TO REASON
38
What the Student Learns
The Socratic Method of Teaching
43
47
CONCLUSION
48
REFERENCES
This research was sponsored by the
Personnel
Training
and
Psychological Sciences Division, Office
Research
Programs,
of Naval Research, N00014-71-C-0228,
Contract
under
No.
Contract Authority Identification
NR 154-330.
Number,
fellowship
Partial support also came ,:rom a
first
the
to
from the John Simon Guggenheim Foundation.
We would
author
like to thank Susan M.
helped
program
who
Graesser
the
contradictions
Bobrow for his comments on a
Daniel G.
and
draft of this paper.
Bobrow
Collins,
appear
D.G.
To A.M.
(Eds.)
in
&
New York: Academic Press,
Representation and Understanding.
Page
2
INTRODUCTION
It doesn't trouble people much
their
heads
that
are
full of incomplete, inconsistenz, and uncertain information.
With
trepidation
little
they
drawing
about
rather
go
doubtful
conclusions
from their tangled mass of knowledge,
for the most
part
tenuousness
unaware
of
their
the
of
reasoning.
very tenuousness of the enterprise is
But
the
bound up with the power it
gives people
with
deal
to
a
language and a world full of ambiguity and uncertainty.
We will describe this kind of human reasoning in
terms
computer
how
made
in the same
can
reason
of be to
a
purpose
SCHOLAR
illogical
will
way. this use
we
For
program
computer
whose
(Carbonell,
1970a,
1970b),
a
semantic
knowledge about the world is stored in
network
a
human memory (Collins and Quillian, 1972).
structured
like
One of SCHOLAR's data bases is about geography, and people's
the nice property, for our
geography
knowledge
about
has
purposes, of being incomplete, inconsistent, and
uncertain.
analysis will concern geography, but
examples
the
So
and
everyman's
geography
stand-in
only
meant
for
as
is
a
knowledge about the world.
SCHOLAR's aim in life is to teach people by carrying on
them (see Collins, Warnock, and
dialogue
with
tutorial
a
Socrates
Once upon a time,
thought
Passafiume, 1975).
he
teach people to reason by such a tutorial method.
We
could
Page
3
will attempt to show that a person can
learn
infer
to
at
least
some
what he doesn't know about geography by the
of
Socratic method, and to show
how
Program
SCHOLAR
like
a
might even play the role of Socrates with some finesse.
OPEN VERSUS CLOSED WORLDS
Recently Carbonell and Collins (1973) have stressed the
distinction
between
open
worlds, such as geography, where
knowledge is incomplete, and
closed
worlds,
such
the
as
blocks world of Winograd (1972) or the lunar rocks catalogue
of Woods, Kaplan, and Nash-Webber (1972), where the complete
objects and relations is known.
The distinction is
set
of
important, because many
procedures
of
the
rules
and
of
inference
have been developed for dealing with closed
that
worlds oo not apply to open worlds.
The distinction between open and closed worlds comes up
in a variety of ways.
For example, if there are no basaltic
rocks stored in a closed data base, then it makes
sense
to
the question "Were any basaltic rocks brought
say
"no"
to
back?".
But, if no volcanoes are stored in a data base
for
does not follow that the auestion "Are there
the
U.S.,
it
any volcanoes in the U.S.?" should necessarily
answered
be
appropriate answer might be "I don't know".
more
"no".
A
Furthermore, it makes sense to ask what the
smallest
block
Page
4
a scene is, but it makes little sense to ask what is the
in
shortest river or the least famous lawyer in
the
U.S.
It
would
strategy
deciding how many
appropriate
be
an
for
blocks in a scene are red, to consider each block and
count
many
how
not be an appropriate
are
would
red.
But
it
strategy to consider each person stored in
limited
data
a
base
(such as humans have), in order to answer the question
"How many people in the U.S.
are over 30 years old?".
Within open worlds there are closed sets, however.
For
example,
be possible to say how many states are on
may
it
Since closed sets
the Pacific, if they are all stored.
are
the closed sets in memory
makes
mark
rare, sense
to
it
possible
rather than the open-ended sets.
Then
is
it
to
apply closed-set strategies where the entire set is known.
The reason most sets are open is that most concepts are
ill-defined.
plausibly
that there is a
argue
One could
smallest city in the U.S., if we
arbitrary
agree
some
on
definition
of a city (e.g., incorporation by a st.te).
But
to use Wittgenstein's (1953) example, there
way
no
to
is
Even if we
precisely
specify
and is not a game.
what
is
definition,
agree
would
were
some
get
into
to
on
we
Outside of
difficulty
when
to apply it to cases.
try
we
simply
concepts
mathematics
most
not
are
logic,
and
susceptible to precise definition.
S
Page
5
Where a concept is relatively well-defined, like states
the U.S., we still may not know all the examples, and so
in
means
that
we have to treat it as an open set.
the
This
is not in the
distinction
closed
sets
between
open
and
person's
each
head.
Your
rather
outside world, 'pot
in
closed set may be my open one.
considering
by
issues
We can illustrate some of
the
ever considers it, except
anybody
hardly
Moldavia,
since
know
the
Americans
all
Most
adult
perhaps Moldavians.
they know that Moldavia is not a
U.S.,
the
so
states
in
but
states,
They may not be able to name
the
all
state.
states enough times that they've stored
they've
heard
the
know
may
even
They
each of them as recognizably a state.
either explicitly (to name) or implicitly (to recognize) all
Moldavia
say
the countries in South America well enough to
is not one of those.
implicit
explicit
and
between
distinction
The same
The states would be stored
SCHOLAR.
exists
knowledge
in
data
base
the
implicitly if each appeared as an entry
in
They
link to state.
(superordinate)
instance-of
with
an
stored
were
all as
they
explicitly
would be stored
if
states.
instances under U.S.
some
on
set
The same objects can be part of a closed
Even though a person
an open set on others.
occasions
and
(or SCHOLAR) may know all the countries in South America, he
rage
6
may
not know all the countries in the world.
So he may not
be able to say whether Moldavia is
a country
or
even
not,
though
can
is not a country in South America.
say
he
it
Similarly none of us really knows whether Moldavia is
a city
town
or
the
U.S., unless of course it is one.
in
But by
restricting the set to, say, the major cities in
the
U.S.,
we can exclude Moldavia.
Whether Des Moines is a major city
in the U.S.
may be debatable, but there is no way
Moldavia
can make it.
Words like "major" or "typical" (Lakoff, 1972)
make it possible to restrict a
exclude
borderline
set
to
cases, such as the likes of Moldavia.
What it takes for a computer
system
SCHOLAR
like
to
discriminate
between
Moldavia and Des Moines are tags that
indicate
relative
different
importance
the
cities
of
(Carbonell
Collins,
Collins,
Warnock,
and
1973;
and
Passafiume, 1975).
Suppose there is a particular data
base
configuration
where
number cities are stored,
of U.S.
a
with Moldavia not one of them and Des Moines tagged to be of
minor
importance.
decision
as to what are the
The
rule
major cities would be something
include
those
like
this:
that
tagged
as important, exclude any not stored, and
are
any objects stored, but not clearly important, are
excluded
hedged about, depending on their relative importance and
or
In this way people can apply
the size of the set stored.
a
modified closed-set strategy to deal with open sets.