Download Formalization and Declarative Implementation of an Executable

Formalization and Declarative Implementation
of an Executable Concept Map
Reva Freedman
Department of Computer Science
Northern Illinois University
DeKalb, IL 60115
[email protected]
http://www.cs.niu.edu/~freedman
Abstract
CIRCSIM-Tutor, an intelligent tutoring system in the domain
of cardiovascular physiology, teaches students to solve
problems according to a concept map taught in class.
Although students believe that the concept map provides a
unique solution to each problem, the solution is in fact
dependent on a set of implicit assumptions that determine a
unique reading of the concept map. In this paper we analyze
the ambiguities in the CIRCSIM-Tutor concept map, then
derive a set of rules that can be used to produce the unique
correct reading for this map. We have implemented these
rules in CAPE, a reimplementation of CIRCSIM-Tutor based
on a fully declarative representation.
Introduction
CIRCSIM-Tutor (Michael et al., 2003) is an intelligent
tutoring system (ITS) that uses a simplified model of blood
circulation to help students learn the basic concepts of
blood pressure regulation. When something happens to
change the blood pressure, such as a change in blood
volume or the administration of a drug, the body tries to
compensate. This negative feedback loop is known as the
baroreceptor reflex. Students are taught to solve problems
about the baroreceptor reflex using a concept map
presented in class. Although students believe that the
concept map provides a unique solution to each problem,
in fact obtaining the correct solution depends on a set of
implicit assumptions that determine a unique reading of the
concept map. In this paper we describe the assumptions
that need to be formalized in order for the concept map to
accurately model the problem-solving algorithm. Then we
describe our implementation of the algorithm in CAPE
(Freedman et al., 2004), a reimplementation of CIRCSIMTutor based on a fully declarative representation.
CIRCSIM-Tutor does not implement the concept map
directly; rather, it uses its own code to solve the problems.
In addition to possible discrepancies introduced as a result,
the problem solver cannot be used with other concept maps
of the same form. Furthermore, since the solution does not
include a trace of the problem-solving process we wish the
student to follow, it cannot be used to generate
explanations for the student. Our implementation solves all
three of these problems.
Background
Physiology of the Concept Map
CIRCSIM-Tutor (and thus also CAPE) gives students
problems to work. In each problem, a perturbation changes
the processing of the heart. The student is then asked to
predict the value (increase, decrease or no change) of
seven core physiological parameters at three points in time.
Students enter their responses on a tabular worksheet
called a prediction table (Figure 1) (Rovick & Michael,
1992). Here is a sample problem:
A person has a pacemaker that has been running
at 72 beats/minute. Suddenly it malfunctions and
the rate changes to 120 beats/minute.
What is the effect on the seven core variables
immediately after this event, after the nervous
system reacts, and after a new steady state is
reached?
First, the change in heart rate will propagate through the
system, changing the value of other core variables. One of
the variables changed will be blood pressure, which the
baroreceptor reflex is trying to maintain. Thus mean
arterial pressure (MAP) is called the regulated variable of
the negative feedback loop. The change in blood pressure,
sensed by the baroreceptors in the neck, changes the signal
sent through the nervous system to other organs in the
body, which changes the values of parameters measured at
these organs. These parameters are called controlled
variables. In the baroreceptor reflex, the controlled
variables are the three variables controlled directly by the
nervous system: inotropic state (IS), heart rate (HR), and
total peripheral resistance (TPR). These changes are again
propagated through the system. The concept map in
Figure 2 shows the causal relationships between the
regulated variable, the controlled variables, and a small
number of other important variables.
The concept map was developed to model the solutions
that the CIRCSIM-Tutor domain experts, professors Joel
Michael and the late Allen Rovick of Rush Medical
College, want the students to assimilate, both in sequence
of steps and in level of detail. It shows the relationships
DR
RR
SS
Central Venous Pressure
Inotropic State
Stroke Volume
Heart Rate
Cardiac Output
Total Peripheral Resistance
Mean Arterial Pressure
relationship, which states that the more muscle fibers are
stretched, the more force they can develop.)
At higher values of inotropic state (IS), the same degree
of ventricular filling causes a higher stroke volume. Thus
an increase in IS causes an increase in SV.
Finally, an increase in mean arterial pressure (MAP)
causes SV to decrease. When mean arterial pressure
increases, it becomes more difficult for blood to exit the
heart. This causes stroke volume to decrease. The pressure
that the ventricle has to pump against, i.e., the arterial
pressure, is called afterload. Since this effect is less
important than the other determinants of SV, in our
simplified model it only applies when other determinants
of SV are inapplicable. In the CIRCSIM-Tutor model, such a
determinant is called a minor determinant.
Figure 1: Prediction table
Stages of the Feedback Loop
among seven parameters:
• Heart rate (HR). Pulse in beats per minute.
• Inotropic state (IS). How much (or, equivalently, how
forcefully), the heart contracts with every beat.
• Stroke volume (SV). Blood pumped per beat.
• Cardiac output (CO). Blood pumped per minute.
• Mean arterial pressure (MAP). Blood pressure as
measured in the arteries.
• Total peripheral resistance (TPR). Resistance to blood
flow through the circulatory system. Since vessels
smaller in diameter resist the flow of blood more,
peripheral resistance is a large component of total
resistance.
• Central venous pressure (CVP). Blood pressure in the
large central veins outside the heart.
As the reader can see, there is a tautological relationship
between CO, HR, and SV, namely HR * SV = CO, based
solely on conversion of units. The concept map, which is a
qualitative device, simply shows that an increase in HR or
SV will cause an increase in CO. In some ways, the
qualitative model is more useful, because the equation does
not show that the causality runs left-to-right only.
When the heart pumps more blood per minute into the
arteries, pressure in the arteries goes up because the
peripheral circulation has resistance. The equation MAP =
CO * TPR, the physiological equivalent of Ohm’s Law,
describes this relationship. Again, the concept map shows
that when TPR or CO increases, MAP increases also.
When cardiac output increases, increased quantities of
blood are transferred from the venous system into the
arterial system, decreasing the central blood volume and
thus decreasing central venous pressure. In other words, an
increase in CO causes a decrease in CVP.
As pressure increases in the central veins that provide
the input to the heart, more blood flows into the heart on
each beat. This increase in ventricular filling, also known
as preload, causes the heart to beat more forcefully, which
causes more blood to be pushed out per beat. In other
words, an increase in CVP causes an increase in SV. (The
cause of this phenomenon is the length-tension
The negative feedback loop can be summarized as follows:
When mean arterial pressure (MAP) goes up, the heart rate
(HR) goes down, so the heart beats fewer times per minute,
reducing cardiac output (CO), and thus reducing MAP.
Additionally, when MAP goes up, up the blood vessels
become wider, decreasing total peripheral resistance (TPR)
and thus MAP. Finally, when MAP goes up, inotropic state
(IS) goes down, so less blood is pumped per beat, reducing
stroke volume (SV), then cardiac output (CO), and finally
MAP.
Rather than being represented directly, the negative
feedback loop is divided into three stages, and students
study the change in each variable at each of the three
stages. Since the same principles apply at each stage, the
same concept map can be used to represent all three stages.
The three stages are the direct response (DR) stage,
consisting of those changes that happen before the
baroreceptors are activated; the reflex response (RR) stage,
which includes changes that occur as a result of the
activation of the baroreceptors; and the steady state (SS)
stage, which describes the state of the system after it has
restabilized. In the human body, a steady state is achieved
within a couple of minutes.
The variables directly controlled by the nervous system,
namely HR, IS, and TPR, are called neural variables. The
nervous system controls heart rate (HR) by stimulating the
sino-atrial node; it controls total peripheral resistance
(TPR) by constricting the arterioles; and it controls
inotropic state (IS) by changing the concentration of
calcium ions, which controls the force of contraction of the
heart muscle. Since the nervous system is not activated in
the initial (DR) stage, the neural variables do not change in
DR unless they are affected directly by the perturbation.
Perturbations of the System
Perturbations can be caused by an event such as a
hemorrhage or by administering a drug to the patient. In
general, students are taught that all they need to know is
the initial variable that changes, called the procedure
variable, and whether that variable increases or decreases.
-
CVP
+
SV
+
+
CO
+
MAP
+
+
IS
HR
TPR
-
-
-
+
Baro
+
NS
+
Figure 2: The concept map
This term is derived from the fact that many perturbations
are medical procedures. The procedure variable determines
the initial variable on the concept map that will be affected,
which is called the primary variable. For example, a
hemorrhage causes the central blood volume to go down,
causing a drop in central venous pressure. If the first
variable that changes is on the concept map, then the
procedure variable and the primary variable are the same.
Only four of the seven core variables can be primary:
central venous pressure (CVP), inotropic state (IS), heart
rate (HR), and total peripheral resistance (TPR). That’s
because SV and CO are derived values, and MAP is the
regulated variable.
In general, knowing the primary variable is sufficient to
determine the behavior of the system, although there are
two categories of exceptions. In one type of exception, the
perturbation has other effects not shown on the concept
map, so knowledge of the perturbation is required. The
second category of exception refers to the fact that a
primary variable can be clamped. In general, when the
nervous system is activated in the reflex response (RR)
stage, it can cause further changes in the value of any
variable. But there is one exception: some perturbations
involve physical restrictions that the nervous system cannot
override. For example, a broken pacemaker always clamps
HR. Sometimes the problem statement will tell the student
whether a variable is clamped. For example, drugs can
cause a primary variable to be clamped if given in
sufficient concentration.
Note that the definition of a single problem in the system
does not mean that there is only one way to present that
problem to the student. In fact, Khuwaja (1994) has studied
various ways to present a problem to the student and their
respective levels of difficulty.
Problems with the Concept Map
Students are given copies of the concept map during
lecture and encouraged to use it to think about problems.
Each box in the concept map represents a parameter. When
two parameters are connected by an arrow, we say that A is
a determinant of B. An arrow with a plus sign indicates a
direct relationship, i.e., when the first variable changes, the
second variable changes in the same direction. An arrow
with a minus sign indicates an inverse relationship, i.e., the
second variable changes in the opposite direction. The
concept map directly represents only the following links
between variables described in the previous section:
Determinants:
HR, TPR and IS are neural.
The determinants of SV are CVP and IS, and
MAP is a minor determinant (inverse
direction).
The determinants of CO are SV and HR.
The determinants of MAP are CO and TPR.
CO is the sole determinant of CVP
(inverse direction).
Along with knowledge of the determinants, students are
taught several facts about concept map operation. When a
variable has only one determinant, i.e., only one incoming
link, then the value of the “sending” variable determines
the value of the receiving variable. When there are two
incoming links, if both sending variables have the same
value, then that value is propagated. However, more
complex cases are taught only by example.
Although the concept map is a useful memory aid for
students, it does not uniquely define the causal model.
Several issues arise when trying to formalize the operation
of the concept map. First, in order to have an algorithm, we
need to know where to start and in what order to follow the
links.
Second, there are many cases where the instructions
given to the students are insufficient to uniquely determine
the value of a variable. This issue has two facets. One is
that changes in the body during a physiological stage
happen in parallel, but the concept map models them as a
sequential process in order to emphasize the causal
reasoning involved. Thus, in addition to specifying a
sequence, the algorithm must recognize that a variable may
not have an assigned value if it is used as a sending
variable before it has received a value. The other is that
when a variable has multiple determinants, the algorithm
needs to specify how the calculation is done, remembering
that incoming links may have contradictory values or none
at all. Additionally, when one of the variables is a minor
determinant, this fact must be recognized also.
Third, the concept map does not indicate constraints on
the links, for example, that a determinant relationship only
holds for specific problems.
Finally, we need to prove that the algorithm is fully
specified, i.e., that each variable will be given one and only
one value.
These issues are handled in a variety of ways in the
classroom. Some of them, such as the sequence of
calculations, are taught to students conceptually, enabling
students to solve the problems even though the algorithm is
not specified sufficiently for a program to do so. Others,
such as the fact that variables that do not have values do
not enter into a calculation, are treated implicitly—the
teacher ignores them, and the students model that
approach. Again, this solution works for human beings but
is not sufficient for a program. Finally, issues such as
exceptions for clamped variables and exceptional
procedures are taught as additional world knowledge that is
not represented on the concept map.
Modeling the Concept Map
In this section we show how to represent the CIRCSIMTutor concept map as an algorithm. This algorithm has
been implemented as part of CAPE (Freedman et al.,
2004), a fully declarative rule-based reimplementation of
CIRCSIM-Tutor. CAPE is implemented with the APE
reactive planner (Freedman, 2000; Freedman et al., 2000).
APE-based systems include two knowledge bases, one
permanent and one that can be updated at run time. Both
knowledge bases contain facts, i.e., first-order predicates
without quantifiers or uninstantiated variables. Primitives
are provided to query the knowledge bases. Expert system
or Prolog-style rules can be used to add new facts to the
transient knowledge base.
In this section we describe the structure of facts that
CAPE requires in the permanent knowledge base in order
to solve concept map problems. Then we describe the types
of facts that the problem solver adds to the transient
knowledge base at run time. We describe the basic
algorithm used for each stage, along with a list of rules for
determining the value of a variable within a stage.
Knowledge Base
The permanent knowledge base contains five predicates.
The first predicate provides information about variables.
The system needs to know which variables are neural.
(kd-is-neural is)
(kd-is-neural hr)
(kd-is-neural tpr)
The second predicate gives the essential features of each
concept map problem. For each perturbation, these facts
identify the procedure variable and its direction of change.
The third argument specifies whether the primary variable
is clamped. This argument has three values, t, no, and na,
which mean yes, no, and N/A, respectively. The latter
value is used for non-neural variables, where clamping
does not apply. In general, one fact is required per
problem. Where clamping depends on concentration, two
different problems are specified, one where the primary
variable is clamped and one where the primary variable is
not clamped. The following rule is an example:
(kd-has-proc-vbl pacemaker-increase hr up t)
The third predicate provides information about physiology.
Each procedure variable is linked to its corresponding
primary variable, and the correspondence is labeled as a
direct or inverse relationship. The primary variable may or
may not be the same as the procedure variable:
(kd-proc-to-primary hr
(kd-proc-to-primary ra
hr direct)
tpr direct)
Once this information is obtained for a particular problem,
a new fact that directly connects the problem to its primary
variable is added to the transient knowledge base for
convenience. For example, the facts above give rise to the
following one, which says that HR is the primary variable
for the pacemaker-increase problem, and that it
increases in the DR stage.
(kd-has-primary-vbl hr up pacemaker-increase
dr)
Fourth, additional physiology information is provided in
terms of the determinant table. For ease of reading, we
maintain the determinant knowledge base using the
following nested representation.
(kd-has-determinants
inverse)))
(kd-has-determinants
(kd-has-determinants
(kd-has-determinants
sv
(cvp is (map minor
co (sv hr))
map (co tpr))
cvp ((co inverse)))
However, the algorithmic rules are simpler to write with a
flat representation, so at startup the system expands the
nested representation into a flat representation with a fact
for every determinant in the transient knowledge base. We
number the determinants of each variable and provide a
determinant count so that a program can pick up all the
determinants of a variable without having to use a
collection predicate like Prolog bagof. Thus the
determinants of CO would look like this:
(kd-has-determinant-count co 2)
(kd-has-determinant-no co 1 sv direct major)
(kd-has-determinant-no co 2 hr direct major)
Finally, some information on qualitative mathematics must
be provided. Although people can combine an incoming
value and a type of propagation to provide a new value, the
system needs to know how to do it.
(kd-multiply-dirs
(kd-multiply-dirs
(kd-multiply-dirs
(kd-multiply-dirs
up direct up)
up inverse down)
down direct down)
down inverse up)
The goal of the problem solver is to create a fact of the
following form for each variable in each stage of a
problem. This fact states that HR increases in the DR stage
of the pacemaker-increase problem.
(kd-has-value hr up pacemaker-increase dr)
Although our theoretical solution requires storing the paths
in the knowledge base, our implementation calculates the
paths in the correct sequence by checking the propagation
rules sequentially so that each variable will be emitted at
the appropriate time. Therefore we do not show any
predicates here for storing the paths as permanent
knowledge, although the system will store each path in the
transient knowledge base as a simple list when they are
created.
Paths through the Concept Map
It is useful to start by defining two terms, the primary path
to MAP and the secondary path. Together, these two lists
form a partition of the non-neural variables, and can be
used to show that the algorithm does in fact give each
variable a unique value. These two paths are used in the
initial (DR) and steady state (SS) stages. The following
conceptual rule defines the primary path to MAP:
• Start with the primary variable.
• Move forward along the most direct route until
MAP is reached.
The following similar rule gives a conceptual definition of
the secondary path:
• If the primary path contains CVP, then the
secondary path is nil (i.e., there are no
variables left for the secondary path)
else if the primary path contains CO, then the
secondary path starts with CO
else the secondary path starts with MAP.
• Then move forward until all variables have
values.
However, it is difficult to implement these rules directly, as
we would need to prove that at every step we can uniquely
identify the correct next variable and its value. There is an
implicit assumption that the correct path does not
recalculate the value of any variable already calculated,
because that would contradict the causal nature of the
reasoning the concept map is designed to teach. To
guarantee that all of these assumptions hold, for our
theoretical analysis, we store in the knowledge base the
following rules for calculating the primary path to MAP.
Determine-primary-path:
The shortest path is determined by the primary
variable.
HR primary:
HR → CO → MAP
HR and IS primary:
HR → CO → MAP
No primary variable: HR → CO → MAP
IS primary:
IS → SV → CO → MAP
TPR primary:
TPR → MAP
CVP primary: CVP → SV → CO → MAP
Similarly, the rules for the secondary path are shown
below. Additionally, for the secondary path, although it is
not necessary to make the algorithm work we would like to
show that the secondary path is always a connected path
that contains all the remaining variables that do not have
values, and only those. However, we have been unable to
prove this fact except by enumerating the cases.
Biologically, the secondary path contains the important
link from CO to CVP unless CVP is the primary variable.
Determine-secondary-path:
The secondary path is determined by the path
which has already been traversed.
HR → CO → MAP:
CO → CVP → SV
IS → SV → CO → MAP: CO → CVP
TPR → MAP: MAP → SV → CO → CVP
CVP → SV → CO → MAP: Nil
The reflex response (RR) stage requires an additional path.
In the RR stage, the most important path to MAP is the
path where the most significant changes take place. In this
stage, the now-activated nervous system sends signals to
the neural variables that will be propagated to the rest of
the system. Thus the most important path to MAP starts
with the most powerful neural variable, namely HR, unless
that variable is clamped. For the same reasons as given
above, we store in the knowledge base the following rules
for creating this path.
Determine-most-important-path:
The most important path is determined by the
clamped status of the neural variables.
No clamped variable: HR → CO → MAP
IS clamped:
HR → CO → MAP
TPR clamped:
HR → CO → MAP
HR clamped:
IS → SV → CO → MAP
HR and IS clamped:
TPR → MAP
Rules for the DR Stage
The algorithm for assigning values to the variables in the
DR stage is given below.
Determine-DR:
1. Determine the procedure variable and its
direction from the perturbation.
2. Derive the primary variable and its direction
from the procedure variable.
3. Determine the values of the neural variables.
4. Propagate values to variables on the primary
path to MAP.
5. Propagate values to the variables on the
secondary path.
The first step in solving a problem is to determine the
procedure variable, whether the perturbation causes it to
increase or decrease, and whether it is clamped in this
procedure. This information can be determined from the
problem name alone. The second step is to determine the
primary variable and its direction, which can be determined
from the procedure variable and its direction.
The third step is to determine the values of the three
neural variables. They are chosen next because they can be
ascertained without reference to variables other than the
primary variable. Since the neural variables are controlled
by the nervous system and DR is the period before nervous
system functioning is activated (i.e., before the changes
being propagated through the system reach the
baroreceptors), neural variables are not affected during the
DR period. There is one exception to this rule: If the
primary variable is neural, we already know from the
previous step that it has changed. Thus the following rule
can be used to determine the value of the neural variables:
Neural-DR:
Neural variables which are not primary do not
change in DR.
The fourth and fifth steps are to determine the values of the
variables along the primary path to MAP and then along
the secondary path. In the following section, we give rules
for calculating the values of individual variables based on
their determinants. Since the paths themselves have been
precomputed and stored in the knowledge base, we know
that the determinants for each variable will be available
when it becomes time to calculate the value. Because the
two paths are disjoint, one will never come across a
variable that already has a value assigned. Since the two
paths form a partition, the algorithm is guaranteed to assign
a value to every variable.
Non-neural Propagation Rules
The following rules can be used to determine the value for
any variable in any stage. Since neural variables do not
have determinants within the same stage, these rules apply
to the non-neural variables.
When a variable has only one determinant, there is only
one possible case:
Prop-1:
When a variable has one determinant, then the
value of that determinant (increased, decreased
or unchanged) determines the value of the
variable.
If a variable has two determinants, there are several
possibilities: neither has a value, only one has a value, both
have values but both are unchanged, both have values but
one of them is unchanged, both have the same value, or
they have conflicting values. In the DR stage, only two
rules are needed to handle the case of two determinants.
Prop-2n:
(no value) If a variable has two determinants and
one of them has a value and the other one does
not have a value yet, then the value of the one
with a value determines the value of the variable.
Prop-2u:
(unchanged value) If a variable has two
determinants and one of them has increased or
decreased and the other one is unchanged, then
the value of the one that has changed determines
the value of the variable.
The following additional rules are needed in RR.
Prop-2e:
(equal values) If a variable has two determinants
and both of them have the same value, then that
value becomes the value of the variable.
Prop-2sv:
(conflicting values for SV) If the two
determinants of SV (i.e., IS and CVP) have
conflicting values (one increases and the other
decreases), then the value of CVP determines the
value of SV.
Rule Prop-2sv expresses the fact that CVP usually has a
stronger effect on SV than IS. This results from the fact
that HR, which determines CVP, is usually more powerful
than IS. Rule Prop-2sv is needed in DR when problems
with multiple primary variables are considered.
One additional rule is needed to complete propagation in
SS. The intent of the following rule is to permit
propagation along the path SV → CO → MAP even
when there is conflicting data from HR and TPR.
Prop-2c:
(conflicting determinants for CO and MAP) If a
variable other than SV has two determinants with
conflicting values, and one determinant is neural
and the other is not, then the non-neural
determinant takes precedence unless the neural
determinant is primary.
There is also the possibility of a variable with three
determinants. In CIRCSIM-Tutor, this case only arises when
one of the three is a minor determinant. The minor
determinant is only used when neither major determinant
has a value or both major determinants are unchanged. The
following rule applies when there are three determinants.
Prop-minor:
If a variable has two determinants and neither of
them has a value other than “unchanged,” but
there is a minor determinant with a value, then
the value of the minor determinant determines
the value of the variable.
If one follows the paths correctly, one never comes across
a variable where a value cannot be assigned because none
of the determinants have values yet. Thus this set of rules
can be used to uniquely determine the values on any of the
paths. If the rules were updated to give the same results
independently of the order in which they were tested, it
would be possible to use these rules alone to calculate the
values of the non-neural variables. In other words, it would
be possible to generate the paths instead of precomputing
them and storing them in the knowledge base.
Rules for the RR stage
In the RR stage, the baroreceptors have responded to the
change in MAP in the DR stage. They activate the nervous
system, which sends signals to various parts of the body.
These signals cause a change in any neural variable whose
value is not clamped. Due to the nature of negative
feedback systems, a change in MAP in the initial (DR)
stage causes neural variables to move in the opposite
direction in the reflex response (RR) stage.
The following propagation rules can be used to
determine the values of the variables in RR.
Determine-RR:
1. Determine values for the neural variables.
2. Propagate values to variables on the most
important path to MAP.
3. Propagate values to variables on the secondary
path.
The following two rules can be used to determine values
for the neural variables.
Neural-RR:
If MAP went up in DR, then non-clamped neural
variables will go down in RR, and vice versa.
Clamped-RR:
Clamped neural variables do not change in RR.
Values are assigned to the variables on the most important
path to MAP and the secondary path using the non-neural
propagation rules above. The secondary path in RR is
determined using the same rules as in DR.
Rules for the SS Stage
In the SS stage, the system returns to a steady state. The
following propagation rules can be used to determine the
values of the variables in SS.
Determine-SS:
1. Determine the value of the primary variable.
2. Determine values for the remaining neural
variables.
3. Propagate values to variables on the primary
path to MAP.
4. Propagate values to variables on the secondary
path.
Neural variables have done all the changing they are going
to do in RR, so they have no further changes to make to
come to a steady state in SS. But for primary variables, the
majority of the change took place in DR. Thus we have the
following rules for primary variables, whether neural or
not, and for other neural variables in SS:
Primary-SS:
If a variable is primary, it has the same value in
SS as it did in DR.
Neural-SS:
If a neural variable is not primary, it has the
same value in SS as it did in RR.
If MAP decreases in DR and thus increases in RR, it will
usually still be decreased in SS relative to its initial value.
This is an important principle which is usually expressed to
the student as follows:
• The reflex never fully compensates (for the
perturbation).
This is a basic principle of negative feedback systems. For
example, suppose we give a patient a transfusion. This will
cause MAP to increase and thus cause the values of the
neural variables to decrease. In the new steady state, MAP
will remain elevated and the neural variables decreased
until the extra fluid is excreted. This logic provides the
following rule:
Compensate-MAP:
The value of MAP in SS is the same as its value
in DR.
We could work backward from MAP to obtain values for
the other variables. However, we prefer to work forward to
be consistent with the previous stages. Thus we do not use
Compensate-MAP in our solutions.
The following rule can be used along with the rules for
primary and neural variables given above to solve SS
problems without using any propagation rules.
Algebraic-SS:
The value of a variable in SS is the “algebraic
sum” of its qualitative predictions in DR and RR.
If the DR and RR values have opposite signs, the
DR value prevails.
This rule is simple and easy to explain. However, because
the propagation rules may give a deeper understanding of
the mechanism, we prefer to use them instead.
Conclusions and Future Work
This paper describes our work in making explicit the
implicit rules used by students to solve problems using the
CIRCSIM-Tutor concept map. It also describes our
implementation of these rules in CAPE, a rule-based
reimplementation of CIRCSIM-Tutor that uses a fully
declarative representation. In addition to eliminating
possible discrepancies between the concept map and a
procedural implementation, the new problem solver
produces a trace of the problem-solving process that can be
used to generate explanations for the student. In this
section we discuss some proposed extensions to this
project.
First, we would like to update the propagation rules to
ensure that all the propagation rules are independent of the
order in which they are executed. That would make it
possible to calculate the three paths through the concept
map instead of storing them in the knowledge base. One
approach to this goal is to note that rule Prop-2c, which is
order-independent, could be used to replace all the other
forms of Prop-2 except for Prop-2sv. In a similar vein, we
would also like to experiment with fully domainindependent rules.
Next, we would like to extend the scope of the system to
cover all the CIRCSIM-Tutor problems. Two types of
problems require only changes in the propagation
algorithms. One case includes physiological conditions that
require two paths through the concept map to be followed
simultaneously, a condition called multiple primary
variables. For example, beta-blockers, a class of drugs used
to reduce blood pressure, affect both heart rate and
inotropic state. A second case is multiple sequential
perturbations, which require a path through the concept
map to be immediately followed by another one. For
example, a pacemaker can break after a drug has been
administered to the patient.
Other problems require an update to some of the system
predicates to allow a link to be dependent on a particular
problem. For example, in the problem called enervating the
baroreceptors, the link from the baroreceptors to the
nervous system is disabled. In that case, the baroreceptors
cannot affect the nervous system, so a change in MAP will
not affect the neural variables. This problem can be added
to the CAPE implementation by allowing the Neural-RR
rule to depend on the problem. Similarly, in the problem
known as a change in intrathoracic pressure, a decrease in
space available for the central veins causes an increase in
central venous pressure (CVP) without the usual
accompanying increase in stroke volume (SV). This
problem could also be handled by adding the possibility of
links dependent on a problem name.
Finally, we would like to build a new concept map that
differentiates causal and functional knowledge. Stevens,
Collins and Goldin (1979) use the term causal for
relationships that involve causation in the physical world
and functional for dependencies which involve only a
logical notion of causation, such as those involving a
definition or role relationship. A causal model can contain
two kinds of knowledge, knowledge about the causal
sequence of events and knowledge relating factors inside a
given event. The latter would fit under the definition of
functional knowledge. The CIRCSIM-Tutor concept map
treats both of these types of relationships as equivalent
links.
Acknowledgments
Professors Joel Michael and the late Allen Rovick of Rush
Medical College originated the CIRCSIM-Tutor concept
map and the pedagogical principles behind it. Along with
Professor Martha Evens of Illinois Institute of Technology,
they were the principal investigators on the CIRCSIM-Tutor
project, which was sponsored by the Office of Naval
Research. Professor Greg Hume of Valparaiso University
taught me how the original CIRCSIM-Tutor problem solver
worked.
References
Freedman, R. (2000). Using a reactive planner as the basis
for a dialogue agent. In J. Etheredge & B. Manaris (Eds.),
Proceedings of the 13th International Florida Artificial
Intelligence Research Society Conference (FLAIRS 2000),
Orlando (pp. 203-208). Menlo Park, CA: AAAI Press.
Freedman, R., Haggin, N., Nacheva, D., Leahy, T., &
Stilson, R. (2004). Using a domain-independent reactive
planner to implement a medical dialogue system. In
Dialogue Systems for Health Communication: Papers from
the AAAI Fall Symposium, Palo Alto (pp. 24-31). Menlo
Park, CA: AAAI Press.
Freedman, R., Rosé, C. P., Ringenberg, M., & VanLehn,
K. (2000). ITS tools for natural language dialogue: A
domain-independent parser and planner. In G. Gauthier, C.
Frasson, & K. VanLehn (Eds.), Proceedings of the Fifth
International Conference on Intelligent Tutoring Systems
(ITS 2000), Montreal, (pp. 433-442). LNCS 1839. Berlin:
Springer.
Khuwaja, R. (1994). A Model of Tutoring: Facilitating
Knowledge Integration using Multiple Models of the
Domain. Ph.D. thesis, Department of Computer Science,
Illinois Institute of Technology.
Michael, J., Rovick, A., Glass, M., Zhou, Y. and Evens, M.
(2003). Learning from a Computer Tutor with Natural
Language Capabilities. Interactive Learning Environments.
11(3): 233–262.
Rovick, A., & Michael, J. (1992). “The Predictions Table:
A Tool for Assessing Students’ Knowledge,” American
Journal of Physiology, 263(6, part 3): S33–S36. Also
available as Advances in Physiology Education, 8(1): S33–
S36.
Stevens, A., Collins, A., & Goldin, S. 1979. “Misconceptions in Students’ Understanding,” International
Journal of Man-Machine Studies 11(1): 145–156.
Reprinted in Sleeman, Derek H. and John S. Brown, eds.,
1982, Intelligent Tutoring Systems , New York: Academic
Press.