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Componential Analysis of the Recognition of Semantic Relations Between Concepts
Componential Analysis of the Recognition of Semantic Relations Between Concepts F. KUKLA
The recognition of semantic relations between concepts is an essential condition for many cognitive processes. It is part, for instance, of processes of language understanding, conceptual classification and differentiation. Semantic relations between concepts can themselves be part of individual memory structure and as such can be recalled and identified in a cognitive process. But if they are not explicitly stored and recallable, then they must be derived in the process of recognition from the representations of the concepts. We shall examine this process here. The forms of representation of concepts in memory are an important condition for procedures of obtaining semantic relations between concepts. We proceed from the assumption that concepts are represented in memory on the basis of features which make it possible to recognize the objects assignable to them in a multitude of situations requiring such recognition. Which particular features are then actualized and become operative depends on the specific requirements (= tasks) and on the conditions of situation and context. Thus, the relation between concepts which is derived from the features is usually specified by the requirement situation. Therefore, the present inquiry is focused on the process of recognizing semantic relations between concepts, which relations are not explicitly stored. Its aim is to identify individual components of this process in order to render understandable the complex operations of which these components are a part. We particularly wanted to know if component processes (components) of recognition can be traced to the features of concept representation. The underlying hypothesis is that recognition takes place through individual comparisons of conceptual features that are actualized. As to the method, in view of the foregoing, the material and requirements had to be selected in such a manner that the same set of features of concepts is actualized in the subjects and that the operations involved in relation recognition are then linked to that set. In one case we selected 12 in another case 8 concepts for this purpose, which can be subordinated to a common generic term (the category “waters”) (cf. fig. 1). It encompasses a set of features common to all these concepts. The features specifying the individual concepts had been determined in an analysis carried out by HUNDSNURCHER (1970) in such a manner that they made it possible fully to differentiate between the concepts (cf. fig. 1). In the first case there were eight and in the second case 6 features that are classifiable as values of three attributes: F (flowinglstagnant), N (natural/artificial), G (very large/large / small/very small). The object was to test the utilization of the features by the subjects through three successive requirements: definition, classification and discrimination of the concepts prior to the critical experimental requirement (analogy solution) and to have them actualize a uniform set of,features of the quantity of concepts (cf. fig. 2). Nineteen 169
different features were used by the subjects the first time the concepts were presented for definition, Only 58 per cent of the definition features corresponded to the features of the three attributes F, N, G . The agreement between the test persons’ use of the
I. ( 12 concepts)
1 ( 8 concepts)
3c w
4
features
2
flowing standing natural. artifical large G small -------very large very small
++++----I++-- - - - + +
t
t
--,t
+ - -
t
+
+II
- - + +. - - + + I -
- t t t t
-
t
- I + - + + - - + I - - - + - + - + + - I - - - _--_------_+------ - - - - - --I+ - + - - - - - - - - I -, t - +
Pair combinations of concepts with number of features changed between them ( M D I :
I MDin:
G , F, N
2 MD in : N/G,F/N8FIG 3 MD in : F/NIG
river:brook brook:canal cana1:pool
(GI
(NIG) ( F l NIGI
Fig. : Experimental material: Concepts, attributes and features.
features increased in the subsequent free classification of the concepts: 83 per cent of the classification criteria mentioned corresponded to the six features of the attributes F, N, G. In the subsequent differentiation between the concepts of all pair combinations, only the six features of the three attributes (F, N, G ) were named almost exclusively (92 per cent). It was to be ensured in this manner that representations of the concepts by means of the features of the attributes F, N, G became operative (for all subjects) in the subsequent task of relation recognition. It is now assumed that the semantic relations between the concepts of all combinations of pairs are determined through concurrent and differing features. They can be classified according to the number of features and to the features by which they differ. According to this classification there exist relations with 1, 2 or 3 feature differences (MD) (cf. fig. 1 with examples). The recognition of semantic relations between the concepts was examined on the basis of the solution of conceptual analogy tasks in the form of a : b = c : ? Here the subjects had to recognize the relation existing between the concepts a, b and being given the third concept c, to establish the relation c : d analogonsly by selecting a 4th concept from the set (di), which had been learned. The analysis of the process of recognition was based on the times required for solving the analogy problem and for recognizing the relation a : b contained therein, given different types of relation. The presentation of c was delayed by from 1 to 5 and 7 s after a : b in order to isolate the relation recognition a : b from the complete analogy solution process. The 1 70
tasks
feature utilization verbal. definition - features
1. definition
of concepts
concepts
12 34 5 61 789 10 11 12 13 14 15 16 1718 G for example: dirtv, source rain
F N
50%
I
verbal. classification features
2 free classification of concepts
concept. classes
I
1234561789 F N G I
83% 3. distinction of concepts
I
I
verbal. distinction features pairs
92 Yo assumed feature differences
4. analogy solution 0.6 = c : 7
relations
' . . a8/12
(reaction time measure) with varied delay of presentation a : b - c : ? presentation :
a:b
&I
Fig. 2: Experimental procedure.
C : ?
I
analogy solution time
delay (VT) between the presentation of a : b and the presentation of c : ? and the time that elapsed between the presentation of c and the answer of the test person (cf. fig. 2) were measured. The object was to determine precisely that time of delay in the presentation of c which it takes to complete the recognition of the relation a : b (optimum time of delay). If the relation a : b has not been recognized by the time c is presented, the time spent for recognizing the relation is still contained in the time it takes to answer, thereby increasing it in relation to the optimum delay time. The rest time reaches its minimum when relation recognition is completed in the time of delay. Any additional delay in the presentation of c was not to have any influence on the measured time. The experiment was carried out with 12 concepts and with simultaneous presentation of both parts of the task. The effect of the delay in presentation was examined only in analogy tasks involving eight c0ncepts.l Having gone through tasks 1 (definition), 2 (classification) and 3 (differentiation), the subjects were acquainted with the paradigm of analogy formation with the aid of other spheres of concepts (family relations, geometric forms). They were then asked to solve the analogy tasks that Considerable burdening of the memory and difficulties in differentiation of 4 features of attribute G encountered with the 12 concepts prompted us to reduce the number to 8.
171
could be formed from all combinations of pairs of concepts, the time being measured with the aid of a microphone. The times of delay were realized in experimental blocks which were permutated and distributed over two days. Twenty-three test persons took part in the experiment.
We shall first consider the results obtained with the simultaneous presentation of the complete analogy task, i.a., without delay between a : b and c : ? (cf. fig. 3). They show that the time it took to find the analogy solution is dependent on the specific RT Is1 12
F/G/N FIG
'/'
FIG, o--
6 G"
L 12 concepts ,-a
1.8 concepts
.
1 2 MD 3 Fig. 3: Relation between number of features changed between the concepts of a pair a : b timeI (RT) for solution of the analogy a : b = c : d.
'
and
type of relation involved. The time it takes to work out the analogy solution increases with increasing number of features distinguishing concepts of each pair. This is observed in tests with both 12 and 8 concepts. But the time increase in relation to the feature differences is not a linear one. Individual evaluations and opinions expressed by the subjects suggested the assumption that part of the subjects did not solve the analogy in the form specified. Instead, they reduced the number of feature differences that were to be rendered analogous by transposing the concepts. Instead of solving an analogy a : b = c : d with three feature differences between a and b and c and d, they solved the analogy a : c = b : d with one feature difference between a and c and b and d, thereby reducing the time it took to work out the solution. In addition the time required for the analogy solution within one relation class differs for individual feature differences and their combinations (cf. fig. 3). The question that remains of interest is whether the times spent for solving the entire analogy problem, which are dependent on the relation type (feature differences), can themselves be determined already for the process of relation recognition a : b.2 Information is to be obtained, Under the present conditions, the times required for solving analogy problems do not make it possible as yet to say something about the process of relation recognition itself, because in addition to the time required for recognizing the relation a : b, they include times for search, comparison and decision processes involved in establishing analogies. Thus, the fact that the time increases as the feature differences grow must not be due to more time being spent for relation recognition, but can be due, for instance, to differences in difficulty of the search processes involved in establishing the 2nd relation c : d or to differences in the number of individual comparisons between the 1st and the 2nd pair of concepts formed.
I72
by way of relation recognition, through experiments with successive presentation of both analogy parts -a : b and c : ? First of all, fig. 4 shows that the time still required for solving the analogy problem decreases as the delay between the presentation of a : b and the presentation of c increases. This was to be expected, because the relation must be recognized more and more completely during the delay time. Figure 4 also VT
R T tsl
n
3L
2
1
2 MD
3
Fig. 4: Rest-time for analogy solution (RT) for concept pairs with different number of feature differences (MD) after delay-time (VT) between presentation of a : b and presentation of c:?
shows that there is a linear relationship between the remaining time (= rest time) for establishing the analogy in the case of a long delay in the presentation of c on the one hand and the number of feature differences on the other. This supports the aforementioned explanation of the non-linear increase in the solution time with the increasing number of feature differences if both parts of the analogy are presented simultaneously, because if the presentation of c after a :b is delayed, then the possibility of rearranging the set analogy task a : b = c : d into a : c = b : d and thus of reducing the time required for the solution is forfeited. The time for relation recognition can be determined indirectly in two independent ways: Firstly, it can be calculated using the difference between the total time for solving the analogy problem and the remaining time used for establishing the analogy. Secondly, it should be determined as an optimum delay time, which is just enough to conclude the relation recognition before c is presented. Figure5 shows that the remaining time (rest time) that is still needed for solving the analogy problem diminishes as the delay in the presentation of c increases until the relation recognition a : b can be performed entirely before the presentation of c. From this optimum time of delay on, the time for establishing the relation b : d remains nearly constant. I t is clear that a maximum saving in the time required for solving the analogy problem if the number of feature differences between the concepts a, b increases can be achieved only by increasing the delay in presenting c. The optimum delay, after which only negligible changes are measured in the rest time, increases with the number of differences in the features of the concepts of a relation. 3, 4 and 5 s limit the ceilings of intervals in which lie the optimum times of delay for relations with 1,2 and 3 feature differences and represent the approximate time spent for recognizing these relations. The approximate equidistance of the position of the optimum times of delay shown in 173
RT - rest
opt. VT
g 2-0 8 -
---..' \,Lo-\
76 54 321 -
I
MD3 MD2
./'
MD1
fl-m-e-
/-
I
I
I
I
I
I
I
and presentation of c:? for concept-pairs with different feature differences (MD). analogy solution time (measured)
recognition of the relation a : b total rest after (computed as a:b=c:d opt,VT c : d difference to to1- rest I
1 MD
322 470
2 MD
3 MD
presentation
306 a ': b
C
a)
I
>
>
opt. delay-time measured
2...3
!40
3 ... 4
436
:?
,
4...5 or-reaction
t
total-RT difference RT Csl
1
2 MD
3
Fig. 6: a) Decomposition of total solution time; b) Relation between time of relation recognition a : b (RT) (determined as difference) and number of features changed between the concepts of the pair a : b (MD).
174
fig. 5 suggests that the corresponding times of relation recognition are in a linear relationship with the quantity of feature differences. The second way of determining the time required for recognizing the relation a : b as a saving in the time required for solving the problem is determined when a : b is given and when the presentation of c is optimally delayed. Here the additivity of the two distinguished parts of the entire analogy solution (relation recognition a : b relation establishment c : d = analogy solution) is assumed and the unknown relation recognition is calculated on the basis of the times measured for the entire analogy solution and for the establishment of the relation (cf. fig. 6). There is a linear relation between the differences between the measured total time for solving the analogies and the rest time that is still required for establishing the analogy after an optimum delay (and hence after relation recognition) on the one hand and the number of feature differences between the concepts of a relation on the other hand.3 As expected, they lie in (or in the case of 3 MD, very close to) the intervals, which have been assumed in accordance with the rest time changes with varying delay time as an approximation of the optimum delay time (cf. Table in fig. 6). The times of recognition of the relations determined by the two independent methods are in an almost linear relation to the number of feature differences constituting the relations.
+
What do these results mean with reference to our inquiries and hypotheses? We have assumed that relations not explicitly entered in the memory must be derived from the representations of concepts in the process of recognition. The differences in time spent for recognizing conceptual types of relation are attributed, La., to the differences in the degree of difficulty of the processes of relation derivation involved. The close relationship that has been proved to exist between the time of recognition of relation and the feature differences of conceptual representation confirms the expectation that processes of relation recognition can be attributed to actualized concept features. The aim of the inquiry was to identify components of relation recognition. This means that answers must be found to questions concerning what the time for recognizing the conceptual relations examined is made up of. We assume that relation recognition is based on feature comparisons of concepts that have been related. The features of all three attributes of the two concepts of a relation must always be compared in order to arrive at the correct solution of the analogies, for it is after all the purpose of the relation recognition. Thus, the different amounts of time spent for recognizing relations with different numbers of feature differences cannot be attributed to the differences in the number of necessary feature comparisons. Owing to the fact that the amount of time required increases with increasing feature differences, the result suggests that processes of recognizing differences between features (as opposed to feature concurrences) have a decisive bearing on relation recognition. This is understandable in view of the significance of feature differences between concepts for solving analogies : Two relations are analogous only if they differ in the same features and in the same direction. For instance, if a : b decreases from “large” to “small”, then c : d must also decrease from “large” to “small” and not from “small” to “large”. Knowing only the concurring features The mean value for the total time needed for solving an analogy problem involving 3 feature differences was determined only for those subjects here who arrived at the solution without transposing the analogy.
175
between the two concepts is not enough to arrive at correct relation recognition and analogy solution. Concurring features can be forgotten again in relation recognition, but each of the different features involved in feature comparison must be identified with the direction of differentiation and retained. This requires more time than in the case of recognition of concurring features. For the time being nothing can be said about the additional operations connected with this. The fact that the time required for relation recognition varies linearly with the number of feature differences means that a nearly constant amount of time is added to the amount of time spent for recognition with each feature difference, i.e., the additional time required varies additively. This suggests that the comparisons of concept features take place successively. Owing to the fact that all (actualized) features of related concepts must always be compared for each relation recognition, no inferences can be made from the recognition times concerning the sequence of feature comparisons. However, the nearly constant 1.42 s by which the recognition time increases with each additional feature difference cannot be attributed solely to the recognition of this difference. The determination of each additional feature difference means that there is one agreement less each time. Thus there are at least two different components involved in the time i n ~ r e m e n t An . ~ estimate of the shares of time involved (the additivity of these components being assumed) based on the times measured in experimental relation recognition shows that 0.26 s are required for determining feature identity and 1.69 s for recognizing a feature difference. Additional time for encoding the concepts cannot be determined. It is to be assumed that no separate and uniform encoding of the concepts takes place as an independent process prior to relation recognition, but that their features are recalled only within the comparison. And this takes place-just as the comparisons themselves-successively for the features of attributes. Thus the encoding of concepts into their feature representations takes place in a broken down form as part of the successive attribute-by-attribute feature comparisons. According to this, the time spent on encoding the two concepts of a relation would already be part of the time required for the recognition of this relation.
Summing up, it can be said that the results mentioned in the foregoing support the following view of the components of recognition of conceptual relations : Relations between concepts not entered in memory, which concepts are represented on the basis of similar feature attributes, are recognized by means of successive attribute comparisons of features of conceptual representations. The feature comparisons are made successively and comprehensively with regard to the conceptual features actualized through the requirement and context. They require more time in the case of a feature difference than in the case of identical features. Results of comparisons are retained (for a short while) as an attribute-by-attribute listing of the feature differences and are then available for other cognitive operations (e.g., for establishing analogies between such relations). References HUNDSNURCHER, F. : Neuere Methoden der Semantik. Germanistische Arbeitshefte 2, Tubingen I970 Each time the number of feature differences increases there is one feature difference more and one concurrence less for the three necessary feature comparisons. Relations with 1 feature difference require the determination of 2 concurrences and the recognition of 1 difference, while relations with 2 feature differences require 1 concurrence and 2 differences, etc.
176
The recognition of semantic relations between concepts is an essential condition for many cognitive processes. It is part, for instance, of processes of language understanding, conceptual classification and differentiation. Semantic relations between concepts can themselves be part of individual memory structure and as such can be recalled and identified in a cognitive process. But if they are not explicitly stored and recallable, then they must be derived in the process of recognition from the representations of the concepts. We shall examine this process here. The forms of representation of concepts in memory are an important condition for procedures of obtaining semantic relations between concepts. We proceed from the assumption that concepts are represented in memory on the basis of features which make it possible to recognize the objects assignable to them in a multitude of situations requiring such recognition. Which particular features are then actualized and become operative depends on the specific requirements (= tasks) and on the conditions of situation and context. Thus, the relation between concepts which is derived from the features is usually specified by the requirement situation. Therefore, the present inquiry is focused on the process of recognizing semantic relations between concepts, which relations are not explicitly stored. Its aim is to identify individual components of this process in order to render understandable the complex operations of which these components are a part. We particularly wanted to know if component processes (components) of recognition can be traced to the features of concept representation. The underlying hypothesis is that recognition takes place through individual comparisons of conceptual features that are actualized. As to the method, in view of the foregoing, the material and requirements had to be selected in such a manner that the same set of features of concepts is actualized in the subjects and that the operations involved in relation recognition are then linked to that set. In one case we selected 12 in another case 8 concepts for this purpose, which can be subordinated to a common generic term (the category “waters”) (cf. fig. 1). It encompasses a set of features common to all these concepts. The features specifying the individual concepts had been determined in an analysis carried out by HUNDSNURCHER (1970) in such a manner that they made it possible fully to differentiate between the concepts (cf. fig. 1). In the first case there were eight and in the second case 6 features that are classifiable as values of three attributes: F (flowinglstagnant), N (natural/artificial), G (very large/large / small/very small). The object was to test the utilization of the features by the subjects through three successive requirements: definition, classification and discrimination of the concepts prior to the critical experimental requirement (analogy solution) and to have them actualize a uniform set of,features of the quantity of concepts (cf. fig. 2). Nineteen 169
different features were used by the subjects the first time the concepts were presented for definition, Only 58 per cent of the definition features corresponded to the features of the three attributes F, N, G . The agreement between the test persons’ use of the
I. ( 12 concepts)
1 ( 8 concepts)
3c w
4
features
2
flowing standing natural. artifical large G small -------very large very small
++++----I++-- - - - + +
t
t
--,t
+ - -
t
+
+II
- - + +. - - + + I -
- t t t t
-
t
- I + - + + - - + I - - - + - + - + + - I - - - _--_------_+------ - - - - - --I+ - + - - - - - - - - I -, t - +
Pair combinations of concepts with number of features changed between them ( M D I :
I MDin:
G , F, N
2 MD in : N/G,F/N8FIG 3 MD in : F/NIG
river:brook brook:canal cana1:pool
(GI
(NIG) ( F l NIGI
Fig. : Experimental material: Concepts, attributes and features.
features increased in the subsequent free classification of the concepts: 83 per cent of the classification criteria mentioned corresponded to the six features of the attributes F, N, G. In the subsequent differentiation between the concepts of all pair combinations, only the six features of the three attributes (F, N, G ) were named almost exclusively (92 per cent). It was to be ensured in this manner that representations of the concepts by means of the features of the attributes F, N, G became operative (for all subjects) in the subsequent task of relation recognition. It is now assumed that the semantic relations between the concepts of all combinations of pairs are determined through concurrent and differing features. They can be classified according to the number of features and to the features by which they differ. According to this classification there exist relations with 1, 2 or 3 feature differences (MD) (cf. fig. 1 with examples). The recognition of semantic relations between the concepts was examined on the basis of the solution of conceptual analogy tasks in the form of a : b = c : ? Here the subjects had to recognize the relation existing between the concepts a, b and being given the third concept c, to establish the relation c : d analogonsly by selecting a 4th concept from the set (di), which had been learned. The analysis of the process of recognition was based on the times required for solving the analogy problem and for recognizing the relation a : b contained therein, given different types of relation. The presentation of c was delayed by from 1 to 5 and 7 s after a : b in order to isolate the relation recognition a : b from the complete analogy solution process. The 1 70
tasks
feature utilization verbal. definition - features
1. definition
of concepts
concepts
12 34 5 61 789 10 11 12 13 14 15 16 1718 G for example: dirtv, source rain
F N
50%
I
verbal. classification features
2 free classification of concepts
concept. classes
I
1234561789 F N G I
83% 3. distinction of concepts
I
I
verbal. distinction features pairs
92 Yo assumed feature differences
4. analogy solution 0.6 = c : 7
relations
' . . a8/12
(reaction time measure) with varied delay of presentation a : b - c : ? presentation :
a:b
&I
Fig. 2: Experimental procedure.
C : ?
I
analogy solution time
delay (VT) between the presentation of a : b and the presentation of c : ? and the time that elapsed between the presentation of c and the answer of the test person (cf. fig. 2) were measured. The object was to determine precisely that time of delay in the presentation of c which it takes to complete the recognition of the relation a : b (optimum time of delay). If the relation a : b has not been recognized by the time c is presented, the time spent for recognizing the relation is still contained in the time it takes to answer, thereby increasing it in relation to the optimum delay time. The rest time reaches its minimum when relation recognition is completed in the time of delay. Any additional delay in the presentation of c was not to have any influence on the measured time. The experiment was carried out with 12 concepts and with simultaneous presentation of both parts of the task. The effect of the delay in presentation was examined only in analogy tasks involving eight c0ncepts.l Having gone through tasks 1 (definition), 2 (classification) and 3 (differentiation), the subjects were acquainted with the paradigm of analogy formation with the aid of other spheres of concepts (family relations, geometric forms). They were then asked to solve the analogy tasks that Considerable burdening of the memory and difficulties in differentiation of 4 features of attribute G encountered with the 12 concepts prompted us to reduce the number to 8.
171
could be formed from all combinations of pairs of concepts, the time being measured with the aid of a microphone. The times of delay were realized in experimental blocks which were permutated and distributed over two days. Twenty-three test persons took part in the experiment.
We shall first consider the results obtained with the simultaneous presentation of the complete analogy task, i.a., without delay between a : b and c : ? (cf. fig. 3). They show that the time it took to find the analogy solution is dependent on the specific RT Is1 12
F/G/N FIG
'/'
FIG, o--
6 G"
L 12 concepts ,-a
1.8 concepts
.
1 2 MD 3 Fig. 3: Relation between number of features changed between the concepts of a pair a : b timeI (RT) for solution of the analogy a : b = c : d.
'
and
type of relation involved. The time it takes to work out the analogy solution increases with increasing number of features distinguishing concepts of each pair. This is observed in tests with both 12 and 8 concepts. But the time increase in relation to the feature differences is not a linear one. Individual evaluations and opinions expressed by the subjects suggested the assumption that part of the subjects did not solve the analogy in the form specified. Instead, they reduced the number of feature differences that were to be rendered analogous by transposing the concepts. Instead of solving an analogy a : b = c : d with three feature differences between a and b and c and d, they solved the analogy a : c = b : d with one feature difference between a and c and b and d, thereby reducing the time it took to work out the solution. In addition the time required for the analogy solution within one relation class differs for individual feature differences and their combinations (cf. fig. 3). The question that remains of interest is whether the times spent for solving the entire analogy problem, which are dependent on the relation type (feature differences), can themselves be determined already for the process of relation recognition a : b.2 Information is to be obtained, Under the present conditions, the times required for solving analogy problems do not make it possible as yet to say something about the process of relation recognition itself, because in addition to the time required for recognizing the relation a : b, they include times for search, comparison and decision processes involved in establishing analogies. Thus, the fact that the time increases as the feature differences grow must not be due to more time being spent for relation recognition, but can be due, for instance, to differences in difficulty of the search processes involved in establishing the 2nd relation c : d or to differences in the number of individual comparisons between the 1st and the 2nd pair of concepts formed.
I72
by way of relation recognition, through experiments with successive presentation of both analogy parts -a : b and c : ? First of all, fig. 4 shows that the time still required for solving the analogy problem decreases as the delay between the presentation of a : b and the presentation of c increases. This was to be expected, because the relation must be recognized more and more completely during the delay time. Figure 4 also VT
R T tsl
n
3L
2
1
2 MD
3
Fig. 4: Rest-time for analogy solution (RT) for concept pairs with different number of feature differences (MD) after delay-time (VT) between presentation of a : b and presentation of c:?
shows that there is a linear relationship between the remaining time (= rest time) for establishing the analogy in the case of a long delay in the presentation of c on the one hand and the number of feature differences on the other. This supports the aforementioned explanation of the non-linear increase in the solution time with the increasing number of feature differences if both parts of the analogy are presented simultaneously, because if the presentation of c after a :b is delayed, then the possibility of rearranging the set analogy task a : b = c : d into a : c = b : d and thus of reducing the time required for the solution is forfeited. The time for relation recognition can be determined indirectly in two independent ways: Firstly, it can be calculated using the difference between the total time for solving the analogy problem and the remaining time used for establishing the analogy. Secondly, it should be determined as an optimum delay time, which is just enough to conclude the relation recognition before c is presented. Figure5 shows that the remaining time (rest time) that is still needed for solving the analogy problem diminishes as the delay in the presentation of c increases until the relation recognition a : b can be performed entirely before the presentation of c. From this optimum time of delay on, the time for establishing the relation b : d remains nearly constant. I t is clear that a maximum saving in the time required for solving the analogy problem if the number of feature differences between the concepts a, b increases can be achieved only by increasing the delay in presenting c. The optimum delay, after which only negligible changes are measured in the rest time, increases with the number of differences in the features of the concepts of a relation. 3, 4 and 5 s limit the ceilings of intervals in which lie the optimum times of delay for relations with 1,2 and 3 feature differences and represent the approximate time spent for recognizing these relations. The approximate equidistance of the position of the optimum times of delay shown in 173
RT - rest
opt. VT
g 2-0 8 -
---..' \,Lo-\
76 54 321 -
I
MD3 MD2
./'
MD1
fl-m-e-
/-
I
I
I
I
I
I
I
and presentation of c:? for concept-pairs with different feature differences (MD). analogy solution time (measured)
recognition of the relation a : b total rest after (computed as a:b=c:d opt,VT c : d difference to to1- rest I
1 MD
322 470
2 MD
3 MD
presentation
306 a ': b
C
a)
I
>
>
opt. delay-time measured
2...3
!40
3 ... 4
436
:?
,
4...5 or-reaction
t
total-RT difference RT Csl
1
2 MD
3
Fig. 6: a) Decomposition of total solution time; b) Relation between time of relation recognition a : b (RT) (determined as difference) and number of features changed between the concepts of the pair a : b (MD).
174
fig. 5 suggests that the corresponding times of relation recognition are in a linear relationship with the quantity of feature differences. The second way of determining the time required for recognizing the relation a : b as a saving in the time required for solving the problem is determined when a : b is given and when the presentation of c is optimally delayed. Here the additivity of the two distinguished parts of the entire analogy solution (relation recognition a : b relation establishment c : d = analogy solution) is assumed and the unknown relation recognition is calculated on the basis of the times measured for the entire analogy solution and for the establishment of the relation (cf. fig. 6). There is a linear relation between the differences between the measured total time for solving the analogies and the rest time that is still required for establishing the analogy after an optimum delay (and hence after relation recognition) on the one hand and the number of feature differences between the concepts of a relation on the other hand.3 As expected, they lie in (or in the case of 3 MD, very close to) the intervals, which have been assumed in accordance with the rest time changes with varying delay time as an approximation of the optimum delay time (cf. Table in fig. 6). The times of recognition of the relations determined by the two independent methods are in an almost linear relation to the number of feature differences constituting the relations.
+
What do these results mean with reference to our inquiries and hypotheses? We have assumed that relations not explicitly entered in the memory must be derived from the representations of concepts in the process of recognition. The differences in time spent for recognizing conceptual types of relation are attributed, La., to the differences in the degree of difficulty of the processes of relation derivation involved. The close relationship that has been proved to exist between the time of recognition of relation and the feature differences of conceptual representation confirms the expectation that processes of relation recognition can be attributed to actualized concept features. The aim of the inquiry was to identify components of relation recognition. This means that answers must be found to questions concerning what the time for recognizing the conceptual relations examined is made up of. We assume that relation recognition is based on feature comparisons of concepts that have been related. The features of all three attributes of the two concepts of a relation must always be compared in order to arrive at the correct solution of the analogies, for it is after all the purpose of the relation recognition. Thus, the different amounts of time spent for recognizing relations with different numbers of feature differences cannot be attributed to the differences in the number of necessary feature comparisons. Owing to the fact that the amount of time required increases with increasing feature differences, the result suggests that processes of recognizing differences between features (as opposed to feature concurrences) have a decisive bearing on relation recognition. This is understandable in view of the significance of feature differences between concepts for solving analogies : Two relations are analogous only if they differ in the same features and in the same direction. For instance, if a : b decreases from “large” to “small”, then c : d must also decrease from “large” to “small” and not from “small” to “large”. Knowing only the concurring features The mean value for the total time needed for solving an analogy problem involving 3 feature differences was determined only for those subjects here who arrived at the solution without transposing the analogy.
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between the two concepts is not enough to arrive at correct relation recognition and analogy solution. Concurring features can be forgotten again in relation recognition, but each of the different features involved in feature comparison must be identified with the direction of differentiation and retained. This requires more time than in the case of recognition of concurring features. For the time being nothing can be said about the additional operations connected with this. The fact that the time required for relation recognition varies linearly with the number of feature differences means that a nearly constant amount of time is added to the amount of time spent for recognition with each feature difference, i.e., the additional time required varies additively. This suggests that the comparisons of concept features take place successively. Owing to the fact that all (actualized) features of related concepts must always be compared for each relation recognition, no inferences can be made from the recognition times concerning the sequence of feature comparisons. However, the nearly constant 1.42 s by which the recognition time increases with each additional feature difference cannot be attributed solely to the recognition of this difference. The determination of each additional feature difference means that there is one agreement less each time. Thus there are at least two different components involved in the time i n ~ r e m e n t An . ~ estimate of the shares of time involved (the additivity of these components being assumed) based on the times measured in experimental relation recognition shows that 0.26 s are required for determining feature identity and 1.69 s for recognizing a feature difference. Additional time for encoding the concepts cannot be determined. It is to be assumed that no separate and uniform encoding of the concepts takes place as an independent process prior to relation recognition, but that their features are recalled only within the comparison. And this takes place-just as the comparisons themselves-successively for the features of attributes. Thus the encoding of concepts into their feature representations takes place in a broken down form as part of the successive attribute-by-attribute feature comparisons. According to this, the time spent on encoding the two concepts of a relation would already be part of the time required for the recognition of this relation.
Summing up, it can be said that the results mentioned in the foregoing support the following view of the components of recognition of conceptual relations : Relations between concepts not entered in memory, which concepts are represented on the basis of similar feature attributes, are recognized by means of successive attribute comparisons of features of conceptual representations. The feature comparisons are made successively and comprehensively with regard to the conceptual features actualized through the requirement and context. They require more time in the case of a feature difference than in the case of identical features. Results of comparisons are retained (for a short while) as an attribute-by-attribute listing of the feature differences and are then available for other cognitive operations (e.g., for establishing analogies between such relations). References HUNDSNURCHER, F. : Neuere Methoden der Semantik. Germanistische Arbeitshefte 2, Tubingen I970 Each time the number of feature differences increases there is one feature difference more and one concurrence less for the three necessary feature comparisons. Relations with 1 feature difference require the determination of 2 concurrences and the recognition of 1 difference, while relations with 2 feature differences require 1 concurrence and 2 differences, etc.
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