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Affirmation and denial in the structure of inference rules
JOURNAL OF VERBAL LEARNING AND VERBAL BEHAVIOR 8, 705-712
(1969)
A f f i r m a t i o n and Denial in the Structure of Inference Rules I PETER B. WARR AND THOMAS L. COFFMAN
Medical Research Council, Social and Applied Psychology Unit, University of Sheffield, England Judged associations between personal characteristics are examined in a study designed to test three models of inference. These models are based upon the notions of material implication, material equivalence, and symmetry. Not one of the models receives support from the data. In their stead an interpretation of inference rule structures is suggested which predicts that inferences of similar magnitude will be made in conditions of dual affirmation or of dual denial. When two inferences about the same characteristics both affirm or both deny their consequent, then those inferences are on average of equal magnitude. This interpretation is supported by the results of the study described, and is seen to have relevance to studies of judgments about personality and to work on positive and negative information.
This paper examines models o f j u d g m e n t drawn f r o m the propositional calculi of formal logic. The judgments to be studied are inferences a m o n g a variety of adjectives comm o n l y used to describe people. A l t h o u g h it has been demonstrated that judges make quite similar and consistent inferences from one such adjective to another (Bruner & Tagiuri, 1954; W a r r & Knapper, 1968), little is k n o w n about the general pattern or structure by which these inferences might be related. One possibility is that inferences about the characteristics o f stimulus persons follow certain rules o f formal logic, as discussed by W a r r and K n a p p e r (1968, Ch. 3). The framework of the propositional calculus is an attractive one because it suggests useful hypotheses and because it could plausibly account for the general structure o f inferential judgment, one which applies regardless o f the population o f descriptive terms or stimulus objects concerned. There are two fundamental types o f logical relationship which m a y be relevant to the structure o f inferences. First, it might be the
case that decision rules are expressions of material equivalence. This relationship has four defining conditions as follows: (1) (2) (3) (4)
p q -p -q
-~ q --~ p -+ - q ~ -p
(p implies q) (q implies p) (not-p implies not-q) (not-q implies not-p)
where p and q are particular terms, and where - p and - q are the negations o f those terms. As an example o f material equivalence, consider the terms honest and truthful. It might be the case that honest -+ truthful, truthful --~ honest, not-honest---~not-truthful, and nottruthful ~ not-honest. In these conditions it would be said that the two adjectives were materially equivalent. But material equivalence is unlikely to be a widely observed relationship, since its four conditions probably are met only in the case of synonyms or near-synonyms. A relationship o f greater interest is that o f material implication. The defining case for this relationship is the one in which p --~q and - q ~ - p are true, but q ---~p and - p --~ - q are not true. Material implication is exemplified in those 1 The authors are grateful to Stuart Smith for his trait-pairs of which one trait (p) is a subdivision assistance during the preparation of this paper, and of the other (q). For instance, where p stands to the Social Science Research Council (London) for financial support. for musical (or poetic, or artistic) and q for 705
706
WARR AND COFFMAN
talented, a relationship of material implication possible relationship which may be introduced. probably obtains, permitting such inferences This is the simpler notion of symmetry. A p :q as musical -+ talented and not-talented ~ not- relationship is symmetrical if the inferences musical, but disallowing the inferences talented p ~ q and q - - ~ p are equivalent in direction and magnitude, regardless of the values of the musical and not-musical -+ not-talented. Note that in comparison with material impli- related propositions, p ~ - q, q ~ - p , etc. A cation, material equivalence is actually a two- relationship of this kind is not permitted in the propositional calculus, since its definition way implicative relationship. Of course', these relationships--material runs counter to that of material implication equivalence and material implication--might and the single defining condition is only one hold only for terms which are synonymous or aspect of the broader notion of material subordinate-superordinate pairs. Many deci- equivalence. sion rules link characteristics which apparently METHOD are quite different (impulsive and irritable, The procedure adopted in the present study was to precise and sincere, for example; see Warr & have subjects make judgments about the strength of Knapper, 1968, p. 138), and one might ask implicative relationships between personal characwhether a model from formal logic will be teristics. Eight trait-names and their negated counterrelevant to the structure of decision rules in parts were used. These were divided into two compargeneral. To put this question empirically, we able sets, referred to here as Set A and Set B. Half shall test predictions from the proposed models of the items in each set were chosen on the basis of pretests to he desirable characteristics, and half were against inferences among a sample of widely known to be judged as undesirable. Desirability is differing terms. indicated below as " + " and undesirability as " - "" However, relationships among dissimilar terms are seldom of an all-or-none kind. In SET A Unmodified terms order to translate the propositional calculus aggressive (-) to the general case, its two-valued logic (which honest (+) requires that the proposition p -~ q be either prejudiced (-) "true" or "false") must be modified accordreliable (+) ingly. In the present investigation it was Negatively modified terms decided to obtain estimates of the magnitude unaggressive (+) of associations (that is, the degree to which p dishonest (-) unprejudiced (+) is seen to imply q) and to examine the pattern unreliable (-) of these probabilistic estimates. Thus the truefalse dichotomy is replaced here by a con- SET B tinuum running through varying degrees of Unmodified terms positive and negative inference values. Note conceited (-) that with this translation a negative association friendly (+) intelligent (+) or inference is just as "true" as is a positive selfish (-) association or inference; a proposition is "false" only if the p --~ q value is zero. Never- Negatively modified terms unconceited (+) theless, as will be seen below, it is important unfriendly (-) to preserve the distinction between those unintelligent (-) cases in which p implies q positively (here unselfish (+) written p -~ q) and those in which p implies q negatively (written p ~ q). Each of the sixteen terms served as a "cue trait" (the In addition to material equivalence and given trait from which inferences were to be drawn), material implication, there is a third type of and aNo as a "response trait" (inferred from the cue
INFERENCE RULE STRUCTURE trait) relative to each of the eight adjectives in the set to which it did not belong. Thus, when an A trait was given as a cue trait, B traits appeared in the response list; and when a B trait was given as a cue trait, A traits appeared in the response list. Altogether then, there were 128 judgments about inferences between Sets A and B. This design yielded data on all the possible inference types but reduced the burden on the Ss by eliminating half of the permutations. Instead, to introduce greater variety into the Ss' task, eight additional terms were included among the response items. These filler items may be referred to as Set F; they accounted for a further 128 judgments per S: SET F Unmodified terms ambitious cautious dignified excitable Negatively modified terms unambitious incautious undignified unexcitable
The perceived implications between these terms were ~measured by a version of the procedure first used by Brunet, Shapiro, and Tagiuri (1958). Subjects were asked how likely it is that persons described as, say, aggressive are conceited, friendly, honest, and so on. Responses were made by placing check-marks on a six-point scale from "nearly always are" (+ 3) to "hardly ever are" ( - 3) with no neutral position. Data were collected in eight-page booklets, each page of which introduced a single cue trait and involved inferences to eight response traits. Four separate booklets were used, these beir~gcompleted in counterbalanced orders at half-hour intervals during an experimental session involving several tasks. Booklets were made up so that the eight response traits on each page were either all unmodifig~d or all modified, and within each booklet the eight cue traits were themselves either all unmodified or all modified. Response traits were always presented alphabetically on a page. Subjects were 64 undergraduates from several departments of Sheffield University. Thirty-five men and twenty-nine women took part. RESULTS The m e a n value o f each o f the 256 implications was first c a l c u l a t e d s e p a r a t e l y for males a n d for females. Significant sex differences
707
were present in the case o f only nine implicative relationships, a frequency in keeping with o t h e r studies o f this k i n d ( W a r r & K n a p p e r , 1968, Ch. 3), a n d the d a t a for males a n d females were therefore c o m b i n e d . The 128 m e a n values involving the filler traits were then discarded, a n d the r e m a i n i n g m a t e r i a l served for testing the m o d e l s described above. These 128 cases to be a n a l y z e d m a y be split into eight categories a c c o r d i n g to the direction o f the A : B inferences a n d to w h e t h e r each t e r m is modified, as follows: A to B, - A to - B , A to - B , - A to B, B to A, - B to - A , B to - A , - B to A. As was i n d i c a t e d h a l f o f the terms in each set (A or B) were j u d g e d to be desirable a n d h a l f to be undesirable. Since desirable terms are in general j u d g e d to positively i m p l y other desirable terms (and similarly for undesirable terms), h a l f o f the inferences in each o f the eight categories were here f o u n d to be positive a n d h a l f to be negative. As an illustration, consider the 16 A - t o - B inferences. E a c h o f the two desirable A terms was f o u n d to positively i m p l y the two desirable B terms, a n d each o f the two undesirable A terms was f o u n d to positively i m p l y the two undesirable B terms. Hence there were eight cases where A ~ B. Since the two desirable A terms were f o u n d to negatively i m p l y the undesirable B terms, a n d the two undesirable A terms to negatively i m p l y the desirable B terms, t h e r e w e r e also eight cases where A ~ B. A similar p a t t e r n o f results for each o f the eight classes o f relationship n o t e d in the previous p a r a g r a p h g e n e r a t e d sixteen categories o f eight cases each: 2 A - - ~ B, A~B; -A~-B, -A~-B; A~-B, 2 The letters "A" and "B" will be used here (rather than "p" and "q") in order to identify the two sets of trait-names studied. Note that for some comparisons to be made, the distinction is a crucial one, for example, A ~ B versus B ~-A, whereas for other comparisons the two sets of values are formally equivalent and may be regarded as replications. For instance, the comparison of A + B versus - B ~- - A is formally the same as the comparison of B + A versus - A ~ -B, but with different terms appearing as cue traits and as response traits.
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WARR. AND COFFMAN
A ~> - B ; - A ~ B , - A ~> B;B -:~ A,B _z> A; - B ~> - A , - B ~> - A ; B ~> - A , B ---> - A ; - B -~ A, - B ~ A. The structure of inferences was examined by comparing the values in each pair of categories noted above. This was initially achieved by plotting the material graphically as in Figure 1. In this figure are presented two of twenty-eight such scatter-plots which were examined. The left-hand diagram shows the relationships between all the instances of A to B
But the right-hand diagram in Figure 1 ,presents a different picture. In these cases the A:B inferences are compared with the inferences arising when A and B are simultaneously negated and transposed, that is, the comparison is between A --->B and - B ---> - A . On the average, the - B ~> - A inferences are smaller than the A -~ B inferences, whereas the - B ~ - A inferences are greater than the A - ~ B inferences, leading to marked departure of the points from the diagonal axis in Figure 1.
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versus
B ---)" - A
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to A
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to
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versus
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to
-A
FIG. 1. Comparisons between pairs of inference classes.
versus B to A inferences. The positive inferences are exemplified by that between prejudiced (an A term) and conceited (a B term); the mean prejudiced --->conceited value is +2.41, and the conceited-->prejudiced mean is +2.37. A sample pair of negative inferences is honest --->selfish (whose value is -1.97) and selfish --->honest (-1.55). In general it is clear from the left-hand diagram that transposing p:q relationship (from A--> B to B - + A) produces an inference of similar magnitude as the original, and that this is true for both positive and negative inferences. 3
The statistical significance of these systematic deviations (and of those observed in other comparisons) may be established by a Wilcoxon T test applied to the relevant pairs of inference values. This procedure has been adopted for each of the possible comparisons 3 There are, of course, clear departures from this general rule. For instance, the mean value of the aggressive:friendly inference is -1.08, but the value of friendly --->aggressive is -2.41. However, at this point we are concerned to identify the central tendencies of inference relationships rather than their individual differences.
709
INFERENCE RULE STRUCTURE
TABLE 1 EIGHT TESTS OF THE MATERIAL IMPLICATION MODEL SHOWING MEAN INFERENCE V A L U E S a AND WILCOXON T TESTS. (THE NULL HYPOTHESIS IS AN ASSERTION OF MATERIALIMPLICATION BETWEEN m :B INFERENCES.)
Inference pairs
T
p<
Affirmation or denial of the consequent Inference 1 Inference 2
A ~ B (2.00) vs. - B ~ - A (1.22) A ~ B (1.23) vs. - B --~ - A (1.88)
3 0
.05 .01
affirmation denial
denial affirmation
- A ~- - B (1.13) vs. B -+~A (1.91) - A ~ - B (1.72) vs. B ~ A (1.24)
0 3
.01 .05
denial affirmation
affirmation denial
A ~ - B (1.34) vs. B ~ - A (1.38) A ~ - B (1.84) vs. B ~ - A (1.76)
16 5.5
n.s. n.s.
denial affirmation
denial affirmation
- A ~ B (2.01) vs. - B -*~ A (2.22) - A ~ B (1.08) vs. - B ~ A (1.16)
10 7b
n.s. n.s.
affirmation denial
affirmation denial
" Shown in parentheses are mean absolute values each based on N = 8. Directions of inferences are indicated by the plus and minus signs over the arrows. b T is in this case based on 7 difference scores, since one pair showed no difference. o f inference types. C e r t a i n o f these c o m p a r i s o n s p r o v i d e direct tests o f the m o d e l s o u t l i n e d above. These m a y be discussed first; t h e n we can t u r n to the r e m a i n i n g c o m p a r i s o n s to a t t e m p t a general interpretation.
Material Implication It m a y be inferred f r o m the brief account o f m a t e r i a l i m p l i c a t i o n presented earlier that c e r t a i n relationships between pairs o f inference ought to be observed if this m o d e l is to a c c o u n t for the data. It should, for example, be the case t h a t the A - ~ B i m p l i c a t i o n s are o f the same m a g n i t u d e as the - B ~ - A ones. W e have seen f r o m the r i g h t - h a n d d i a g r a m in F i g u r e 1 t h a t this is n o t in fact so. W h a t a b o u t the other relevant relationships ? These a r e set o u t in Table 1, together with i n f o r m a tion a b o u t their b e a r i n g u p o n the m a t e r i a l i m p l i c a t i o n possibility. T h e second c o l u m n o f Table 1 lists the W i l c o x o n T values for the pairs o f inferences e x a m i n e d , a n d the p r o b a b i l i t i e s are given in the third column. 4 I n the first two c o m parisons, as we have seen in F i g u r e 1, the two 4 All the probabilities given in this p a p e r are for two-tailed tests.
sets o f values are significantly different so that the m o d e l o f m a t e r i a l implication, which requires no difference between them, must be rejected. N o t e that a significant difference means that the inferences in one set are consistently greater or smaller t h a n their t r a n s f o r m s in the other set. In the final c o l u m n are considerations to be discussed later. F o r the present it m a y be n o t e d t h a t m a t e r i a l i m p l i c a t i o n can be accepted as an a p p r o p r i a t e m o d e l in only four o f the eight c o m p a r i s o n s m a d e here.
Symmetry T u r n n o w to the crucial cases of the symm e t r y model. W h a t h a p p e n s to the p a t t e r n o f decision rules when A : B, - A : - B , A : - B , a n d - A : B inferences are t r a n s p o s e d ? The o b s e r v e d o u t c o m e s are s u m m a r i z e d in Table 2. It c a n be seen once again t h a t the m o d e l is a p p l i c a b l e only in certain cases. In four instances there is a systematic d e p a r t u r e f r o m the s y m m e t r y hypothesis, a n d three o f these are significant at the .05 level or greater.
Material Equivalence A s we n o t e d earlier, m a t e r i a l equivalence requires b o t h m a t e r i a l i m p l i c a t i o n a n d sym-
710
WAR~RAND COFFMAN TABLE 2
EIGHT TESTS OF TIlE SYMMETRYMODEL SHOWING MEANINFERENCEVALUESa AND WlLCOXON T TESTS. (THE NULL HYPOTHESIS IS AN ASSERTION OF SYMMETRY BETWEEN A :B INFERENCES.) Affirmation or denial of the consequent Inference pairs A -~ B (2.00) vs. B ~- A A ~ B (1.23) vs. B ~ A
(1.91) (1.24)
- A -~ - B (1.13) vs. - B ~ - A (1.22) - A ~ - B (1.72) vs. - B ~ - A (1.88) A -~ - B (1.34) vs. - B ~ A A _z~ - B (1.84) vs. - B ~ A
T
p <
Inference 1
Inference 2
13 14
n.s. n.s.
affirmation denial
affirmation denial
15 8~
n.s. n.s.
denial affirmation
denial affirmation
0 5
.01 n.s.
denial affirmation
affirmation denial
2b 4
.05 .05
affirmation denial
denial affirmation
(2.22) (1.16)
- A -~ B (2.01) vs. B ~- - A (1.38) - A -~ B (1.08) vs. B -~ - A (1.76)
Shown in parentheses are mean absolute values, each based on N = 8. b Tis here based on 7 difference scores, since one pair showed no difference. metry. Sixteen tests o f the equivalence m o d e l have
therefore
Tables
already
been
presented
in
1 a n d 2. T h e r e are, h o w e v e r , e i g h t
a d d i t i o n a l cases to be considered. These cases
departures from the predicted equivalence-all but one at the .05 level of confidence or greater. So the material equivalence prediction is also rejected.
involve negation without transposition and hence are n o t relevant to material implication
Affirmation and Denial
o r s y m m e t r y . T h e y are p r e s e n t e d i n T a b l e 3.
None of the three models under discussion satisfactorily accounts for the structure of
All of these c o m p a r i s o n s reveal systematic
TABLE 3 EIGHT ADDITIONAL TESTS OF THE MATERIAL EQUIVALANCE MODEL SHOWING MEAN INFERENCE VALUES a AND W1LCOXON Z TESTS. (THE NULL HYPOTHESIS ASSERTS THAT A I B INFERENCES CAN BE NEGATED WITHOUT TRANSPOSITION~ AS IN MATERIAL EQUIVALENCE RELATIONSHIPS.)
Affirmation or denial of the consequent Inference pairs A -~ B A ~ B
T
p <
Inference 1
Inference 2
0 3
.01 .05
affirmation denial
denial affirmation
(2.01) (1.08)
0 1
.01 .02
denial affirmation
affirmation denial
(1.91) vs. - B ~ - A (1.22) (1.24) vs. - B ~ - A (1.88)
1 2
.02 .02
affirmation denial
denial affu-mation
0 3b
.01 n.s.
denial affirmation
affirmation denial
(2.00) vs. - A ~ - B (1.13) (1.23) vs. - A ~ - B (1.72)
A ~- - B (1.34) vs. ~ A ~ B A ~ - B (1.84) vs. - A ~ B B ~, A B~ A
B -~ - A (1138) vs. - B ~ A B -~ - A (1.76) vs. - B ~ A
(2.22) (1.16)
a Shown in parentheses are mean absolute values, each based on N = 8. b T is here based on 7 difference scores, since one pair showed no difference.
INFERENCE RULE STRUCTURE
decision rules which is observed in this study. Each model is applicable in a limited range of cases, but no model is manifestly superior to any of the others. This suggests that a quite different concept is required, one which cuts across the central notions of all the models. An interesting, possibility is found in the difference between what may be referred to as the affirmation and the denial of a statement's consequent. It is clear that in the proposition p ~ q the consequent (q) is being affirmed as an associate of the antecedent p (which is given), whereas in the proposition p ~ q the consequent (q) is being denied as an associate of p. But how should propositions such as p -+ - q be interpreted? Suppose we consider p ~ - q as an affirmation of q, and p -~ - q as a denial of q, and so on. Then we find by the comparison shown in Table 4 that the inferences which affirm q are consistently greater in magnitude than the parallel inferences which deny q. (Sets A and B are combined for these comparisons, since half the inferences in each set fall into each category of propositions.) And, looking back at Tables 1 to 3, it is apparent that this difference between affirmation and denial of the consequent provides a key to TABLE 4 EIGHT TESTS OF THE AFFIRMATION-DENIAL MODEL. MEAN INFERENCE VALUESa AND WILCOXON T TESTS COMPARING p:q INFERENCES WHERE q IS AFFIRMED WITH THOSE INFERENCES WHERE q IS DENIED C o n s e q u e n t affirmed
C o n s e q u e n t denied
T
p <
(1.96) (1.96)
-p~q (1.12) - p -~ - q (1.18)
12 2
.01 .01
p ~ - q (1.80) p _z~ _ q (1.80)
-p ~q (1.12) - p -~ - q (1.18)
10.5 1
.01 .01
p~-q
(1.24) p ~ - q (1.36)
3 0
.01 .01
p ~ q (1.24) p -~ - q (1.36)
9 7
.01 .01
p~q p ~ q
-p-~q - p --+~q
(2.11) (2.11)
_ p _z~ _ q (1.80) _ p _z~ _ q (1.80)
a S h o w n in p a r e n t h e s e s are m e a n absolute values, e a c h based o n N = 16.
711
understanding the applicability or nonapplicability of the three models, material equivalence, material implication, and symmetry. In each situation, the data fit the model only when the inferences compared are both affirmations or both denials. Those cases where significant differences are found are the ones in which affirmation of a consequent is compared with denial of a consequent. Two further considerations are of interest in Table 4. First, consider the parallel forms of affirmation and of denial of the consequent. In Column 1 (Consequent Affirmed) it is seen that a simple affirmation of the consequent through a positive inference ( p - ~ q or - p ~ q) produces somewhat greater values than does the parallel double negative form using the same root term for the consequent (p -~ - q or - p ~ -q). In each case the difference is found to be significant. For the first comparison, T = 2 3 , p < . 0 2 , and for the second, T = 0, p < :01. Similarly, in Column 2 (Consequent Denied) propositions containing positive inferences (now coupled with negated consequents, - p -~ - q or p ~ - q ) are slightly greater on average than the parallel propositions which deny by virtue of a negative inference value ( - p -~ q or p ~ q); however, these differences do not occur here with enough consistency for us to reject the null hypothesis. Secondly, consider the form of the antecedent in each of the propositions of Table 4. In half the propositions the antecedent is unqualified (p), and in the remaining half the antecedent is negated (-p). Obviously, when the form of an antecedent is changed, for example, dishonest (--P) instead of honest (p), the nature of the inference to each consequent is changed as well, for example from affirmation of q to denial of q. It is therefore not possible to make direct comparisons between antecedent forms using the same basic terms, as has been done in all previous tests. However, it is interesting to note that the 'smallest inference values are obtained when there is both a negative antecedent and a denial of the
712
WARR AND COFFMAN
consequent ( - p -7 q and - p - ~ - q ) . On the other hand, when the consequent is affirmed, the form of the antecedent appears to have little or no effect. DISCUSSION These findings and interpretations are of importance in two fields. Firstly, they suggest certain revisions to models of intertrait inference. And secondly, they shed further light on the more general differences between positive and negative information. As far as inference rules about personal characteristics are concerned, this study has revealed that models which ignore the difference between forms of propositions, especially affirmation versus denial of the consequent, can be too simple. The logical models which generated the study are in their original form inadequate. We can now adopt a more parsimonious interpretation of inference rule structures: Rules about pairs of characteristics (negated or not) are on the whole of the same magnitude as long as only affirmation of the consequent or only denial of the consequent is involved. It should again be stressed that affirmation or denial both embrace positive ( ~ ) and negative (-~) inferences. It is not the direction of inferences per se that is important, but this direction coupled with information about whether or not the consequent is a negated term. However, many investigations of inference rules in person perception examine only unqualified trait-names, and in these cases (where no negated consequents occur) the difference between positive and negative inferences is the crucial one. If we apply the notions of affirmation and denial to other studies, it becomes clear that the res.ults of the present investigation have parallels in several quite different areas. There is evidence that subjects use positive information much more readily and efficiently than negative information in concept attainment tasks (Bruner, Goodnow & Austin, 1956; Donaldson, 1959; Hovland & Weiss, 1953). Since the present results indicate that Ss' own
affirmatory inferences are more definite than their denials, it may be that positive information in a concept attainment task is more useful because it confirms the sort of inferences which the S himself tends to make more readily or strongly. On the other hand, both of these features could derive from the fact that most of a person's everyday experience in concept attainment is largely a matter of building up positive information. In a close parallel to the present conclusions, Wason (1959, 1961) and Eifermann (1961) report that "agree" or "disagree" responses to affirmatory statements ate made more rapidly than are responses to statements of denial. Taken together these various findings suggest that inference tendencies are primarily attuned to positive information and positive instances, rather than to those of a negative form. REFERENCES BRUNER, J. S., & TAGIURI, R. The perception of people. In G. Lindzey (Ed.), Handbook of social psychology. Reading, Mass.: Addison-Wesley,
1954. BRUNER,J. S., GOOI~NOW,J. L., & AUSTIN,G. A. A study of thinking. New York: Wiley, 1956. BRUNER, J. S., SHAPIRO, D., & TAGIURI, R. The
meaning of traits in isolation and in combination. In R. Tagiuri and L. Petrullo (Eds.), Person perception and interpersonal behavior. Stanford: Stanford University Press, 1958. DONALDSON,M. Positive and negative information in matching problems. British Journal of Psychology, 1959, 50, 235"-262. EIFERMANN, R. R. Negation: A linguistic variable. Acta Psychologica, 1961, 18, 258-273. HOVLAND,C. I., & WEISS,W. Transmission of information concerning concepts through positive and negative instances. Journal of Experimental Psychology, 1953, 45, 175-182. WARR,P. B., & KNAPPER,C. The perception of people and events. New York: Wiley, 1968. WASON,P. C. The processing of positive and negative information. Quarterly Journal of Experimental Psychology, 1959, 11, 92-107. WASON, P. C. Response to affirmative and negative binary statements. British Journal of Psychology, 1961, 52, 133-142. (Received May 5, 1969)
(1969)
A f f i r m a t i o n and Denial in the Structure of Inference Rules I PETER B. WARR AND THOMAS L. COFFMAN
Medical Research Council, Social and Applied Psychology Unit, University of Sheffield, England Judged associations between personal characteristics are examined in a study designed to test three models of inference. These models are based upon the notions of material implication, material equivalence, and symmetry. Not one of the models receives support from the data. In their stead an interpretation of inference rule structures is suggested which predicts that inferences of similar magnitude will be made in conditions of dual affirmation or of dual denial. When two inferences about the same characteristics both affirm or both deny their consequent, then those inferences are on average of equal magnitude. This interpretation is supported by the results of the study described, and is seen to have relevance to studies of judgments about personality and to work on positive and negative information.
This paper examines models o f j u d g m e n t drawn f r o m the propositional calculi of formal logic. The judgments to be studied are inferences a m o n g a variety of adjectives comm o n l y used to describe people. A l t h o u g h it has been demonstrated that judges make quite similar and consistent inferences from one such adjective to another (Bruner & Tagiuri, 1954; W a r r & Knapper, 1968), little is k n o w n about the general pattern or structure by which these inferences might be related. One possibility is that inferences about the characteristics o f stimulus persons follow certain rules o f formal logic, as discussed by W a r r and K n a p p e r (1968, Ch. 3). The framework of the propositional calculus is an attractive one because it suggests useful hypotheses and because it could plausibly account for the general structure o f inferential judgment, one which applies regardless o f the population o f descriptive terms or stimulus objects concerned. There are two fundamental types o f logical relationship which m a y be relevant to the structure o f inferences. First, it might be the
case that decision rules are expressions of material equivalence. This relationship has four defining conditions as follows: (1) (2) (3) (4)
p q -p -q
-~ q --~ p -+ - q ~ -p
(p implies q) (q implies p) (not-p implies not-q) (not-q implies not-p)
where p and q are particular terms, and where - p and - q are the negations o f those terms. As an example o f material equivalence, consider the terms honest and truthful. It might be the case that honest -+ truthful, truthful --~ honest, not-honest---~not-truthful, and nottruthful ~ not-honest. In these conditions it would be said that the two adjectives were materially equivalent. But material equivalence is unlikely to be a widely observed relationship, since its four conditions probably are met only in the case of synonyms or near-synonyms. A relationship o f greater interest is that o f material implication. The defining case for this relationship is the one in which p --~q and - q ~ - p are true, but q ---~p and - p --~ - q are not true. Material implication is exemplified in those 1 The authors are grateful to Stuart Smith for his trait-pairs of which one trait (p) is a subdivision assistance during the preparation of this paper, and of the other (q). For instance, where p stands to the Social Science Research Council (London) for financial support. for musical (or poetic, or artistic) and q for 705
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WARR AND COFFMAN
talented, a relationship of material implication possible relationship which may be introduced. probably obtains, permitting such inferences This is the simpler notion of symmetry. A p :q as musical -+ talented and not-talented ~ not- relationship is symmetrical if the inferences musical, but disallowing the inferences talented p ~ q and q - - ~ p are equivalent in direction and magnitude, regardless of the values of the musical and not-musical -+ not-talented. Note that in comparison with material impli- related propositions, p ~ - q, q ~ - p , etc. A cation, material equivalence is actually a two- relationship of this kind is not permitted in the propositional calculus, since its definition way implicative relationship. Of course', these relationships--material runs counter to that of material implication equivalence and material implication--might and the single defining condition is only one hold only for terms which are synonymous or aspect of the broader notion of material subordinate-superordinate pairs. Many deci- equivalence. sion rules link characteristics which apparently METHOD are quite different (impulsive and irritable, The procedure adopted in the present study was to precise and sincere, for example; see Warr & have subjects make judgments about the strength of Knapper, 1968, p. 138), and one might ask implicative relationships between personal characwhether a model from formal logic will be teristics. Eight trait-names and their negated counterrelevant to the structure of decision rules in parts were used. These were divided into two compargeneral. To put this question empirically, we able sets, referred to here as Set A and Set B. Half shall test predictions from the proposed models of the items in each set were chosen on the basis of pretests to he desirable characteristics, and half were against inferences among a sample of widely known to be judged as undesirable. Desirability is differing terms. indicated below as " + " and undesirability as " - "" However, relationships among dissimilar terms are seldom of an all-or-none kind. In SET A Unmodified terms order to translate the propositional calculus aggressive (-) to the general case, its two-valued logic (which honest (+) requires that the proposition p -~ q be either prejudiced (-) "true" or "false") must be modified accordreliable (+) ingly. In the present investigation it was Negatively modified terms decided to obtain estimates of the magnitude unaggressive (+) of associations (that is, the degree to which p dishonest (-) unprejudiced (+) is seen to imply q) and to examine the pattern unreliable (-) of these probabilistic estimates. Thus the truefalse dichotomy is replaced here by a con- SET B tinuum running through varying degrees of Unmodified terms positive and negative inference values. Note conceited (-) that with this translation a negative association friendly (+) intelligent (+) or inference is just as "true" as is a positive selfish (-) association or inference; a proposition is "false" only if the p --~ q value is zero. Never- Negatively modified terms unconceited (+) theless, as will be seen below, it is important unfriendly (-) to preserve the distinction between those unintelligent (-) cases in which p implies q positively (here unselfish (+) written p -~ q) and those in which p implies q negatively (written p ~ q). Each of the sixteen terms served as a "cue trait" (the In addition to material equivalence and given trait from which inferences were to be drawn), material implication, there is a third type of and aNo as a "response trait" (inferred from the cue
INFERENCE RULE STRUCTURE trait) relative to each of the eight adjectives in the set to which it did not belong. Thus, when an A trait was given as a cue trait, B traits appeared in the response list; and when a B trait was given as a cue trait, A traits appeared in the response list. Altogether then, there were 128 judgments about inferences between Sets A and B. This design yielded data on all the possible inference types but reduced the burden on the Ss by eliminating half of the permutations. Instead, to introduce greater variety into the Ss' task, eight additional terms were included among the response items. These filler items may be referred to as Set F; they accounted for a further 128 judgments per S: SET F Unmodified terms ambitious cautious dignified excitable Negatively modified terms unambitious incautious undignified unexcitable
The perceived implications between these terms were ~measured by a version of the procedure first used by Brunet, Shapiro, and Tagiuri (1958). Subjects were asked how likely it is that persons described as, say, aggressive are conceited, friendly, honest, and so on. Responses were made by placing check-marks on a six-point scale from "nearly always are" (+ 3) to "hardly ever are" ( - 3) with no neutral position. Data were collected in eight-page booklets, each page of which introduced a single cue trait and involved inferences to eight response traits. Four separate booklets were used, these beir~gcompleted in counterbalanced orders at half-hour intervals during an experimental session involving several tasks. Booklets were made up so that the eight response traits on each page were either all unmodifig~d or all modified, and within each booklet the eight cue traits were themselves either all unmodified or all modified. Response traits were always presented alphabetically on a page. Subjects were 64 undergraduates from several departments of Sheffield University. Thirty-five men and twenty-nine women took part. RESULTS The m e a n value o f each o f the 256 implications was first c a l c u l a t e d s e p a r a t e l y for males a n d for females. Significant sex differences
707
were present in the case o f only nine implicative relationships, a frequency in keeping with o t h e r studies o f this k i n d ( W a r r & K n a p p e r , 1968, Ch. 3), a n d the d a t a for males a n d females were therefore c o m b i n e d . The 128 m e a n values involving the filler traits were then discarded, a n d the r e m a i n i n g m a t e r i a l served for testing the m o d e l s described above. These 128 cases to be a n a l y z e d m a y be split into eight categories a c c o r d i n g to the direction o f the A : B inferences a n d to w h e t h e r each t e r m is modified, as follows: A to B, - A to - B , A to - B , - A to B, B to A, - B to - A , B to - A , - B to A. As was i n d i c a t e d h a l f o f the terms in each set (A or B) were j u d g e d to be desirable a n d h a l f to be undesirable. Since desirable terms are in general j u d g e d to positively i m p l y other desirable terms (and similarly for undesirable terms), h a l f o f the inferences in each o f the eight categories were here f o u n d to be positive a n d h a l f to be negative. As an illustration, consider the 16 A - t o - B inferences. E a c h o f the two desirable A terms was f o u n d to positively i m p l y the two desirable B terms, a n d each o f the two undesirable A terms was f o u n d to positively i m p l y the two undesirable B terms. Hence there were eight cases where A ~ B. Since the two desirable A terms were f o u n d to negatively i m p l y the undesirable B terms, a n d the two undesirable A terms to negatively i m p l y the desirable B terms, t h e r e w e r e also eight cases where A ~ B. A similar p a t t e r n o f results for each o f the eight classes o f relationship n o t e d in the previous p a r a g r a p h g e n e r a t e d sixteen categories o f eight cases each: 2 A - - ~ B, A~B; -A~-B, -A~-B; A~-B, 2 The letters "A" and "B" will be used here (rather than "p" and "q") in order to identify the two sets of trait-names studied. Note that for some comparisons to be made, the distinction is a crucial one, for example, A ~ B versus B ~-A, whereas for other comparisons the two sets of values are formally equivalent and may be regarded as replications. For instance, the comparison of A + B versus - B ~- - A is formally the same as the comparison of B + A versus - A ~ -B, but with different terms appearing as cue traits and as response traits.
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WARR. AND COFFMAN
A ~> - B ; - A ~ B , - A ~> B;B -:~ A,B _z> A; - B ~> - A , - B ~> - A ; B ~> - A , B ---> - A ; - B -~ A, - B ~ A. The structure of inferences was examined by comparing the values in each pair of categories noted above. This was initially achieved by plotting the material graphically as in Figure 1. In this figure are presented two of twenty-eight such scatter-plots which were examined. The left-hand diagram shows the relationships between all the instances of A to B
But the right-hand diagram in Figure 1 ,presents a different picture. In these cases the A:B inferences are compared with the inferences arising when A and B are simultaneously negated and transposed, that is, the comparison is between A --->B and - B ---> - A . On the average, the - B ~> - A inferences are smaller than the A -~ B inferences, whereas the - B ~ - A inferences are greater than the A - ~ B inferences, leading to marked departure of the points from the diagonal axis in Figure 1.
B-5,A
-B+-~
-A
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versus
B ---)" - A
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to A
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to
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versus
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to
-A
FIG. 1. Comparisons between pairs of inference classes.
versus B to A inferences. The positive inferences are exemplified by that between prejudiced (an A term) and conceited (a B term); the mean prejudiced --->conceited value is +2.41, and the conceited-->prejudiced mean is +2.37. A sample pair of negative inferences is honest --->selfish (whose value is -1.97) and selfish --->honest (-1.55). In general it is clear from the left-hand diagram that transposing p:q relationship (from A--> B to B - + A) produces an inference of similar magnitude as the original, and that this is true for both positive and negative inferences. 3
The statistical significance of these systematic deviations (and of those observed in other comparisons) may be established by a Wilcoxon T test applied to the relevant pairs of inference values. This procedure has been adopted for each of the possible comparisons 3 There are, of course, clear departures from this general rule. For instance, the mean value of the aggressive:friendly inference is -1.08, but the value of friendly --->aggressive is -2.41. However, at this point we are concerned to identify the central tendencies of inference relationships rather than their individual differences.
709
INFERENCE RULE STRUCTURE
TABLE 1 EIGHT TESTS OF THE MATERIAL IMPLICATION MODEL SHOWING MEAN INFERENCE V A L U E S a AND WILCOXON T TESTS. (THE NULL HYPOTHESIS IS AN ASSERTION OF MATERIALIMPLICATION BETWEEN m :B INFERENCES.)
Inference pairs
T
p<
Affirmation or denial of the consequent Inference 1 Inference 2
A ~ B (2.00) vs. - B ~ - A (1.22) A ~ B (1.23) vs. - B --~ - A (1.88)
3 0
.05 .01
affirmation denial
denial affirmation
- A ~- - B (1.13) vs. B -+~A (1.91) - A ~ - B (1.72) vs. B ~ A (1.24)
0 3
.01 .05
denial affirmation
affirmation denial
A ~ - B (1.34) vs. B ~ - A (1.38) A ~ - B (1.84) vs. B ~ - A (1.76)
16 5.5
n.s. n.s.
denial affirmation
denial affirmation
- A ~ B (2.01) vs. - B -*~ A (2.22) - A ~ B (1.08) vs. - B ~ A (1.16)
10 7b
n.s. n.s.
affirmation denial
affirmation denial
" Shown in parentheses are mean absolute values each based on N = 8. Directions of inferences are indicated by the plus and minus signs over the arrows. b T is in this case based on 7 difference scores, since one pair showed no difference. o f inference types. C e r t a i n o f these c o m p a r i s o n s p r o v i d e direct tests o f the m o d e l s o u t l i n e d above. These m a y be discussed first; t h e n we can t u r n to the r e m a i n i n g c o m p a r i s o n s to a t t e m p t a general interpretation.
Material Implication It m a y be inferred f r o m the brief account o f m a t e r i a l i m p l i c a t i o n presented earlier that c e r t a i n relationships between pairs o f inference ought to be observed if this m o d e l is to a c c o u n t for the data. It should, for example, be the case t h a t the A - ~ B i m p l i c a t i o n s are o f the same m a g n i t u d e as the - B ~ - A ones. W e have seen f r o m the r i g h t - h a n d d i a g r a m in F i g u r e 1 t h a t this is n o t in fact so. W h a t a b o u t the other relevant relationships ? These a r e set o u t in Table 1, together with i n f o r m a tion a b o u t their b e a r i n g u p o n the m a t e r i a l i m p l i c a t i o n possibility. T h e second c o l u m n o f Table 1 lists the W i l c o x o n T values for the pairs o f inferences e x a m i n e d , a n d the p r o b a b i l i t i e s are given in the third column. 4 I n the first two c o m parisons, as we have seen in F i g u r e 1, the two 4 All the probabilities given in this p a p e r are for two-tailed tests.
sets o f values are significantly different so that the m o d e l o f m a t e r i a l implication, which requires no difference between them, must be rejected. N o t e that a significant difference means that the inferences in one set are consistently greater or smaller t h a n their t r a n s f o r m s in the other set. In the final c o l u m n are considerations to be discussed later. F o r the present it m a y be n o t e d t h a t m a t e r i a l i m p l i c a t i o n can be accepted as an a p p r o p r i a t e m o d e l in only four o f the eight c o m p a r i s o n s m a d e here.
Symmetry T u r n n o w to the crucial cases of the symm e t r y model. W h a t h a p p e n s to the p a t t e r n o f decision rules when A : B, - A : - B , A : - B , a n d - A : B inferences are t r a n s p o s e d ? The o b s e r v e d o u t c o m e s are s u m m a r i z e d in Table 2. It c a n be seen once again t h a t the m o d e l is a p p l i c a b l e only in certain cases. In four instances there is a systematic d e p a r t u r e f r o m the s y m m e t r y hypothesis, a n d three o f these are significant at the .05 level or greater.
Material Equivalence A s we n o t e d earlier, m a t e r i a l equivalence requires b o t h m a t e r i a l i m p l i c a t i o n a n d sym-
710
WAR~RAND COFFMAN TABLE 2
EIGHT TESTS OF TIlE SYMMETRYMODEL SHOWING MEANINFERENCEVALUESa AND WlLCOXON T TESTS. (THE NULL HYPOTHESIS IS AN ASSERTION OF SYMMETRY BETWEEN A :B INFERENCES.) Affirmation or denial of the consequent Inference pairs A -~ B (2.00) vs. B ~- A A ~ B (1.23) vs. B ~ A
(1.91) (1.24)
- A -~ - B (1.13) vs. - B ~ - A (1.22) - A ~ - B (1.72) vs. - B ~ - A (1.88) A -~ - B (1.34) vs. - B ~ A A _z~ - B (1.84) vs. - B ~ A
T
p <
Inference 1
Inference 2
13 14
n.s. n.s.
affirmation denial
affirmation denial
15 8~
n.s. n.s.
denial affirmation
denial affirmation
0 5
.01 n.s.
denial affirmation
affirmation denial
2b 4
.05 .05
affirmation denial
denial affirmation
(2.22) (1.16)
- A -~ B (2.01) vs. B ~- - A (1.38) - A -~ B (1.08) vs. B -~ - A (1.76)
Shown in parentheses are mean absolute values, each based on N = 8. b Tis here based on 7 difference scores, since one pair showed no difference. metry. Sixteen tests o f the equivalence m o d e l have
therefore
Tables
already
been
presented
in
1 a n d 2. T h e r e are, h o w e v e r , e i g h t
a d d i t i o n a l cases to be considered. These cases
departures from the predicted equivalence-all but one at the .05 level of confidence or greater. So the material equivalence prediction is also rejected.
involve negation without transposition and hence are n o t relevant to material implication
Affirmation and Denial
o r s y m m e t r y . T h e y are p r e s e n t e d i n T a b l e 3.
None of the three models under discussion satisfactorily accounts for the structure of
All of these c o m p a r i s o n s reveal systematic
TABLE 3 EIGHT ADDITIONAL TESTS OF THE MATERIAL EQUIVALANCE MODEL SHOWING MEAN INFERENCE VALUES a AND W1LCOXON Z TESTS. (THE NULL HYPOTHESIS ASSERTS THAT A I B INFERENCES CAN BE NEGATED WITHOUT TRANSPOSITION~ AS IN MATERIAL EQUIVALENCE RELATIONSHIPS.)
Affirmation or denial of the consequent Inference pairs A -~ B A ~ B
T
p <
Inference 1
Inference 2
0 3
.01 .05
affirmation denial
denial affirmation
(2.01) (1.08)
0 1
.01 .02
denial affirmation
affirmation denial
(1.91) vs. - B ~ - A (1.22) (1.24) vs. - B ~ - A (1.88)
1 2
.02 .02
affirmation denial
denial affu-mation
0 3b
.01 n.s.
denial affirmation
affirmation denial
(2.00) vs. - A ~ - B (1.13) (1.23) vs. - A ~ - B (1.72)
A ~- - B (1.34) vs. ~ A ~ B A ~ - B (1.84) vs. - A ~ B B ~, A B~ A
B -~ - A (1138) vs. - B ~ A B -~ - A (1.76) vs. - B ~ A
(2.22) (1.16)
a Shown in parentheses are mean absolute values, each based on N = 8. b T is here based on 7 difference scores, since one pair showed no difference.
INFERENCE RULE STRUCTURE
decision rules which is observed in this study. Each model is applicable in a limited range of cases, but no model is manifestly superior to any of the others. This suggests that a quite different concept is required, one which cuts across the central notions of all the models. An interesting, possibility is found in the difference between what may be referred to as the affirmation and the denial of a statement's consequent. It is clear that in the proposition p ~ q the consequent (q) is being affirmed as an associate of the antecedent p (which is given), whereas in the proposition p ~ q the consequent (q) is being denied as an associate of p. But how should propositions such as p -+ - q be interpreted? Suppose we consider p ~ - q as an affirmation of q, and p -~ - q as a denial of q, and so on. Then we find by the comparison shown in Table 4 that the inferences which affirm q are consistently greater in magnitude than the parallel inferences which deny q. (Sets A and B are combined for these comparisons, since half the inferences in each set fall into each category of propositions.) And, looking back at Tables 1 to 3, it is apparent that this difference between affirmation and denial of the consequent provides a key to TABLE 4 EIGHT TESTS OF THE AFFIRMATION-DENIAL MODEL. MEAN INFERENCE VALUESa AND WILCOXON T TESTS COMPARING p:q INFERENCES WHERE q IS AFFIRMED WITH THOSE INFERENCES WHERE q IS DENIED C o n s e q u e n t affirmed
C o n s e q u e n t denied
T
p <
(1.96) (1.96)
-p~q (1.12) - p -~ - q (1.18)
12 2
.01 .01
p ~ - q (1.80) p _z~ _ q (1.80)
-p ~q (1.12) - p -~ - q (1.18)
10.5 1
.01 .01
p~-q
(1.24) p ~ - q (1.36)
3 0
.01 .01
p ~ q (1.24) p -~ - q (1.36)
9 7
.01 .01
p~q p ~ q
-p-~q - p --+~q
(2.11) (2.11)
_ p _z~ _ q (1.80) _ p _z~ _ q (1.80)
a S h o w n in p a r e n t h e s e s are m e a n absolute values, e a c h based o n N = 16.
711
understanding the applicability or nonapplicability of the three models, material equivalence, material implication, and symmetry. In each situation, the data fit the model only when the inferences compared are both affirmations or both denials. Those cases where significant differences are found are the ones in which affirmation of a consequent is compared with denial of a consequent. Two further considerations are of interest in Table 4. First, consider the parallel forms of affirmation and of denial of the consequent. In Column 1 (Consequent Affirmed) it is seen that a simple affirmation of the consequent through a positive inference ( p - ~ q or - p ~ q) produces somewhat greater values than does the parallel double negative form using the same root term for the consequent (p -~ - q or - p ~ -q). In each case the difference is found to be significant. For the first comparison, T = 2 3 , p < . 0 2 , and for the second, T = 0, p < :01. Similarly, in Column 2 (Consequent Denied) propositions containing positive inferences (now coupled with negated consequents, - p -~ - q or p ~ - q ) are slightly greater on average than the parallel propositions which deny by virtue of a negative inference value ( - p -~ q or p ~ q); however, these differences do not occur here with enough consistency for us to reject the null hypothesis. Secondly, consider the form of the antecedent in each of the propositions of Table 4. In half the propositions the antecedent is unqualified (p), and in the remaining half the antecedent is negated (-p). Obviously, when the form of an antecedent is changed, for example, dishonest (--P) instead of honest (p), the nature of the inference to each consequent is changed as well, for example from affirmation of q to denial of q. It is therefore not possible to make direct comparisons between antecedent forms using the same basic terms, as has been done in all previous tests. However, it is interesting to note that the 'smallest inference values are obtained when there is both a negative antecedent and a denial of the
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WARR AND COFFMAN
consequent ( - p -7 q and - p - ~ - q ) . On the other hand, when the consequent is affirmed, the form of the antecedent appears to have little or no effect. DISCUSSION These findings and interpretations are of importance in two fields. Firstly, they suggest certain revisions to models of intertrait inference. And secondly, they shed further light on the more general differences between positive and negative information. As far as inference rules about personal characteristics are concerned, this study has revealed that models which ignore the difference between forms of propositions, especially affirmation versus denial of the consequent, can be too simple. The logical models which generated the study are in their original form inadequate. We can now adopt a more parsimonious interpretation of inference rule structures: Rules about pairs of characteristics (negated or not) are on the whole of the same magnitude as long as only affirmation of the consequent or only denial of the consequent is involved. It should again be stressed that affirmation or denial both embrace positive ( ~ ) and negative (-~) inferences. It is not the direction of inferences per se that is important, but this direction coupled with information about whether or not the consequent is a negated term. However, many investigations of inference rules in person perception examine only unqualified trait-names, and in these cases (where no negated consequents occur) the difference between positive and negative inferences is the crucial one. If we apply the notions of affirmation and denial to other studies, it becomes clear that the res.ults of the present investigation have parallels in several quite different areas. There is evidence that subjects use positive information much more readily and efficiently than negative information in concept attainment tasks (Bruner, Goodnow & Austin, 1956; Donaldson, 1959; Hovland & Weiss, 1953). Since the present results indicate that Ss' own
affirmatory inferences are more definite than their denials, it may be that positive information in a concept attainment task is more useful because it confirms the sort of inferences which the S himself tends to make more readily or strongly. On the other hand, both of these features could derive from the fact that most of a person's everyday experience in concept attainment is largely a matter of building up positive information. In a close parallel to the present conclusions, Wason (1959, 1961) and Eifermann (1961) report that "agree" or "disagree" responses to affirmatory statements ate made more rapidly than are responses to statements of denial. Taken together these various findings suggest that inference tendencies are primarily attuned to positive information and positive instances, rather than to those of a negative form. REFERENCES BRUNER, J. S., & TAGIURI, R. The perception of people. In G. Lindzey (Ed.), Handbook of social psychology. Reading, Mass.: Addison-Wesley,
1954. BRUNER,J. S., GOOI~NOW,J. L., & AUSTIN,G. A. A study of thinking. New York: Wiley, 1956. BRUNER, J. S., SHAPIRO, D., & TAGIURI, R. The
meaning of traits in isolation and in combination. In R. Tagiuri and L. Petrullo (Eds.), Person perception and interpersonal behavior. Stanford: Stanford University Press, 1958. DONALDSON,M. Positive and negative information in matching problems. British Journal of Psychology, 1959, 50, 235"-262. EIFERMANN, R. R. Negation: A linguistic variable. Acta Psychologica, 1961, 18, 258-273. HOVLAND,C. I., & WEISS,W. Transmission of information concerning concepts through positive and negative instances. Journal of Experimental Psychology, 1953, 45, 175-182. WARR,P. B., & KNAPPER,C. The perception of people and events. New York: Wiley, 1968. WASON,P. C. The processing of positive and negative information. Quarterly Journal of Experimental Psychology, 1959, 11, 92-107. WASON, P. C. Response to affirmative and negative binary statements. British Journal of Psychology, 1961, 52, 133-142. (Received May 5, 1969)