From: AAAI-87 Proceedings. Copyright ©1987, AAAI (www.aaai.org). All rights reserved.
Compiling
Plan
Expressed
in Qualitative
Operators
from Domains
recess
Theory
John C. Mogge
Qualitative Reasoning Group
Department
of Computer Science
University of Illinois at Urbana-Champaign
Abstract
The study of Qualitative
Physics has concentrated
on
expressing
qualitatively
how the physical world behaves.
Qualitative
Physics systems accept partial descriptions
of
the world and output
the possible changes that can occur. These systems currently
assume that the world is
left untouched
by human or robot agents, limiting
them
to certain types of problem solving.
For instance, a stateof-the-art
qualitative
physics system can diagnose faulty
electrical
circuits
but can not construct
plans to rewire
circuits to change their behavior.
This paper describes an
approach to planning
in physical domains and a working
implementation
which integrates
Forbus’ Qualitative
Prointerval-based
plancess Engine (QPE) with a temporal
ner. The approach
involves compiling
QPE expressions
describing
a physical domain into a set of operators
and
rules of the planner. The planner can then construct
plans
involving
processes, existence of individuals,
and changes
in quantities.
We describe
how the compilation
is performed, the types derivable
plans, and current limitations
in our approach.
capabilities
without
rest
Introduction
The
study
requires
ing qualitatively
how the
Physics
accept
systems
output
the possible
rently
assume
robot
For
agents,
rewire
circuits
domains
ticular
gine
electrical
Sections
Operator
Compiler
sion in section
QPE
is an implementation
as the deductions
it sanctions.
erator
[F or b us, 861, with
Compiler,
domain
goals that require
inition
processes
The
(TPLAN)
expressions
describing
operators
the Operator
of liquid
Operator
Compiler
can happen
could
the
two powerful
prove
in the world.
constructed
and
Furthermore,
debugged
useful
systems.
states,
on
Op-
using
QPE,
Introduction
database
outputs
solve
increased
envisions
while TPLAN
once a domain
3
given the defcan
physics
adding
physics
inequalities
the
the-
such
but
as
mea-
have two components:
by D).
of five components:
preconditions
quantity
(outside
conditions
process,
Figure
of in-
quantities
and uses sym-
(signified
process,
during
Examples
sources,
and influences
1 shows
of
(inequal-
a typical
the
process
definition.
planner
in applications,
QPE
asserted
on quantities.
for describ-
are meaningful,
as a collection
in the
such
are liquid
how processes
order
Thus,
with
aspects
qualitative
Quantities
on the process,
puts
TPLAN
operator
involved
relations
a physical
Compiler
This
values.
quantitya)
a process
knowledge)
process
liquid
by A) and derivative
defines
individuals
QPT’s
for achievmg
flow, such as the
in the world from various
QPT
other
a syntax
as a partial
are irrelevant.
(signified
(QPT)
En-
based
called
For instance,
flows.
a par-
Process
of liquid in a container.
due to its integration
changes
which integrates
implementation,
liquid
in physical
the Qualitative
to occur.
the effects
can
plans to
amounts
ities),
a set of TPLAN
for creating
matching
amount
been
QPE
system
to planning
a planner
The
for a liquid flow process.
an operator
goals
accepts
and compiles
sured
Theory
individuals.
Like other
numeric
cur-
behavior.
system,
831.
physics
but can not construct
than
(GREATER-THAN quantity1
solving.
The
by discus-
of processes
provides
affect
quantities
and
ignoring
fluid paths,
and processes.
models
Process
and for expressing
and how they
are containers,
rather
4, followed
Examples
QPT
in a domain
active
amount
to
rele-
does.
to refer to the language
processes,
flow, and boiling.
bolic,
and TPLAN
Compiler
of Qualitative
physical
Qualitative
or
actions
to Q
which one models
QPT
of QPE
in section
841. We use the term QPT
flow, heat
systems
then
5.
ing individuals
by human
the
actions)
(to relate
the Operator
is presented
Introduction
ories,
of problem
qualitative
implementation
physics
[Allen and Koomen,
types
an approach
and a working
qualitative
These
the physics
Formalizing
possible
vocabulary
aspects
what
2
(Forbus,
world
as an agent’s
2 and 3 describe
vant to understanding
on express-
of the
untouched
to certain
their
describes
behaves.
can occur.
is left
circuits
to change
paper
(QPE)
that
world
them
world
descriptions
a state-of-the-art
faulty
This
the
limiting
instance,
diagnose
physical
partial
changes
that
has concentrated
(such
of planning.
for instance).
of individuals,
Physics
The user can design
the task
some use of the physics
processes,
dividuals
of Qualitative
little work.
about
of the domain
become
1
requires
worrying
what
plans
has
planning
is an implementation
described
TPLAN
qualified
temporal
the possible
adopts
1. Intervals
2. Variables
temporal
831.
by intervals
runs on top of a time
maintains
ble 1 shows
of the
in [Allen and Koomen,
of facts
The planner
which
to TPL
over
between
values a relation
are denoted
are denoted
which
logic described
relationships
the following
interval-based
TPLAN
by symbols
in :Allen,
831,
Ta-
conventions:
starting
starting
a
hold.
intervals.
can have.
syntactic
by symbols
keeps
they
with
with
“9’.
“?“.
OPERATOR pickup
PRECONDITIONS: (clear ?object) $clear-object
(on ?object ?surface) $on
EFFECTS: (pickup ?object ?surface) $pickup
(clear ?surface) $clear-surface
CONSTRAINTS: $clear-object ( :M) $pickup
$on (:O) $pickup
$on (:M) $clear-surface
Process : (LIQUID-FLOW ?src-can ?dst-can ?liq)
Individuals: (CONTAINER ?src-can)
(CONTAINER ?dst-can)
(CONTAINED-LIQUID (CL ?liq ?src-can))
(FLUID-PATH (FP ?src-can ?&t-can))
Preconditions: (VALVE-OPEN (FP ?src-can ?dst-can))
quantity Conditions:
(GREATER-THAM (A (PRESSURE ?src-can))
(A (PRESSURE ?dst-can)))
Relations: (IJUANTITYFLOW-RATE)
(q= FLOW-RATE (- (PRESSURE ?src-can)
(PRESSURE ?dst-can)))
Influences: (I+ (AMOUNT-OF (CL ?liq ?dst-can))
(A FLOW-RATE))
(I- (AMOUNT-OF (CL?liq ?src-can))
(A FLOW-RATE))
Figure
Table
1: Definition
of Process
1: Seven
Possible
Values
Value
Description
Inverse
:<
before
:>
Liquid
of Interval
Figure
chaining,
express
I
:O’
I overlaps
3
meets
Relations
and their
1 :OI
finishes
:D
! during
..-
equals
relation
/
* started
as a disjunction
means
finished
:DI
..-
encloses
and written
“is before
4. Facts
by
Figure
with
the
3: A Temporally
Rule definitions
4
equals
two intervals
as a list.
interval
tecedents
For instance,
(:<
:>)
over which
they
hold.
(OH A TABLE) $IHTERVAL~ denotes a fact
(ON A TABLE) which holds over $IHTERVAL~.
facts
assigning
These
3.1
the same
separate
intervals
interval
constrained
to
world.
‘Allen
adopts
831, with
and Koomen,
operator
ure 2 defines
object
TPLAN
an operator
if it is clear
the object’s
the temporal
preconditions
old location.
relations
among
can perform
of action
temporally
qualified
and effects.
The
facts
to change
presented
patterns
For instance,
which can be applied
on something.
PICKUP’s
constraints
unifying
to intersect
:D :DI
in
deFig-
to an
effects
field constrains
with
the precondi-
230
temporal
Planning
laws of the domain
operators
for solving
TPLAN
goals,
Our time logic supports
tempo-
their
a rule until antecedents
relation
is a subset
to assert
consequents
3 demonstrates
these
of (:S
over
features.
intersect,
Given
(OVER
A C)
intersection.
perator
physics
fixed
sets
water
resting
burner.
the
does
uses rules as
as well as forward
QPE
such
action
The
Operator
situations
given
can envision
not
burner
what might
what
at some
in process
modeling
of possible
water
point
happen
and
might
definitions.
(implemented
is temporally
containing
a pot containing
of the
envision
actions
the support
unless we
While
as additional
weak and multiplies
world states
the
happen
the
by the number
combinations.
Compiler
by modeling
states
can
agent
size of the envisionment
about
temperatures
pot off of the
support
of consistent
QPE
relative
to model
assumptions),
reason
For instance,
on a burner,
on the
if we move
QPE
systems
However,
attempt
Compiler
of individuals.
depending
possible
chaining
over their
The Operator
Rules
backward
Figure
conamong
and
:=))
field: temporal
temporal
us to inhibit
:OI
be-
behav-
relations
(meaning
:0
intersection.
torics
Rules-model
:FI
is asserted
tions and effects.
3.2
allowing
:SI
constraints
The additional
the antecedents.
are known
:F
and consequent
on the
with an-
consequents
to be (:=).
model
PICKUP
and resting
matching
Qualitative
the agent
the
facts
effects,
preconditions
and rule defi-
each in turn.
an action
and
Rule
definitions,
preconditions,
(ON A B) and (ON B C) w h ose intervals
is equivalent
are used in operator
defines
Inference
to operator
like operator
constraints.
places
ral intersections,
their
Operators
scribing
clear
with
conventions
We describe
An operator
the
them
syntactic
nitions.
paired
Qualified
are similar
behaving
like operator
ditions,
is expressed
Thus,
5. Two
if we
by
or after.”
are paired
Thus,
infer processes
by
:FI
between
rules.
occurence.
ing like operator
temporal
inference
as rules, we can both
RULE
Antecedents: (ON ?x ?y) $on-xy
(ON ?y ?z) $on-yz
Temporal Conditions:
Exists (INTERSECTION $on-xy $on-yz)
called $intersection
Consequents: (OVER ?x ?z) $intersection
Consequent Constraints:
having
3. The
constrained
processes
PICKUP
met bv.a
overlapped
I :SI
starts
:F
after
I
of Operator
Flow
Description
:MI
I
temporally
QPT
plan for their
Inverses
:M
2: Definition
actions
is more
Compiler
is an attempt
within
TPLAN,
constrained
approach
1. The user models in QPT
than
involves
to avoid this combinawhose search
QPE’s
three
the individuals
through
envisionment.
steps:
and physical
pro
cesses
2. The
of the domain.
Operator
compiles
Compiler
operators
ing processes
the model
of step
“OC”
marks rules
and operators
’ ‘USER’ ’ marks rules
and operators
!les goale
are indented
under the
1 and
plans involv-
and individuals.
3. The user models
in TPLAN
form in the domain
These
analyzes
and rules for constructing
actions
the actions
and the temporal
must
be made
an agent
can per-
laws of the domain.
relevant
to
the
output
of
step 2.
For example,
erate
plans
assume
involving
flow process
and individuals
and valved fluid paths.
output
operators
a simple
underneath
it.
position
of faucets.
The
vocabulary
container
FAUCET
SINK
fluid path
We then
underneath
following
model
FAUCET
relevant
operators
to the
operator
would allow
such as the valve
three
steps
can now be
For example,
on the
amount
one
to any con-
one geometric
scenarios.
and re-
For instance,
actions
Other
initially
a non-zero
rules that
from faucets
by these
planning
POT1
having
TPLAN
in the physics,
produced
would
by which a
for the kitchen
For instance,
quantities
used to solve specific
assert
Compiler
descriptions.
us to move objects.
certain
liquid sources,
the means
World geometry
and the physics.
us to modify
a liquid
In step 3 we construct
an exterior
would permit
and gen-
1 we model
such as containers,
to the process
rule establishes
geometry
a kitchen
In step
In step 2, the Operator
Blocks
late the geometry
tainer
to model
and rules which include
liquid flow is initiated.
describe
we want
liquid flows.
counter,
of water,
we could
liquid
solve
any of the
problems:
1. Increase
the amount
2. Increase
the pressure
of water
COAL, Increase
the amount of water
in the liquid
state
in POT1
SOLUTION Apply OC rule
that
increases
POTl’s
amount of
water
by creating
a liquid
flow from some source
and fluid
path
Over the course
of planning,
“some
source”
is unified
with FAUCET
The rest
of the trace
assumes
this
GOAL Make POT1 a container
SOLUTION Unify
this
goal with an initial
given.
GOAL Make FAUCET a container
SOLUTION Apply OC rule which says
liquid
sources
are
containers
GOAL. Wake FAUCET a liquid
source
SOLUTION Unify
this
goal with an initial
given
GOAL Get some water
znto container
FAUCET.
SOLUTION Unify this
goal rlth
an Initial
given
GOAL Find a flurd
path from FAUCET to POT1
SOLUTION Apply an OC rule
which says exterior
fluid
paths
are fluid
paths
GOAL Find an exterior
fluid
path from FAUCET to POT1
SOLUTION. Apply a USER rule
which says
that
an exterior
fluid
path exists
when a container
is under
FAUCET
GOAL. Make POTl’s
location
be underneath
FAUCET
SOLUTION. Apply USER operator
to move POT1 from the
counter
to underneath
FAUCET.
GOAL Make FAUCET’B pressure
be greater
than POTl’s
pressure
SOLUTION. Unify
this
goal with an initial
given
GOAL: Make the fluid
path’s
valve
position
be open
SOLUTION. Apply USER operator
for opening
FAUCET’s valve
Figure
amples
problems
and assert (CONTAINER
inference engine will assert
in POT1
may seem trivial.
However,
our running
require
complex
plans such as the one traced
domain
model
Figure
4 shows
generated
to initiate
a liquid
is used to infer
source.
of the
Operator
the
because
of QPT’s
encoded
as a set of preconditions
achieving
causal
the
faucet
a process
ordering
initial
of simple
and their
for influencing
rules and operators
Later,
QPT
a rule
expressions
processes
creating
Similarly,
are
a rule for
QPT
permitting
enforces
compilation
quantities.
the primary
Water
to POT1
expressions
of QPT
a
POTI)
in certain situations,
QPE’s
the following in those situations:
Expressmg
a DEFENTITY
as a TPLAN
rule is simple. The
antecedent
and consequents
are left unchanged,
except that the
consequents
hold over the same time intervalas the antecedent.
In the above example,
(HAS-qUA!JTITYPOT1 VOLUME) and
(GREATER-THAN (A (VOLUME ~0~111 ZERO) would hold over the
interval over which (CONTAINER POTI) holds. For TPLAN
the
above DEFENTITY
would be expressed
as:
RULE
Antecedents: (CONTAINER ?X) $C
Consequents:
(HAS-QUAHTITY ?X VOLUME) $C
(GREATER-THAN (A (VOLUME ?x)) ZERO) $c
Since
TPLAN
treats
rules.
Section
4.3 describes
as well as forward
to all QPT
domain
models.
the above
into TPLAN
applicable
use of
if it is a liquid
from QPT
and effects,
changes,
4.1 and 4.2 describe
compilation
4,
rule is used
goal.
Since
is straightforward.
operators
Sections
of causality.
on all quantity
One
is a container
Such rules are simple to construct
notion
in Figure
backward-chaining
Compiler.
flow to solve
that
for Adding
(HAS-QUAIITITYPOT1 VOLUME)
(GREATER-THA~J(A (voLu14EeoT1)) ZERO)
ex-
is detailed.
examples
by the
of a Plan
in POT1
since our QPT
rules
4: Trace
(DEFEIITIT~(CONTAINER ?x)
(HAS-quAfJT1~y?x VOLUME)
(GREATER-THA~I(A (voLUJ~E?x)) 2~~0)
3. Fill the sink with water
These
Compiler
source
and liquid drain
and have TPLAN
constructed
by the Operator
constructed
by the user
solution
which introduces
rules
chaining
rule to achieve
as backward
inference
goals which
rules,
chaining
operators
TPLAN
could
use
unify with any of the con-
sequents.
4.1
Compilation
.A QPT
entity
definition
is an expression
(DEFENTITY
<pattern>
<consequents>)
<consequents>
are asserted
in every
<pattern>
is true.
This scheme
of Entity Definitions
Thus,
of the form
situation
where
in which
if we have the following
definition
proportionality
is used on all consequents
assertions.
For instance,
except
for qualitative
the following
definition
(DEFENTITY (CONTAII;ED-LI~UID?x)
(HAS-qUAHTITY ?X LEVEL)
(QPROP (LEVEL TX) (AMOUNT-OF ?x)))
gives contained
liquids a quantity
LEVEL which increaseswhen
the A;.IOU:;T-OF
contained liquid increases and decreases when
Hogge
231
AMOUNT-OF decreases.
Encoding the QPROP
as a rule consequent
would not tell the planner that it can increase a contained
liquid’s LEVEL by increasing
the AMOUNT-OF contained
liquid (and
likewise for decreasing
the LEVEL). Thus, the above PEFENTITY
is instead compiled into the following rules.
RULE
Antecedents:'(CONTAINED-LIPUID?X) $cl
Consequents: (HAS-qUANTITY ?X LEVEL) $cl
RULE
Antecedents:
(CONTAINED-LIqUID ?X> $cl
(INCREASING (AM~UMT-OF ?x) mwsE)
$inc
Temporal Conditions:
Exists (INTERSECTION $cl $inc) called $int
Consequents: (INCREASING (LEVEL ?X) ?cAusE) $int
RULE
Antecedents:
(CONTAINED-LIQUID ?X) $cl
(DECREASING (AMOUNT-OF ?x) ?cAusE) $dec
Temporal Conditions:
Exists (INTERSECTION $cl $dec) called $int
Consequents: (DECREASING (LEVEL ?X) ?CAUSE) $int
The
first
rule
is the
the DEFENTITY,
result
while the second
extracted
QPROP.
uid exists
during
The second
The
QPE
The
definitions,
4.2
rule says that
employed
which
rules encode
Compilation
The antecedents
these
their
in the next
section.
of Process Definitions
of a process
definition
(DEFPROCESS)
are its
consequents
are its process
form (such as the PROCESS
l), relations,
and influences.
situation
are asserted.
as a rule which asserts
of the antecedents.
Bow process
antecedent
holds
The temporal
While
lations
refer
unique
in Figure
local
is expressed
in TPLAN
in Figure
inter-
during,
involving
containing
the process,
and after
local quantities
while all others
FLOW-RATE;
depend
process.
other
the process.
the intersection.
5 refer to local quantity
of the
quan-
ality assertions
232
from the DEFPROCESS
each of them.
be compiled
we extract
Thus,
into separate
Planning
the Q=
are asserted
over
Our
goal
water
are asserted
over
LEVEL.
thus, they hold
rules.
all qualitative
and create
assertion
changes
and stoppered
is to make
Assume
uid’s water
the
that
and a qualitative
Figure
As with DEFENTITY,
of planning
we are given a faucet
over $INT.
express
As an example
that
of the effects
Process
Universal QPE Rules
re-
Each
Thus,
LIQUID-FLOW
OPERATOR
Preconditions: (greater-than ?x ?y) $>
(increasing ?y ?cause) $increasing
Consequents: (equal-to ?x ?y> $=
Constraints: $> (:M) $=
$increasing (:M :FI :DI :O) $=
5 the liquid
and influences
quantities
hold only during
of antecedents,
intervals
specifies
the antecedents
form over the temporal
on relations
to any
before,
and influences
the intersection
This
the
field of
$INT, the temporal
intersection
of the
($cl, $c2, $fp, $cl; $vo, and $gt).
local quantities
may exist
matching
For instance,
constraints
they
while
From
The Operator
Compiler enforces consistency
during planning
by including such rules in its compilation
of QPT domains.
Also
included are a set of operators
for planning changes in quantities.
Section 4.1 described
the encoding of qualitative
proportionalities, in which rules of the form “If X is increasing
then Y is increasing”
are output for each qualitative
proportionality.
These
rules allow us to construct
operators
which achieve inequalities
between two quantities
by achieving an increase or decrease
in
one of them.
For instance,
if we are given that quantity
X is
greater
than quantity
Y, we can solve the goal of making X
equal to Y by either decreasing
X or increasing
Y. The latter is
encoded as follows:
over
intervals
on whether
tities
the process
conditions,
A DEFPROCESS
in which facts
hold, the consequents
section
in
in process
and quantity
in every
ex-
expressions
Compiled
1
RULE
Antecedents: (equal-to ?x ?y) $=
(greater-than ?x ?y) $>
Consequents: $= (:< :> :M :MI) $>
in similar
occurrence
Operator
of Figure
QPE encodes a set of universal
rules applicable
to all physical
domains.
For instance,
value X can not be both equal to Y and
greater than Y at the same time. This can be expressed
as the
following TPLAN
rule:
over the in-
preconditions,
that
liq-
over $IFJC,
and
individuals,
Figure
the
if a contained
are handled
in handling
are covered
4.3
from
proportionality
which
5:
Definition
similarly.
of qualitative
is also used to handle
Figure
QPROP
the level is increasing
and Q=)
Q=,
method
DEFENTITY
and third
rule is interpreted
a variety
(QPROP-,
fashion.
then
third
supports
pressions
the
$CL, its AMOUNT-OF is increasing
$CL and $INC intersect,
tersection
of extracting
RULE Process-Liquid-Flow
Antecedents:
(CONTAINER ‘src-can)
$CI
(CONTAINER ‘dst-can)
3~2
<FLUID-PATH (FP 7src-can
‘dst-can))
Sfp
(CONTAINED-LIQUID
(CL 711q ?src-can))
3~1
(VALVE-OPEN (FP ?src-can
7dst-can))
ho
(GREATER-THAN
(A (PRESSURE-DIFFERENCE
(FP ?src-can
‘dst-can)))
ZERO) Sgt
Temporal
Condltlons,
Exists
(INTERSECTION $cl ScZ Ofp Scl Svo $gt) called
Sint
Consequent.
(LIQUID-FLOW ‘src-can
‘dst-can
?liq)
$int
(IJUANTITY (LOCAL-QUANTITY FLOW-RATE
(LIQUID-FLOW ‘src-can
‘dst-can
‘liq) 1) $lnt
(INCREASING (ACCOUNT-OF (CL ?liq
?dst-can))
(A (LOCAL-QUANTITY FLOW-RATE
(LIQUID-FLOW ?erc-can
?det-can
?liq))))
$mt
tsrc-can))
(DECREASING (AMOUNT-OF (cr. ?liq
(A (LOCAL-QUANTITY FLOW-RATE
(LIQUID-FLOW ‘src-can
‘dst-can
71iq))))
$lnt
our domain
proportionality
level increases
6 traces
level
when
in quantities,
suppose
sink containing
be greater
includes
stating
than
water.
SOME-
a liquid flow process
that
the amount
a contained
of water
liq-
increases.
the plan which solves our goal.
proportionrules which
of Figure
1 would
5
Discussion
We have described
an Operator
planning
in physical
problems
Compiler
domains.
which
The
solves
compiler
simple
handlr
6
GOAL: (GREATER-THAN (LEVEL SINK-WATER) SOME-LEVEL)
SOLUTION: Apply an inequality change operator which
achieves (GREATER-THAN ?X ?y) by increasing ?x.
GOAL: (INCREASE (LEVEL SINK-'JATER)?cause)
SOLUTION: Apply QPROP rule which says (LEVEL ?x)
increases when (AMOUNT-OF ?x) increases and ?x is
a contained liquid.
GOAL: (CONTAINED-LIQUID sink-water)
SOLUTION: Unify with initial given.
Acknowledgements
Many
thanks
go to Ken Forbus
ful suggestions
hainer
with
gave
Ken
Collins
helpful
Forbus,
were
Ken
comments
Brian
helpful
on this
Falkenhainer,
The
Barry
through
Contract
Falken-
Discussions
Smith,
QPT
of Naval
and use-
and Brian
document.
the
Office
direction
Forbus
in constructing
used in the examples.
this project
for providing
on this research.
and John
domain
Research
models
supported
No. N00014-85-K-0225.
GOAL: (INCREASE (AMOUNT-OFsrNK-wATER) )
SOLUTION: Apply liquid flow operator with
destination SINK and source FAUCET.
References
[Allen, 831 Allen,
Figure
6: Trace
of a Plan
for Changing
a Quantity
J.F.,
ral Intervals”,
“Maintaining
Knowledge
about
of the ACM,
Communications
Tempo-
vol. 26, pp.
832-843.
most syntactic
from
QPT
features
models
have allowed
Figure
of liquid
generation
1) involving
tities.
This
The
section
tities.
of simple
describes
plans
(such
makes
as that
which
in
in quan-
limitations.
primary
naive
[Allen and Koomen,
ning
is its overly
changes
in quan-
gence,
while
any
influence
negative
causes
it to increase,
on a quantity
causes
decreasing
Under
tively
it to
these
influences
more,
assumptions,
the
assumption
valid, they
flow into
#l
rising
than the sink’s
or
fools the planner
into
Further-
into thinking
the water
maximum
that
level and also
these
by the operators
inequalities.
do solve simple
problems
given
posi-
negatively
inequalities
planning.
are made
instance,
a sink
drain
and lowering.
level, assuming
as goals during
for achieving
For
tities.
greater
assumptions
4.3
by increasing
a liquid
level, assumption
level is both
the minimum
These
section
level and
#2 fools the planner
level will become
are introduced
if a liquid
water
the water
the water
lower than
can be achieved
one of the two quantities.
influences
thinking
some
described
Although
involving
water
they
are
changes
draining
out
in
not
in quanof a sink
and a goal of filling the sink, the planner
can use the inequality
operators
on the faucet.
to generate
lution
is partial
greater
than
be resolved
rates
the drain
through
and quantity
since
text.
Unfortunately,
a rule’s
is beyond
One limitation
pendence
on QPT.
QPT
can
QPT
currently
QPT
rate.
QPE
While
changes
effects
require
TPLAN’s
ambiguities
problems
complex
could
involving
for our compiled
depend
on the
con-
context-dependent
rules
and
capabilities.
of the Operator
The compiler
affect
many
are too
The so-
the flow rate must be
on a quantity
formulating
individuals.
that
such rate
simulation,
Compiler
is bound
the
does not provide
individuals
would
planner.
specifies
be used to model
of interacting
which
a plan which turns
since nothing
rules,
operators
841 Forbus,
[Forbus,
Intelligence
861 Forbus,
Technical
inequality
physical
the
additional
arises
world.
definlGons
process.)
complexity
from its de-
by the limits to which
a mechanism
(Process
Joint
and Koomen,
Model”,
Conference
J.A.,
“Planof the
Proceedings
on Artificial
Intelli-
pp. 741-747.
Conference
ficial
decrease.
2. Any quantity
J.F.
World
K.D.,
“Qualitative
Proceedings
on Artificial
Reasoning
of the Seventh
about
August,
Intelligence,
Phys-
International
1981.
assumptions:
on a quantity
influence
International
Processes”,
Joint
831 Allen,
a Temporal
811 Forbus,
ical
[Forbus,
1. Any positive
Using
Eighth
[Forbus,
shortcoming
goals involving
several
rules
shown
and changes
its current
for solving
strategy
flow, and boiling
individuals,
Compiler’s
strategy
The
It has been used to compile
flow, heat
processes,
Operator
optimistic
of QPT.
Such
For
instance,
for modeling
explicitly
sets
state
imprc~vements
in the compiler
to
and
Report
nois. Department
K.D.,
24,
K.D.,
“Qualitative
Process
Theory”,
Arti-
1984.
“The
Qualitative
UEUCDCS-R-86-1288,
of Computer
Science,
Process
University
December,
Engine”,
of Illi1986.