5
i
difficult) and 2) how robust is this mapping w.r.t. the
nformation processing tasks? Within our framework (1)
w
is answered by counting the mappings and determining
hether or not they involve inspectable facts. The second
s
"
question is really about states, events, and the user's goal
meaning the same things" in both situations.
t
i
The desirability of role correspondence is borne ou
n experiments we have conducted in which subjects were
-
l
asked to translate changes in state between direct manipu
ation tableaus.
Two new Tower of Hanoi isomorphs
f
p
were derived to provide comparisons between pairs o
roblems with and without role correspondence. In the
d
original problem set, the Monster Globe (change) problem
iffers from the other two, in both its violation of object
w
constancy and in the association of state discrimination
ith object roles. In the Tower of Hanoi and Monster
d
Globe move problems both anchored and unanchored
iscriminations are associated with the same object roles
t
(disk/globe).
In the Monster Globe (change) problem
hese discriminations are separated with the unanchored
d
d
discrimination associated with the globe and the anchore
iscrimination with the monster.
The new Monster
-
s
Change Color (MCC) problem retains the object con
tancy violation of MCG but associates both discrimina-
.
T
tions with the same object role as in TOH and MGM
he new Tic-Tac-TOH (TTT) problem eliminates the
s
a
object constancy violation but divides the discrimination
s does MGC and requires an additional rule for the
e
o
anchored discrimination "tokens cannot be moved outsid
f their column".
Each of these problems was implemented as an
t
interactive tableau. Subjects interacted with problem
ableaus by manipulating problem objects directly. The
e
T
interface does not itself constrain the problem. In th
OH tableau, for instance, the subject can perform any
s
action which results in a single change in the problem
tate even if this involves an "illegality" such as moving a
e
l
disk from the bottom of a stack. Problem tableaus ar
inked through a control program which associates tableau
-
l
states between the problems. Buttons for viewing prob
em rules, a correspondence table, and task instructions
a
were available.
An experimental display pairing MGC
nd TTT is shown in Figure 1.
s
Figure 1. Problem tableau
In
the
problem
translation
task
subjects
are
-
c
presented with a pair of tableaus. Their task was to repli
ate changes in the first tableau by manipulating the
b
second tableau.
State changes were evenly divided
etween legal and illegal transitions which alter problem
g
t
state by one action. This task provides measures reflectin
he difficulty of translating between the pairs of tableaus.
l
t
Table 2 shows the average number of successfu
ranslations within a fifteen minute block for the problem
e
a
pairs. The TOH
MGC pairing leads to poor performanc
lthough
the
MCC
MGM
problem
which
requires
-
b
translating from an nonenvisionable though role compati
le
tableau
fares
even
less
well.
The
compatible
t
TTT
MGS pairing leads to more than twice as many
ranslations as MGC's incompatible pairing with TOH.
d
The compatible TOH
MCC pairing, by contrast, pro-
uces the second highest rate of translation suggesting
e
d
that it is not an incompatibility between change and mov
ynamics but an incompatibility between situations which
impairs translation.
_____________________________
T
Table 2
: Successful Translations
OH
MGC
10.0
6
M
TOH
MCC
19.
CC
MGM
8.4
4
_TTT
MGC
25.
____________________________
SITUATIONS AND DISPLAY DESIGN
The objective of our work is to develop methods for
-
f
deriving analogies for use in direct manipulation inter
aces and visualization displays. In this section we illus-
t
trate an approach in which constrained situations are
reated as automata and analogies are found by identifying
d
f
situation types which allow attunements to be substitute
or extrinsic constraints.
In line with our development
s
such analogies should preserve object roles and con-
traints but need not provide type preserving mapping
r
i
between predicates.
Our representational scheme fo
dentifying and matching analogical types is presented in
greater detail in Lewis [5].
The strategy is to represent a constrained situation,
d
as an automaton in which a canonical situation type
efines the states, actions and next state function are
,
a
jointly defined by the determination of object restrictions
nd constraints are defined through the output function
.
B
which assigns polarities of {0,1} to the subsequent state
y limiting the expression of dynamics to object restric-
r
(
tions this scheme provides a lowest common denominato
the entire situation) for expressing constituent relations.
s
As an analogy is assembled by matching constraints, con-
tituent relations which happen to match object role res-
-
s
trictions are re-introduced into the analogical type. Con
traint matching requires exhaustive search because of
t
interaction among constraints. Although this makes the
ask computationally expensive, it is the multiplicity of
t
m
possible ways the same constraints may be expressed tha
akes substitution from a relatively restricted set of