how the basic plan recognition system and heuristic focusing interact, consider the following example. Assume that the interface is monitoring a purchase activity ...
From: AAAI-84 Proceedings. Copyright ©1984, AAAI (www.aaai.org). All rights reserved.
FOCUSING IN PLAN RECOGNITION Norman Department
of Computer
and Information
The University Amherst,
F. Carver,
Victor R. Lesser, Daniel L. McCue* *Digital Equipment
Science
Massachusetts,
Merrimack,
01003 future
ABSTRACT A plan recognition architecture is presented which exploits application-specific heuristic knowledge to quickly focus the search to a small set of plausible plan interpretations from the very large set of possible The heuristic knowledge is formalized interpretations. maintenance system where for use in a truth heuristic assumptions and their interpretation justifications are recorded. By formalizing this knowledge, the system is able to reason about the behind the current state of the assumptions This makes intelligent backtracking and interpretations. error detection possible.
An
issue for plan
search spaces is how to rapidly number
plan
based
interface
has system
in
recognition
in large
and accurately
recognixe
the
[3, 6, 7J.
POISE
the
goals
actions
they
By
accomplish.
in the context
intelligent
POISE
intelligent
plan
that
could
of
user
plans
are
of user actions and recognizing
a
assistance
recognition
is a
recognizer
may be forced
of
interpretations
plan
because
of: 1) concurrency
complex
user‘s
of an
task
active
plan
since
constraints
on the temporal
among
2) sharing
of plan steps among alternative
possibility
that any partial
among
of
alternative
and accurately
and
reduce
in order
provide
the
for most
to the user.
Complete-Purchase
name
are
specified
in
a
formal
and its parameters (Amount,
description
Items,
Vendor)
!
A textual
DESC
When the invoice is received, check with the requester to find out if the goods have been accepted and should be paid for or if they have been returned and so should be canceled.
2
The steps
Receive-Invoice (Pay-For-Goods
’ Check-Goods I Cancel-Goods)
!
The
on the plan
COND
= qtc%&ved”) (Check-GoodsStatus WILL-EXIST Pay-For-Goods = qwlxrmd”) (Check-GoalsStatus WILL-EXIST Cancel-Goods
the
involved
of the plan
IS
cmstmints
and their
relative
ordering
’ sttps
and
objects
Receive-Invoice&em
= Check-Goods&ems
Receive-Invoiceltems
= Pay-For-GoodsJtems Cancel-GoaMtems
A definition
parameters
Amount Items Vendor
of plan
OR
= Receive-Invoice Amount = Receive-InvoiceItems = Receive-Invoice.Vendor
z~plan
is one in a hierarchy of plans *for purchasing in an The plan, Complete-Purchase, consts~ of three steps of which’ the final sten is either Pav-For-Goods or Cancel-goods.
(i.e., loose
Additional COND clause statements umstmin stateme;lts. the parameters of the subplans (e.g., the item being paid for must be the one referred to in the invoice). WhiIe this plan dots not make use of it, the Is chmse language provides for concurrency with the shufffe operator which leaves the relative ordering of the plan steps unqecified. The steps of concurrent toplevel plans are implicitly shuffled W.
clause
plan steps); plans; 3) the
plan might be continued
number
in the design of such a
interpretations
efficient
The plan
!
consideration
in user activities ordering
be
!
system.
to keep a very large number under
to
PROC
to a user
be used as part
assistant for an office automation
Plan
of active
system
assistance
detection and management, error agenda (e-g., correction, and plan completion). Figure 1 describes a simple
disambiguate
is how to rapidly
of this model of possible actions,
POISE is able to provide
to
information
of a small
plan recognixer the number
of a small
intelligent
Hierarchies
used to specify typical combinations
actions
constraint
observation
A key problem
The need for this type of plan
arisen
4) insufficient
the
The descri ‘ens of procedures/plans language [l p” as depicted here:
on the observation
of plan steps.
recognition
from
03054
interpretations.
the
INTRODUCI’ION
important
the current
user
New Hampshire,
user actions;
acquired
I
Corporation Blvd. (MKOl-2GO9)
Continental
of Massachusetts
by
This research was sponsored, in part, by the External Research Program of Digjtal Equipment Corporation and by a grant from Rome Air Development Center.
Figure
42
1 - POISE Complete-Purchase
plan
Our solution a
to this problem
Plan application-specific the constraint knowledge quickly
heuristic
is used
focus
the
search
from
interpretations.
The
likelihood
steps are shared,
deal
plans,
and the
set of
large
heuristics
architecture
to
of
with
the
heuristic
for representing
heuristic
plan recognition
systems.
about
the assumptions
interpretation
and
information to recognize the
behind
represents
heuristic
information
II
they
system
The plan
possible
new ability
the user has made
error led
an has
to
these assumptions,
information.
This
allowing
system
been
can the
We believe
made, used
an to
interpretation,
to
the
that this approach
the new benefit
of
why
not only applies to
heuristic
systems
knowledge
for
Adaptability to different applications and environments with changes to the heuristic control knowledge alone (i.e., without requiring changes to the underlying reasoning system).
The capability users.
backtracking
of explaining
scheme.
its reasoning
considered
in
interpretation
basic
and semantic
i.e., plan by
process
step
providing
validity
a
use
context
which
to be recovered
the current
2.
temporal
It also permits
interpretations
unlikely
invalidates
Figure
were if new
likely interpretations.
tracks a user action, by attempting
it initiates
to integrate
the
as follows:
When the predictions reach the level of the new instantiation, constraint values are checked. If the constraints are satisfied, the monitor integrates the user action instantiation into the higher-level plan instantiations. This is done by “abstracting” from the action instantiation up to the plan level of the predicting instantiation. The uabstraction” creates instantiations and Pro== Plan propagates constraint values. ‘Ihe new and the predicting instantiation structures are copied’ and merged into a single structure which represents a new interpretation. The syntactically and semantically valid continuations of existing interpretations are
The use of an intelligent focus-ofcontrol strategy which can reason about context and the relationships between competing and cooperating interpretations when integrating new information.
The use of an intelligent
previously
allows
of five
If a plan of this type was expected by any interpretation entries in the focus set, the monitor expands the predictions from the higher-level instantiation towards the instantiation of the action. This generates a hierarchy of instantiations on the prediction blackboard.
it
plan.
interpretation
This
consists
An instantiation of the primitive plan which represents the user action is placed on the instantiation blackboard.
to
for it address issues which must be faced by
to exploit
the
explained
user action into existing interpretations
any such system: The ability control.
the
the
contraints.
focusofcontrol
mechanism.
the recognition
an
what
how
user
out a particular
but to complex
uses
to restrict
ARCHITECXLJRE
syntactic
instantiations,
When the monitor
intelligent
decide
has the added
explain
If
plan
heuristic
and
implements
and attribute
information
or that
error.
and how to integrate
believes the user is carrying
plan recognition,
be
invalid
approach to
an error
interpretation
of
of the
When
made.
contradicts
the
how
and
architecture
depicted
which checks
orderings
to reason
state
as
of possible
for
recognition
architecture
machinery
system
the system can use this reasoning
scheme
in general
A formal
for
current
interpretation
the
formalized
the
that
which
has made
assumptions
were
PLAN RECOGNITION
components
the current
into two recognition
shows
strategy
an
has advantages
It becomes
why
backtracking undo
assumptions
is acquired
interpretation,
system [4].
III
application-specific
relative
a new plan.
use in a reason maintence
plan
that plan
of continuing
has been
section
and
the
possible
the likelihood
knowledge
discusses
focus-f-attention
This The
II
search.
plausible
set
likelihood
existing plan versus starting
strategy
of the paper is organized
Section
SectiOnS.
This heuristic
a small
very
which
supplement
focusofcontrol to
the
of alternative
can
in the plans.
by the
interpretations
in
knowledge
information
The remainder
has been to develop
architecture
recognition
’ This copy permits constraint values to be propagated and then easily retracted if the system decides to backtrack (i.e., revise prevmus decisions about which higher-Ieve structure an mstantiation is part of.)
to
43
posted to the focusing system, Continue” facts (see section III).
PLAN LIBRARY
as
“can
l
The monitor also checks to see if the user action could be the start of a new activity. It scans the plan library to determine whether or not the user action could syntactically start a new high-level plan.
l
If a new plan could be started, the monitor “abstracts” from the action instantiation to constraints and higher-level plans, checking propagating constraint values until a top-level The plans which the user plan is reached. action can syntactically and semantically start are posted to the focusing system as “can STart” facts (see section III).
SEMANTIC DATABASE
AGENDA
To
MONITOR
INSTANTIATION BLACKBOARD PREDICI’ION BLACKBOARD
l
l
l
.
.
l
0
consider
the
interface
is monitoring
represented The
whose
step
only
sub-step
Send-Information,
where future
SEMANTIC DATABASE - maintains a representation the state of objects in the users world.
blackboard. current
the
in progress.
mechanism
plan, of
focus plan
interpretation
Send-Information
which,
abstraction The
for
sequence
triggered
44
of other
monitor
partial
monitor
is
action
a
that
this
is the most
likely
seen
so far.
the
A
and its plan
instantiation
in Figure 3.
Send-Information.7, the
indicates
leading
of
instantiation
blackboard. entry, next
AEO9, level
of
(Send-Information.7). up to this point
agenda
entries
has
some of
Note that most agenda
if the focuser
is correctly
user actions.
The
of
the
of an agenda
will not be executed
tracking
interpretation
generate
given
of actions
the creation
plan,
actions
the
would
which are pictured entries
the
on
the
plan,
primitive
has just occurred
the creation
if executed,
primitive
the on
set
of
instantiated
This triggered
Request-Information.
instantiation
action
is Check-Goods
the
partial is
action
Receive-Information.
by
The
is a user
Purchase
is the
plan
The
has been
plan,
followed
Complete-Purchase
Architecture
propagation
that
activity
sub-step
consists
Receive-Information.
action constraint
plan
interact,
l), has as its first step,
only
of Complete
Request-Information
PLAN LIBRARY - contains data structures describing the plans. The monitor makes use of the temporal specifications of the subpIans to predict the next steps in the plans and ma k esuse of the constraint specifications when propagating attribute values between plan instantiations.
the
basic
Assume
a purchase
by the primitive
next
whose
FOCUSOF-ATTENTION DATABASE a data structure where the monitor records its interpretations of user actions and the assumptions it made to arrive at those interpretations. The partial pIan instantiations xseg=;he current best interpretations are listed in .
of
the
focusing
example.
(see Figure
Receive-Invoice,
MONITOR AGENDA - a prioritized list of possibfe next steps for the monitor to take to expand interpretations. The monitor selects actions from this agenda to expand the interpretations that it is currently %est” interpretations). The pusuing (i.e., its current action of constructing an interpretation on the blackboard triggers the addition of new actions to the monitor agenda. If all agenda actions were executed, ah possible (valid) interpretations would be generated.
discussion in [7].
how
heuristic
following
Complete-Purchase
Figure 2 - Plan Recognition
2 A full contained
and
Complete-Purchase
INSTANTIATION BLACKBOARD - a data structure where the monitor records potential interpretations of user activities as hierarchically related sets of partially instantiated plans BLACKBOARD - a data structure “simulates” various predictions of
understand
system
The state of the focus set and instantiation blackboard Figure 3. The depicted in pm are as
MONITOR - the interpreter which tracks user actions and system events, instantiates pIans corresponding to those actions and events, and propagates constraint information?
PREDICTION the monitor actions
better
recognition
compares
the
instantiation,
to the types of actions
interpretations
considers
only
in those
which were expected
entries.
Through
the
monitor
detects
a
the
focus
interpretations
set. for
by The the
by focus set interpretation
use of precomputed match
expected
between
the
tables, plan
the type,
Send-Information, the plan, focus the
and
Check-Goods,
set entry
generate
agenda.
Constraint
the prediction the
level
of
values
the
shown meets
predictions representing
the
user
In this case, parameter
the partial
The action
interpretation
how focusing
interpretations
Send-Information
of
constraint
original
instantiation
Check-Goods. the
from
the
the
from
been
the
Focusing
Figure
integrated
5, the into
action,
focus
set
cannot
the
interpretation.
The
partial
4,
the
top
structure
needs
copied
Check-Goods24 this
revise
of
was
when
copy
its
the previous it
was
operation
decision
that
interpretation
or
could
be
an
a
valid
really error
revised will
because
the existing reuse
to pursue interpretations
later
be
by
make it less likely.
within
interface!
be
should be
of
from further
still
might
heuristics to
is
instance
Complete-Purchase.6,
be interpreted the
the
be part of Complete-Purchase.6.
differently
focus entries
of
noted,
(Send-Information.7
user), the focusing
which
has
should
and
level
Figure
new
to
While
interpreted
set as
Send-Information.7
The
Receive-Information.1,
shows
the
(Complete-Purchase-
system
interpretation
in
instaniations
interpretation
previously
consideration.
of
that
the
also eliminates
structure,
Current best: Complete-Purchase.6 Predictor: CompIete-Purchase.6 Next step: Check-Goods Agenda entry: AEO6
the
If the actions
interpretation
these
“discarded”
previously
thought
to be “unlikely.”
bhudiation
Blackboard Complete-Purchase.6
hi=& AEO6 Predict
Check-Goods
...
AE09
As
Check-Goods24
are considered. In
to
up
Complete-Purchase.6
permits
Send-Information.19 with values
interpretations
values Note
in
integrated.
constraint
This example
plan
prediction.
Complete-Purchase
down through
action,
has created
Complete-Purchase.6.
on
the potentially explosive plans such primitive
by limiting
propagated
to
meets the expectation
in focus.
helps control
The
in Figure 4. When the level of the
compatible
Send-Information.7.
process
on
actions
values are propagated
abstraction
executed
for
removing
of
to actions
be
predictions
are compared.
has
of
could
those
instantiations
instantiation
references
types next.
predictions
instantiates
blackboard,
plan
is expected
which
appropriate
monitor
prediction
which
agenda
the
sub-step
also contains
monitor’s
The
starting
Abstract
from
Rcqucst-Infurmation
Receiy-Invoice3
Complete-Purchase6 from
Send-Information.7
Receive-In&mation.l Send-Lnformatioa.7
Figure 3 Lwtandndon
Blackboard
I’rdlctlon
Gxyylctc-Purchase.6
Agcab ... AE4I9 Abstract
Request-Information
from
Send-Information.7
Rcceiv -Lnvoicc3 2 Receive-Lnformation.1
Black-
Check-Goods.16 I Request-Information.18 Send-I&mation.l9
Send-lnformation.7
Figure 4 FIml
Focus
Iastantlat.lon
Set
Complete-Purch 25 7 / Check-Goods24 Receive-Lnvoiee3 \ / Request-Information21 Receive-Lnformation.l \ Send-Lnformation.7
gerr;znbcst: Complete-Purchas+ . Request-Information21 Receive-Information Next step: Agenda entry: AEll 4Wh ... AEll
Predict
Receive-Information
Blnckboard
from
Request-Lnformatioa21
Figure 5
45
Prcdktion
BIaekboard
aeckiGd-16 Request-Information.18 Send- IJ ormation.19
III Focusing mechanism
POISE
in
which limits
interpretations
is
a
heuristic
the interpretations considers system
the
which
actions
User action k is SHared by plan instantiation Xu and Yv (i.e., the action fulfills parts of two goals).
FOCUSING
deemed
most
control
Heuristics
likely.
User action k has GreaTeR likelihood of fulfilling part of plan instantiation Xu than of plan instantiation Yv.
of the user those to about
the likelihood
of user actions are of three types: 1.) Application-specific - Derived from observations of For example, ua single the application environment. action is most likely to be taken to satisfy some part of a single goal.” That is, sharing a single low-level plan among several high-level plans is unlikely. Also, “initiation of a new top-level plan is a less likely reason for executing some action than completing some plan already in progress.” Since these heuristics are derived from a particular application (e.g., office systems), their relative importance (or usefulness) will depend upon the application. Other applications may have different characteristics. of specific actions 2.) Plan-specific - The likelihood being taken to satisfy particular goals (iz., as steps of particular high-level plans) may be specified as part of the plans. For example, “action A is more likely to be part of plan X than plan Y.” 3.) User Goals - The user may explicitly state goals plans with some or all of their (i.e., high-level accomplished. filled in) to be parameters Interpretations which match these explicit user goals may be considered extremely likely.
A Most Likely Explanation for user action k in “state” w (i.e., after considering the sequence of actions, w) is that it is part of plan instantiation Xu. The interpretation entries in a focus set are the plan instantiations in the union of the MLEs in a particular state. A formal definition of Most Likely Explanation: IF PE(k,Xu) AND NOT [PE(k,Yv) AND GTR(k,Yv,Xu)] THEN MLm%kw. where k stands for a user action, u, v, and w are sequences of user actions, X and Y are high-level plans, and plan instantiations are represented as Xu for the high-level plan underway (X) and the actions which partially fulfill it (u).
The over
these
heuristics facts
application-specific The make
focusing
strategy
uses
these
about
the
most
assumptions
interpretations a form
of nonmonotonic
by default.
A reason
recording along
to be expanded.
and with
retracted scheme proposes
without
having
work
because
assumption
undo
the effects
be
unrelated
of changing
a
the heuristic
are represented
knowledge,
the
as follows:
sT(kJ9
-
User action k can STart plan X.
WJW
-
User action k can instantiation Xu.
WWW
-
A Possible Explanation action k is as part instantiation Xu.
Continue for of
developed
for
rules of
the
the office
are:
Initiation of a new top-level plan is a less likely reason for executing an action than completing some plan already in progress: IF C(k,Xu) AND PE(k,Xuk) AND ST(k,Y) AND PE(k,Yk) AND NOT SH(k,Xuk,Yk) AND CONSISIENT(GTR(k,Xuk,Yk)) THEN GTR(kXuk,Yk).
and
can be inferred.
In order to formal.& facts and assumptions
to
are
backtracking can
heuristics
Three
H2-
assumptions
assumptions
as inference
A single user action is most likely to be taken to satisfy some part of a single goal so it is unlikely that the input action be shared by multiple high-level plans. This is implemented by stating that if no explicit assumption has been made that an input is shared by multiple interpretations, assume that it has not been shared: IF PE(k,Xu) AND PE(k,Yv) AND CONSISTENT(NOT SH(k,Xu,Yv)y THEN NOT SH(k,Xu,Yv).
is used for
Assumptions
formalized assumptions.
Hl -
represent
Assumptions
incorrect
assumptions.
application
as reasoning
system
dependency-directed
identifies
better
known
interpretation
justifications.
a
which
interpretation particular
their
with
retracted
reasoning
to
“reasonable”
The heuristics
maintenance
maintaining
heuristics
are and
plan user plan
3 See [8] for an explanation CONSISTENT.
of the nonmonotonic
modal
upcxator
H3 -
(fact
Of two Possible Explanations for an input action, if one is assumed to be a Most Likely Explanation for a later user action then it has a GReaTer likelihood of being the Most Likely Explanation for this input: IF PE(k,Xukj) AND PE(k,Yvk) AND NOT SH(k,Xukj,Yvk) AND MLE(w,j,Xukj~ AND CONSISTENT(GTR(k,Xukj,Yvk)) THEN GTR(k,Xukj,Yvky
11).
assumed
This must be done because, to continue
l
l
l
l
algorithm
When there
the
is no
only
the focusing
given the
constraint
possible
interpretation process
Explanation”
algorithm
Figure
6.
a
fact
The second
(facts
heuristics
interpretation
formalized is more
likely
(H2), results in interpreting of plan X rather and
10).
new
“Possible
than
part
Explanation”
for
action
partial to
plan
backtrack, that
than starting
interpretation
14).
User
of
action
c Y
the interpretation
of action (facts
c 22
Hl and I-D.
FUTURE RESEARCH system described built.
by the focusing office
is currently
A special-purpose
was
reason
The
additional
heuristics
has been
automation
We are planning
applications
the
of plan
system.
system the
of
as a continuation
AND
provided
existing
the heuristic
the
b (fact
the fact
b to be reinterpreted
POISE
in
studied.
application
being
to explore its effectiveness
which are not as tightly
constrained
in
as the
office. We most
plan
to
be
invloves
whose
order
to retract
scheme
retraction
explained.
reasoning
in
a more
current
A
about
assumptions
interpretation interpretations assumption
developing The
assumption
action
approach
the
allows
the
more the
and to
intelligent locates
intelligent
“quality”
the
identify
or to recognize
of
resulting the
“best”
that the user has
made an error.
One of
a new
currently scheme.
recent
current
only
an
are
backtracking
b, can
b results
4 Implicitly, w includes k and later user actions. s This is a slightly simplified version of the actuaI
of the
knowledge
a, the
continuing
a being
that
a and
STATUS
effective
Another
this action as a continuation of action
Note
from
forward
by action
actions
maintenance
than the start of plan Y (see facts 9
This interpretation
15-17).
some system
is more likely
The plan recognition
actions,
user action,
starting
push
is recognized,
is no
is the
9 generated
and
c,
fully,
3) is the
that
Zu
causes
be interpreted
N
the plan begun by action a above,
a, it is
b action which
it within there
and 23) because of heuristics
“Most Likely
or as the start of a new plan (facts 5 and 7).
now
example
user action, The
(see
as continuing
of
plan,
causes
(i.e.,
an interpretation
Y started
can
Since there is only one
for the first
action
more The
interpretation
information.
in focus.
be interpreted the
plan
than one “Possible heuristic rules to assumptions.
is straightforward.
for
interpretation
in
syntactic
ignoring focusing
a new
action,
interpret
where This
assumption
continuing
user
to
structure
C(c,Zu)
retract
Post the resulting “Most Likely Explanations” for the user action and propagate the results of this latest interpretation back to earlier interpretations.
is
third
way
instantiation).
If there are no “Possible Explanations” for the action, either an interpretation error or a user error has occurred. Backtrack through the assumptions which have been made to find one which could result in an alternate interpretation (previously disregarded because it seemed unlikely) which would explain the current action. Retract this assumption, revise the interpretation of the previous actions and repeat the interpretation process for the current action.
example
considers
form
Use the “can Continue” and “can STart” facts posted by the monitor during the basic interpretation process (see section II) to post “Possible Explanation” assumptions for the user action.
To understand an
plan including
to be “Shared” by two X plans
(i.e., Xab and Xab’ where b’ is another
is as follows:
If an action has more Explanation,” apply the generate relative likelihood
b was
has not yet ocurred).
interpretation The focusing
the partial
possible that a is meant
although
current
approach
exploit
the information
in
in a
the
semantic
knowledge
posted
likelihood creating
rule.
47
direction
about
in which we are extending
is the use of focusing about
database.
objects
heuristics that
the which
is contained
These
heuristics
include
the use of objects
in plans,
e.g., the
that plans share objects new objects.
or the likelihood
of
ACKNOWLEDGEMENTS Bruce
Croft
contributions plan
and
Larry
to the design
recognition
Lefkowitz
have
as
part
of
Croft, W. B., L. Lefkowitz, V. Lesser, and K. Huff, “POISE: An Intelligent Interface for Profession-Based Systems,” Conference on Artificial Intelligence, Oakland, Michigan, 1983.
PI
Doyle, J., “A Truth Maintenance Inielligence, 12231-272.
PI
Gischer, J., “Shuffle Languages, Petri Nets, and Context-Sensitive Grammars,” Communications of the ACM, 24(9)597405.
made
and implementation
architecture
PI
of the
the
POISE
System,” Artificial
project.
REFERENCES
PI
Bates, P., J. Wileden, and V. Lesser, “Event Definition Language: An Aid to Monitoring and Debugging Complex Software Systems,” Technical Report 81-17, Department of Computer and Information Science, University of Massachusetts, Amherst, Massachusetts, 1981.
[fd Huff,
PI
Croft, W. B. and L. Lefkowitz, “An Office Procedure Formalism Used for an Intelligent Interface ,n Technical Report 824, Department of Computer and Information Science, University of Massachusetts, Amherst, Massachusetts, 1982.
PI
McCue, D. and V. Lesser, “Focusing and Constraint Management in Intelligent Interface Design,” Technical Report 83-36, Department of Computer and Information Science, University of Massachusetts, Amherst, Massachusetts, 1983.
PI
McDermott, D. and J. Doyle, uNon-monotonic I,” Artificial In!elligence, l3:41-72.
Plan
Grammar:
The
sets of facts
X = a b d... and assumptions a
1. n(aS) 2. PE(a,Xa) 3. MLE(a,a,Xa) Focus
?&+a}
Y = b c... for
each
User su cewsive
K. and V. Lesser, “Knowledge-Based Command Understanding: An Example for the Software Development Environment ,” Technical Report 82-6, Department of Computer and Information Science, University of Massachusetts, Amherst, Massachusetts, 1982.
Actions:
ab before backtrackina 4. c@Xa) 5. PE ,Xab) 6. ST ,y) 7. PE % ,Yb) 8. -SH@,Xab,Yb)
a b c...
T&ate” (string
of user
actions)
arc:
ab after backtrackina 4. 5. 6. 7. 8.
c@JW PE ,Xab) ST ,Y) PE ! ,Yb) -SH(b,Xab,Yb) &7?HlJ 10. MLE(ab,b,Xab) l14. MLE(ab,b,Yb)
abc
15. qab) 16. PE(c,Ybc) 17. MLE(abc,c,Ybc) 4. CCbSa) 2 E % %“’ 7: PE :Yb) 18. PE(b,Ybc) 19. --SH@,fiSlab)
WV-U
1. 2. 11. 12. GTR(a,Xab,Xa)
20. GTR@,Ybc,Xab) t5,17,lg@31 21. GTR@,Ybe,Yb)
t2,ww3~ l3. MLE(ab,a,Xab) Focus
Set-b)
13. MLE(ab,a,Xab) Focus
t7,17,18J-1 22. MLE(abc,b,Ybc)
Sct=jXab,Yb) 23. MLE(abc,a,Xa) Focus
Sct=(Xa,Ybc}
Facts and assumptions are grouped by the user action to which they refer. only ‘Sn” [4] facts are represented and some obvious -SH assumptions have been ignored. The justifications for assumptions made using the three heuristics formalized in the paper are ’ en in braces ({ )) below the assumptions with the three heuristics denoted as Hl-H3. Thart assumptions cK $ed durin backtracking are denoted with lk C and ST facts arc posted by the monitor as described in stct~on II. t-h e remainder of the facts rcsuIt from the application of various bookeeping ruIes.
Figure 6 - Focusing
in a Sample Grammar
48
Logic
