Strategies during complex conditional inferences

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Strategies duringcomplex conditionalinferencesKristien Dieussaert , Walter Schaeken ,Walter Schroyens & Gery D'YdewallePublished online: 24 Sep 2010.

To cite this article: Kristien Dieussaert , Walter Schaeken , WalterSchroyens & Gery D'Ydewalle (2000) Strategies during complexconditional inferences, Thinking & Reasoning, 6:2, 125-160, DOI:10.1080/135467800402820

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STRATEGIES DURING COMPLEX INFERENCES 125

© 2000 Psychology Press Ltdhttp://www.tandf.co.uk/journals/pp/13546783.html

THINKING AND REASONING, 2000, 6 (2), 125–160

Strategies during complex conditional inferences

Kristien Dieussaert, Walter Schaeken,Walter Schroyens, and Géry d’Ydewalle

University of Leuven, Belgium

In certain contexts reasoners reject instances of the valid Modus Ponens andModus Tollens inference form in conditional arguments. Byrne (1989) observedthis suppression effect when a conditional premise is accompanied by a con-ditional containing an additional requirement. In an earlier study, Rumain,Connell, and Braine (1983) observed suppression of the invalid inferences “thedenial of the antecedent” and “the affirmation of the consequent” when a con-ditional premise is accompanied by a conditional containing an alternativerequirement. Here we present three experiments showing that the results of Byrne(1989) and Rumain et al. (1983) are influenced by the answer procedure. Whenreasoners have to evaluate answer alternatives that only deal with the inferencesthat can be made with respect to the first conditional, then suppression is observed(Experiment 1). However, when reasoners are also given answer alternatives aboutthe second conditional (Experiment 2) no suppression is observed.

Moreover, contrary to the hypothesis of Byrne (1989), at least some of thereasoners do not combine the information of the two conditionals and donot give a conclusion based on the combined premise. Instead, we hypothesise thatsome of the reasoners have reasoned in two stages. In the first stage, they form aputative conclusion on the basis of the first conditional and the categoricalpremise, and in the second stage, they amend the putative conclusion in the lightof the information in the second premise. This hypothesis was confirmed inExperiment 3. Finally, the results are discussed with respect to the mental modeltheory and reasoning research in general.

People can easily make some inferences. The following inference, known asModus Ponens, is an example of such an easy inference:

Correspondence should be addressed to Kristien Dieussaert, Laboratory of ExperimentalPsychology, Department of Psychology, University of Leuven, Tiensestraat 102, B/3000 Leuven,Belgium. Email: [email protected]

This research was carried out with support from the IUAP/PAI P4 (Kristien Dieussaert andGéry d’Ydewalle) and from the Fund for Scientific Research Flanders (Walter Schaeken andWalter Schroyens). We wish to thank the referees, Rosemary Stevenson and Aidan Feeney, fortheir helpful comments.

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126 DIEUSSAERT ET AL.

If she has an essay to write, then she will study late in the library.She has an essay to write.Therefore, she will study late in the library.

Many psychological theories of reasoning postulate that people are equippedwith formal rules of inference akin to those of a logical calculus (see e.g., Braine,1978; Braine, Reiser, & Rumain, 1984; Johnson-Laird, 1975; Oshershon, 1975;Rips, 1983, 1994). The rule theories are syntactic theories: They claim thatdeductive reasoning consists of the application of inference rules to the form ofthe premises and conclusion of an argument.

Consider again the problem just given. According to rule theories, our mindcontains a rule for Modus Ponens:

If p then q, p/q

This rule or reasoning schema matches the form of the problem. Therefore, theinference can be made promptly:

She will study late in the library.

Consider, however, the following problem:

If she has an essay to write, then she will study late in the library.She will not study late in the library.

The correct solution to this Modus Tollens problem is:

She has not an essay to write.

According to rule theories, there is no rule in our mind that corresponds to theModus Tollens problem. Therefore, it is only indirectly that we can come up withthe correct solution. The latter problem requires more reasoning steps. This claimis used by the rule theories to explain the data of many studies which show thatModus Ponens inferences are easier than Modus Tollens inferences.

Consider the following problem:

If she has an essay to write, then she will study late in the library.She does not have an essay to write.

Many participants conclude based on these premises:

She will not study late in the library.

This conclusion, which is called the fallacy of denying the antecedent, is wrong.If the conditional is interpreted as a true conditional, then it is possible that there

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are other alternatives that imply the consequent “she will study late in thelibrary”. Of course, if the conditional is interpreted as a biconditional (if and onlyif), then the conclusion “she will not study late in the library” is correct.

A rule theorist could propose that reasoners are also equipped with invalidinference rules (see e.g., Von Domarus, 1944). However, most of them explainreasoning errors as comprehension errors (see e.g., Braine & Rumain, 1983;Marcus & Rips, 1979; Markovits, 1985; Rumain et al., 1983). The major premiseof the denial of the antecedent problem just described would invite its obverse(but for an alternative invited inference, see Evans, Clibbens, & Rood, 1996;Rips, 1994):

If she does not have an essay to write, then she will not study late in the library.

Reasoners can come up with the conclusion “she will not study late in the library”if they apply the Modus Ponens rule to the obverse of the conditional and thecategorical premise. Rumain et al. (1983) tested this hypothesis by giving partici-pants a possible alternative conditional. Consider the problem again, but nowaccompanied with a so-called alternative conditional:

If she has an essay to write, then she will study late in the library.If she has some textbooks to read, then she will study late in the library.She does not have an essay to write.

If reasoners are given such problems, they will not conclude:


The fact that the fallacy of denying the antecedent (and the similar fallacy ofaffirming the consequent) can be suppressed is taken as evidence that we do notpossess invalid inference rules, but that reasoners make denial of the antecedentconclusions because they translate the original premises.

According to Byrne (1989), this argument has an interesting consequence: Ifvalid inferences could be suppressed, then neither would reasoners possess validinference rules. This would imply that people do not possess mental rules at all,which challenges the mental rule account. In the first experiment, she presentedsome participants with the major premise, accompanied by a so-called additionalconditional . For example:

If she has an essay to write, then she will study late in the library.If the library remains open, then she will study late in the library.She has an essay to write.

For such a problem, reasoners do not come up with the Modus Ponensconclusion:

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She will study late in the library.

In other words, Byrne showed that Modus Ponens can be suppressed. Similarly,Modus Tollens can be suppressed. She concluded that this suppression effectchallenges the assumption of rule theories that formal rules of inference such asModus Ponens are part of our mental logic.

Byrne (1991) argues that an alternative theory, that is, the mental modeltheory (e.g., Johnson-Laird, 1983) can explain the suppression of the validinferences. According to the model theory, reasoning consists of three mainstages. First, the premises are understood: A mental model of the situation theydescribe is constructed on the basis of their meaning and of any relevant generalknowledge triggered during the process of interpretation. Second, reasonersformulate a conclusion based on the model. People will only draw conclusionsthat convey some information that was not explicitly asserted by the premises.Third, a search is made for alternative models of the premises in which theputative conclusion is false. If there is no such model, then the conclusion isvalid; that is, it must be true given that the premises are true. If there is such amodel, then it is necessary to return to the second stage to determine whetherthere is any conclusion that holds over all the models so far constructed. Thetheory’s essential processing assumption is that the more models have to beconstructed, the harder the inferential task will be. This is consistent with studiesof syllogistic reasoning (Johnson-Laird & Bara, 1984), spatial and temporalreasoning (Byrne & Johnson-Laird, 1989; Schaeken, Johnson-Laird, &d’Ydewalle, 1996a,b; Vandierendonck & De Vooght, 1996), propositionalreasoning (Johnson-Laird, Byrne, & Schaeken, 1992, 1994), and reasoning withmultiple quantifiers (Johnson-Laird, Byrne, & Tabossi, 1991).

Byrne (1991) argues that the model theory can explain the suppression.According to her, reasoners will integrate the two premises, dependent on themeaning of that premise and the general knowledge. If the antecedent of thesecond premise is understood as an additional requirement, then it will beconjoined with the antecedent of the first premise (Byrne, 1991):

p q r…

Consequently, reasoners will suppress Modus Ponens conclusions: Affirmationof the first antecedent by itself is not sufficient for drawing the Modus Ponensconclusion. If the antecedent of the second premise is understood as analternative requirement, then the premises will be interpreted such that they areindividually sufficient:

p rq r

…

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As a result, reasoners will suppress the denial of the antecedent in problems withan alternative antecedent: Denial of the first antecedent only is not sufficient fordeciding that “not-r” is the case, because the model indicates that “r” can stillhold given “q”.

Experiment 1 and Experiment 2 focus on the suppression effect as describedby Byrne (1989). Experiment 1 is a replication of Byrne’s Experiment 1 (1989).In Experiment 2, we manipulate the kind of evaluation the participants had tomake. Instead of the traditional three answer alternatives, we presented a set ofmore than ten answer alternatives to the participants. The results of Experiment 2force us to change our view on the nature of suppression and especially on thenature of the underlying reasoning processes: They suggest that reasoners areusing one of (at least) two processing strategies when they are solving these kindsof problems. Therefore, we will focus on the underlying reasoning processes ofsuppression in Experiment 3. In this experiment, we changed the originalevaluation task into a production task. The experiment consists of three parts.While the presentation in the first part does not differ from the one in Experiment1 and 2, the two other parts each encourage the use of a specific strategy.

EXPERIMENT 1

In the first experiment of Byrne (1989) there were three groups of eightparticipants. Each group had to solve 12 problems. The first group (the controlgroup) had to solve three problems with a different content for each of the fourconditional syllogisms, that is, Modus Ponens, Modus Tollens, denial of theantecedent, and affirmation of the consequent. These problems will be called thesimple problems. The participants had to evaluate three alternatives: One of themwas the correct answer, the other was the negation of the correct answer, and thelast answer indicated that you could not know for sure what followed.

The second group received problems with two major conditionals. The secondconditional contained an alternative antecedent, for example:

If she has an essay to finish, then she will study late in the library.If she has some textbooks to read, then she will study late in the library.

Each of these alternative antecedents is a sufficient condition for the consequent.The third group also received two major premises, but now the second con-

ditional contained an additional antecedent, for example:

If she has an essay to write, then she will study late in the library.If the library stays open, then she will study late in the library.

We decided to repeat Experiment 1 of Byrne (1989) to see if the samematerials would elicit the same pattern of answers in a different language(Dutch). Furthermore, we used about three times as many participants in order to

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increase the statistical power. Finally, there was an unexpected but unmentionedaspect of Byrne’s data, which is difficult to explain by either the model theory orthe rule theory: In the condition with simple problems, participants did not givemore Modus Ponens answers than Modus Tollens answers; they even gave moreModus Tollens answers than affirmation of the consequent answers.

Method

Design. There were three groups of participants. The control group receivedsimple conditional arguments, whereas a second group received conditionalarguments accompanied by a conditional containing an alternative antecedentand the third group received arguments accompanied by a conditional containingan additional antecedent. All participants received four sorts of conditionalproblems: Modus Ponens, Modus Tollens, denial of the antecedent, and affir-mation of the consequent. Each sort of problem was presented with three dif-ferent contents. Hence, each participant solved 12 problems, presented in arandomised order.

Materials. We used almost the same lexical materials as Byrne (1989). Theproblems were tested in two separate pilot studies (with 32 and 16 participants,respectively). The translation was rather literal (see Appendix A), except for thesentence “If she meets her friend, then she goes to a play”, which was changed to“If she meets her friend, then she goes to a pub”. All participants could reasoneasily with the sentences. When asked to indicate if the problems soundednatural, all participants responded that the sentences were natural, with anaverage rating of 3.8 on a rating ranging from one (very unnatural) to five (verynatural).

Procedure. The experiment was completed in a single session. Theinstructions were written on the first page of a booklet given to each participant.The participants’ task was to answer a series of questions based on theinformation in the preceding assertions, and they were asked to choose theconclusion they thought followed from the sentences. In the instructions, asimple problem and the accompanying answer alternatives were given as anexample. No answer was given. Each problem, together with its three answeralternatives, was printed on a separate page in the booklet. The experiment hadno time limit. Participants were asked not to go back to a problem once they hadanswered it.

Participants. A total of 70 students from the last year of a secondary schoolparticipated in the experiment. The participants were randomly assigned to one ofthe three groups: 23 participants received the simple problems with a singleconditional, 25 participants received the problems with the second conditional

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containing an alternative antecedent (referred to as alternative problem), and 22participants were faced with problems in which the second conditional had anadditional antecedent (referred to as additional problem). Two participants didnot solve all the problems and were excluded from the analysis of the problemsthey did not solve.

Results and discussion

All statistics in this and following experiments are done with the Mann-Whitney-U test for a between-subjects design and with the Wilcoxon signed ranks test fora within-subject design. As each participant solved three problems of eachinference type, we could score the conditional answer on a specific inference typeof each participant on a scale from 0 to 3. Comparisons between and withinparticipants were done by ranking the scores as described in Siegel and Castellan(1988). Table 1 presents the percentages of conditional inferences made from thethree types of problems. The pattern of the data parallels the one reported byByrne (1989). First, an additional antecedent affected the Modus Ponens andModus Tollens arguments, but not the denial of the antecedent and affirmation ofthe consequent arguments. The participants confronted with an additionalantecedent made fewer Modus Ponens inferences than either the participantsconfronted with an alternative antecedent or the participants who received thesimple problems (respectively: 60.6% vs. 93.3%; U = 121.5, p < .0005; and60.6% vs. 88.3%, U = 142, p < .01). An additional antecedent also loweredperformance on the Modus Tollens problems as compared to the single ante-cedent condition (43.9% vs. 69.6%; U = 159, p < .05). Modus Tollens inferencewas made less often on problems with an additional antecedent than on thosewith an alternative antecedent (43.9% vs. 69.3%; U = 173.5, p < .05).

Second, an alternative antecedent affected the fallacies, but not the validModus Ponens and Modus Tollens arguments. On problems with an alternative

TABLE 1The percentages of conditional inferences made as a

function of the type of contextual informationgiven in Experiment 1

Inference typep not-r not-p r

If p then r. 88.3 69.6 49.3 55.1

If p then r. 93.3 69.3 22.0 16.0If qalt, then r.

If p then r. 60.6 43.9 49.2 53.0If qadd, then r.

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antecedent, fewer denial of the antecedent inferences were made, as compared tothe simple problems (22.0% vs. 49.3%; U = 162.5, p < .01). Analogously, thedenial of the antecedent problems with an alternative antecedent yielded fewerconditional responses than the problems with an additional antecedent (22.0% vs.49.2%; U = 121.5, p < .005). Likewise, in the case of an alternative antecedent,fewer affirmation of the consequent inferences were made, as compared to theperformance on the simple problems (16.0% vs. 55.1%; U = 129, p < .0005). Thesame suppression effect is again observed when comparing the affirmation of theconsequent problems with an alternative antecedent to those with an additionalantecedent (16.0% vs. 53.0%; U = 96, p < .0001). Finally, contrary to the un-expected effect observed by Byrne (1989), participants made more simple ModusPonens arguments than simple Modus Tollens arguments (88.3% vs. 69.6%;T = 50.5, n = 10, p < .0005).

In sum, the results are similar to the results of Byrne (1989), except that theproblematical aspect of her data was absent in our experiment: We did observethat simple Modus Ponens inferences were made more often than simple ModusTollens inferences. Therefore, it appears that not only can invalid inferences besuppressed (by means of an alternative antecedent), but also valid inferences (bymeans of an additional antecedent).

EXPERIMENT 2

The results of Experiment 1 can be explained by the mechanisms proposed byByrne (1991). Dependent on the specific content, reasoners combine the twoconditionals into a conjunction or a disjunction and use mental models tocome up with a conclusion. There is, however, an important problem withExperiment 1. The answer alternatives presented in the conditions with analternative or additional antecedent preclude the subjects giving a conclusiveanswer: For example, they are presented with:

If it is raining, then she will get wet.If it is snowing, then she will get wet.She will get wet.What follows?

(a) It is raining.(b) It isn’t raining.(c) It may or may not be raining.

First, it is clear from the data of Experiment 1 that the presence and the precisesemantic content of the second conditional influences the answers. If reasonerscombine the two premises here into a disjunction, as Byrne (1989) supposes, andreasoners want to give a true conditional (hence, not correct) answer that is basedon all the information in the premises, then reasoners would answer:

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It is raining or it is snowing.

However, reasoners cannot express anything about the relevance of thissecond conditional: They can only select a conclusion that conveys informationbased on the first conditional. In this case, answer alternative (c) might bechosen, but they might also opt to choose answer alternative (a). That is, if wewant to have a better picture about the inferences that are made about bothconditionals, then we must give the participants the opportunity to express whatthey actually want to answer. Therefore, instead of presenting 3 answeralternatives, we now gave the participants an almost exhaustive set of 15 answeralternatives.

In Experiment 2, we only used the problems with either an additional or analternative antecedent. Comparing these problems with the simple problems isalways a bit tricky: The simple problems contain just one conditional, whereasthe more complex problems contain a second conditional. This means that a faircomparison is not possible. However, if one compares the two complex con-ditions, one can make fair comparisons—as illustrated by the analyses conductedon the data of Experiment 1. That is, the suppression hypothesis can be specifiedas follows. First, participants will make fewer Modus Ponens and Modus Tollensinferences in the case of an additional antecedent, when compared to these typesof arguments with an alternative antecedent. Second, they will make fewer denialof the antecedent and affirmation of the consequent inferences if the problemscontain an alternative antecedent, as compared to when these problems includean additional antecedent.

Method

Design. There were two groups of participants: One group receivedalternative problems and the other group received additional problems. Allparticipants received four sorts of conditional problems: Modus Ponens, ModusTollens, denial of the antecedent, and affirmation of the consequent. Each sort ofproblem was presented with three different contents. Hence, each participantsolved 12 problems, which were presented in a randomised order.

Instead of presenting three answer alternatives, we increased that number to15 alternatives, for the reasons mentioned earlier. In the Materials section, the 15different answer alternatives for the problems are listed.

Materials and procedure. We used the same kind of lexical materials andthe same procedure as in Experiment 1 (see Appendix A). We presented 15answer alternatives differing along the content and inference type of the problem.For Modus Ponens and Denial of the Antecedent of the “pub” content, forexample, we presented following alternatives:

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� She goes to a pub for a drink.

� She doesn’t go to a pub for a drink.

� She meets her family.

� She doesn’t meet her family.

� She goes to a pub for a drink OR she meets her family.

� She doesn’t go to a pub for a drink OR she meets her family.

� She goes to a pub for a drink OR she doesn’t meet her family.

� She doesn’t go to a pub for a drink OR she doesn’t meet her family.

� She goes to a pub for a drink AND she meets her family.

� She doesn’t go to a pub for a drink AND she meets her family.

� She goes to a pub for a drink AND she doesn’t meet her family.

� She doesn’t go to a pub for a drink AND she doesn’t meet her family.

� She goes to a pub for a drink OR she doesn’t go to a pub for a drink.

� She meets her family OR she doesn’t meet her family.

� One can’t formulate a conclusion. None of the answer alternatives is the correctone.

The choice of these alternatives was inspired by the integrated mental modelproposed by Byrne (see earlier). We presented all possible combinations inconjunctive and disjunctive form as well as in positive and negative form.Furthermore, we extended the alternative set with a simple answer on the secondconditional premise, also in positive and negative form. Finally, we includedthree alternatives that express that one is undecided about the choice.

What answer choices should we predict following the results in the formerexperiment? If the conditional answers really are suppressed with the denial ofthe antecedent problems and the affirmation of the consequent problems, then theanswers will equal the answers of the former experiment: Many “no validconclusion” answers will be given for the invalid arguments in the alternativegroup. If the correct answers really are suppressed with the Modus Ponens andModus Tollens problems, then the answers will also equal the answers of theformer experiment: Many “no valid conclusion” answers will be given for thevalid arguments in the additional group, which means that many participants willopt for the last answer alternative.

Participants. We tested 70 participants. Of these, 36 participants wereassigned to the group who received the problems with an alternative antecedentand 34 participants received the problems with an additional antecedent. Theywere all first year psychology students, who were fulfilling a course requirement.None of them had yet received a formal training in logic or had participated inprevious experiments on deductive reasoning.

Results

In Table 2, we represent the answers the participants gave for each of the fourproblem types. We will discuss the data for each of the four problem typesseparately. All statistics in this experiment are done with the non-parametric

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Mann-Whitney-U test (between-subjects design). To make our discussion of thedifferent answers more transparent, we used the following notation. We will referto additional problems in the following way:

If p then r.If qadd then r.

The alternative problems will be referred to in the following way:

If p then r.If qalt then r.

TABLE 2Percentages of different types of answer chosen as a function of the type of

contextual information given in Experiment 2

Solutionsr r and q r or not-q null other

pIf p, then rIf qalt, then r 95.3 0.0 4.7 0.0 0.0If qadd, then r 56.9 11.8 17.7 6.9 6.7

Not-p not-p and not-q not-p or not-q null other

not-rIf p, then rIf qalt, then r 0.0 96.3 3.7 0.0 0.0If qadd, then r 4.9 35.3 56.9 1.9 1.0

Not-r not-r or q null other

Not-pIf p, then rIf qalt, then r 9.4 67.3 12.2 11.1If qadd, then r 37.3 22.6 28.4 11.7

p p or q p and q null other

rIf p, then r.If qalt, then r 0.0 90.7 0.9 7.4 1.0If qadd, then r 2.9 65.7 30.4 0.0 1.0

The null group contains the percentage of “one can’t tell” answers cumulated with thepercentage of “r or not r” answers for Modus Ponens and denial of the antecedent.

The “other” group only contains answers given in less than 2% of the cases, except for:r or not q (denial of the antecent, alternative condition; 4.67%)q or not q (denial of the antecent, alternative condition; 2.80%)r or not q (denial of the antecent, additional condition; 3.92%).

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Modus Ponens. In the case of an alternative antecedent, 95.3% of theparticipants made the Modus Ponens argument by giving “r” as their conclusion,whereas with the additional problems “r” was selected in only 56.9%. That is,there is a clear suppression effect (U = 225, p < .000005). More interesting,however, are the other types of answers that were given to the problems with anadditional antecedent. Given a multitude of answer alternatives, theseparticipants did not pick the “you can’t know” answer as their response (only 6.9%). In the majority of the remaining answers “r” was included, for example: “r ornot-qadd” (1 7.7%) and “r and qadd” (11.8%).

Modus Tollens. With alternative problems, none of the participants gave“not-p” or “not-qalt” as a conclusion. The participants confronted with anadditional problem did select this answer alternative (4.9%; U = 522, p < .05).This observation seems to go against the hypothesis of Byrne (1991) and iscertainly in contrast with the frequency by which this alternative was chosen inExperiment 1 (43.9%). However, the alternative problems resulted in theconclusion “not-p and not- qalt” in 96.3%, whereas this answer was selected in35.3% of the additional problems (U = 98, p < .000005). This pattern can beinterpreted as a suppression effect. However, this conclusion should be put intoperspective as well. The additional problems resulted in the conclusion “not-p ornot-qadd” in 56.9%, whereas only 3.7% of the participants confronted with analternative antecedent gave this conclusion (U = 138, p < .00001).

Denial of the antecedent. Problems with an additional antecedent yieldedconclusions of the form “not-r” in 37.3% of the cases, whereas only 9.4% of theconclusions had this form when the problems had an alternative antecedent(U = 321, p < .0005). This supports the suppression hypothesis. However, whengiven an additional antecedent, 22.6% of the conclusions were of the form “not-r or qadd”, whereas participants confronted with an alternative antecedent selectedthis conclusion more often (67.3%; U = 251, p < .00001). The answer “not-r orqadd” can also be considered as a conditional answer: Reasoners would infer that“not-r” is the case, unless “q” is the case. When combining these two sorts ofconditional answers (“not-r” and “not-r or q”), it is even so that participantsconfronted with an alternative antecedent more frequently gave a conditionalanswer than participants confronted with an additional antecedent (76.7% vs.59.9%; U = 406.5, p < .05). This unexpected pattern for Byrne (1991) andRumain et al. (1983) is also present in the percentages of the correct “you can’tknow” answers. For the problems with an additional antecedent, more correctsolutions were given than for the problems with an alternative antecedent (28.4%vs. 12.2%; U = 366.5, p < .005).

Affirmation of the consequent. In the case of an additional problem only in afew cases was the conclusion “p” or “qadd” selected (2.9%), but in the case ofan alternative problem neither one of these answer alternatives was selected

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(U = 558, p < .05). This result could be interpreted as support for the suppressionhypothesis. However, with an additional problem 65.7% of the conclusions wereof the form “p or qadd”, whereas the alternative problems yielded 90.7%conclusions of this form (U = 361, p < .0005). In contrast, with additionalproblems 30.4% of the conclusions were of the form “p and qadd”, whereas withan alternative one only 0.9% of the conclusions were of this form (U = 318.5,p < .00001). The “p and qadd” conclusion can also be interpreted as a conditionalresponse to additional problems. Reasoners infer that “p” is the case (byaffirmation of the consequent on the first conditional) but also infer “qadd” (bymaking the affirmation of the consequent argument with respect to the secondconditional).

Discussion

Given a broad set of answer alternatives, the absolute level of participantscoming up with the standard conditional responses to the four arguments is muchlower than expected. Most answers (especially in the suppressed conditions)contain more than one item. In addition and most importantly, these complexanswers seem to reflect a conditional line of reasoning, as we will argue in thefollowing.

Consider an important problem that emerges when analysing the answers thatwere given to, for instance, the denial of the antecedent problems with analternative antecedent:

If p then r.If qalt then r.Not-p.

In 67.3% of the cases, the participants gave a conclusion “not-r or qalt”. Byrne(1991) argued that reasoners would combine the first conditional and the secondconditional into a disjunctive antecedent. This would lead to the followingimplicit models:

p rqalt r…

Consequently, “r” can still hold even if “not-p” is the case. However, theconclusion “not-r or qalt” requires that at least the following models befleshed out (the fully explicit model is mentioned in Note 1 at the end of thispaper):

not-p not-qalt rnot-p not-qalt not-rnot-p qalt r

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Johnson-Laird et al. (1992) claim that considering multiple models is difficultbecause of the load it places on working memory: As soon as the capacity ofworking memory is exceeded, reasoners are unlikely to reach a conclusion thatdepends on considering multiple models. The answer “not-r or qalt” requires threeexplicit models and each of these models contains three atomic propositions,which is a very serious amount of information for working memory. Indeed, thenumber of models as well as the size of a single model, that is, the number ofentities it contains, taxes working memory. Schaeken and Johnson-Laird (2000)show that the number of events matters in temporal reasoning. As soon as asingle model contains more than six events, reasoning is more difficult. There-fore, reasoning with the complex multiple models that are a result of theintegration of the two premises is likely to be difficult. Thus, the explanation ofthese results in terms of the model theory might not be as straightforward asByrne (1989) suggested. For the other problems the same pattern is found: In thesuppressed conditions, participants gave conclusions that can only be made ifthey considered multiple models that contain many tokens. Other observationsare also problematic for Byrne’s thesis. For denial of the antecedent problems,more than twice as many participants chose “impossible to tell” in the additionalcondition than in the alternative condition. For Modus Tollens, the differencebetween the rate at which “not-p and not-q” and “not-p or not-q” conclusionswere chosen was not as great as might be expected if participants were inter-preting the additional antecedents as being conjointly necessary.

Nevertheless, the answers given in Experiment 2 still seem to reflect a con-ditional line of reasoning. Consider for instance the additional Modus Ponensproblems. Many participants conclude “r or not-q” or “r and q”. Selecting thisconclusion can be interpreted as the result of the following line of reasoning.Reasoners first infer “r”, but notice that this conclusion also depends on thecontent of the second conditional with “r” in its consequent clause. That is, itappears as if reasoners make an amendment to their putative conclusion “r” byconsidering that this conclusion would be falsified if “not-q” were the case. Thesame argument can be made concerning the answers given to the alternativedenial of the antecedent problems. The conclusion “not-r or q” is consistent withthe hypothesis that reasoners make the denial of the antecedent argument thatresults in the conclusion “not-r”, which they subsequently validate by inferringthat “not-r” would not be the case if “q” were the case. The same line ofargumentation can be used for the Modus Tollens and the affirmation of theconsequent problems. That is, it appears that, when reasoners have the op-portunity to give a conclusion about all parts of the problems, they engage inelaborate chains of conditional reasoning.

Johnson-Laird and Byrne (1991, p. 84) wrote that with an additionalantecedent “the subjects’ knowledge leads them to construct one model in whichboth antecedents occur and an implicit alternative model.” This has an importantconsequence for the affirmation of the consequent problems. One would expect

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that reasoners come up more often with a conclusion “p and qadd” than with aconclusion “p or qadd”, if they were interpreted as conjointly necessary. However,we found the opposite: 65.7% of the conclusions were of the form “p or qadd” and30.4% were of the form “p and qadd”. This pattern, however, might reflect aresponse bias. Out of caution some participants might prefer the less stringentconclusion “p or qadd” over the semantically more informative conclusion “p andqadd”.

In sum, the results agree with the findings of Byrne (1989), by showing thatnot only invalid inferences, but also valid inferences can be suppressed. How-ever, if one takes into account the more complex answers, then no suppressionremains (for denial of the antecedent, we even found the opposite result: moreconditional inferences in the case of an alternative antecedent). Moreover, thenature of the more complex answers implies that the explanation of Byrne (1989)of the suppression effect in terms of combining the premises and in terms of themodel theory is more complicated than she suggested. At least some reasonerswere not combining the information of the two premises in the way she proposed.

A new strategy: Amendment

The results can be explained if one hypothesises that some reasoners reasonedwith each premise separately. Consider the following alternative denial of theantecedent problem:

If she has an essay to write, then she will study late in the library.If she has some textbooks to read, then she will study late in the library.She does not have an essay to write.

First, reasoners combine the categorical premise with the first premise, and comeup with the conditional answer:


Next, they consider whether this conclusion holds with respect to the secondpremise. This can explain the answer “not-r or qalt” that was given by 67.3% ofthe participants:

She will not study late in the library or she has some textbooks to read.

Indeed, different answers will occur according the applied strategy. From nowon, we will name the strategy proposed by Byrne (1991) the integration strategy,and the alternative strategy that we propose the amendment strategy. We chosethe latter because after a first conclusion is drawn the second part of the con-clusion may be “amended” in a later stage. We can make theoretical predictionsof the conditional answers that should occur for the four inference types when the

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amendment strategy is applied. The working of the amendment strategy is thefollowing:

Stage 1: The first conditional premise and categorical premise are takeninto consideration. One forms a putative conclusion based on this information.Stage 2: The putative conclusion is analysed and validated in the light of theinformation in the second conditional premise. This leads to an eventualamendment of the putative conclusion. Given the premises “if p, then r”, “if q,then r”, and “not p”, one takes into consideration the first premise “p may occurtogether with r” in Stage 1. When the categorical premise is brought to attention,one may infer a conditional conclusion. In Stage 2, this putative conclusion isreconsidered in the light of the (new) information given (see Note 2 at the end ofthis paper). One could either opt to leave the putative conclusion as it was, whichwould lead to the conditional answer “not r”—37% of the participants inExperiment 2 opted for this solution. On the other hand, one may also think thatthe new information changes the putative conclusion considerably—23% of theparticipants in Experiment 2 opted for amending “or q” to the putative conclusion“not r”.

We expect different answers for the integration and amendment strategies.With the amendment strategy, one can explain a broader set of answers. Indeed,when the relation between the two premises is fixed before the reasoning processstarts, one is bound to that relation during the inference process. However, whenone first makes an inference based on one conditional premise and the categoricalpremise, and then takes into consideration the second conditional premise onlyafter one has formulated this putative conclusion, there is no bound relation thatone has to obey. For that reason, answers in which the second conditional pre-mise is considered useful (or not useful) can be explained by the use of theamendment strategy. We will describe the theoretically predicted answers foreach of the four conditional problems.

Modus Ponens. We expect an “r” answer with an alternative problem, nomatter which strategy is followed. Indeed, only the first of the conditionalpremises contains useful semantic information for the Modus Ponens problem.When a participant uses the amendment strategy, we might additionally expectthat he/she amends the putative conclusion (“r”) with “if qalt”. An answer of thiskind is unexplainable from the point of view of the integration strategy.Following the integration strategy, we would expect a disjunctive model asfollows:

p rqalt r

This means that (first line) “p may occur together with r, whatever the value ofqalt is” or (second line) “qalt may occur together with r whatever the value of p is”.

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Therefore, when “p” is affirmed, “r” can be affirmed, whatever the value of “qalt”is. On the contrary, for the amendment strategy we have concluded that when “p”is affirmed, “r” may be affirmed in Stage 1. This conditional and correct con-clusion may be amended in Stage 2 when stating that the affirmed “r” occurs withthe affirmation of “qalt”.

With an additional problem, we expect an “r and qadd” answer when thepremises are integrated. A predicted answer for the amendment strategy is “r ifalso qadd”. Eventually, one could explain this latter answer by means of theintegration strategy: Stating “r if also qadd” is equal to “r and qadd” in a weakersense. Another possible amendment answer that is not explainable by theintegration hypothesis is simply stating “r”, with which one confirms that thesecond conditional does not matter, or does not have any influence on theputatively inferred conclusion.

Modus Tollens. The predictions for the integration strategy are very clear inthis case: “Not p and not qalt” with an alternative problem and “not p or not qadd”with an additional problem. For the amendment strategy, the predictions are lessdefined. In Stage 1, the conditional answer “not p” is very likely to be inferred,but how precisely the information in the second premise will be included staysunclear for the moment; “not p and/or not q” is our prediction. Furthermore, wecan expect simple answers; reasoners might not want to change their conclusionin the light of the information in the second premise. We do not expect simpleanswers when participants follow the integration strategy.

Denial of the antecedent. With an alternative problem, the answer predictedfrom the integration strategy is something like “not r and not qalt”, or less firmlystated: “not r if not qalt”. The earlier mentioned answers might also count as anamendment answer. Another possibility according to the amendment strategy isthat people consider the second conditional premise to be of no further use oncethey have inferred the initial putative conclusion “not r”.

With an additional problem, we may expect a “not-r” answer for bothstrategies, because participants may think that only the first conditional premisecontains useful semantic information (amendment) or may think that the negationof one of the conjunctively related antecedents is a sufficient condition to negatethe conclusion (integration). Another possible answer according to the amend-ment strategy is that the putative conclusion “not r” is amended with “unlessqadd”. This kind of answer is impossible when a participant uses the integrationstrategy.

Affirmation of the consequent. Similar to Modus Tollens, we predict “p andq” as a conditional answer with an additional problem, and “p or q” with analternative problem, when reasoners use the integration strategy. Again, for theamendment strategy, the predictions are less defined. As a putative conclusion

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we can expect “p”, but how precisely the information in the second premise willbe included stays unclear for the moment: “p and/or q” is what we predict.Furthermore, we can expect simple answers, that is, reasoners might not want tochange their conclusion in the light of the information in the second premise. Wedo not expect simple answers when participants follow the integration strategy.

In conclusion, the integration strategy specifies that people integrate the twoconditionals in a single conditional with a disjunctive or conjunctive antecedent,depending on whether or not the two antecedents determine alternative oradditional conditions with respect to the mutual consequent. That is, beforepeople start making inferences, they integrate the two conditionals in a singleconditional upon which they base their inferences. The amendment strategystipulates that people will first draw an inference with respect to one of theconditionals, and the resulting putative conclusion is amended, if necessary, onthe basis of the second conditional. The results from Experiment 2 indicate thatparticipants use both strategies to infer a conclusion from a complex conditionalproblem. Therefore, rather than opposing one strategy to the other, we want tocontrast the answers resulting from them.

EXPERIMENT 3

We conducted a third experiment in order to contrast the answers resulting fromboth strategies. In the first part we presented the same problems as we did inExperiment 2, but the task was a production task. In the second part, the problemswere presented in such a way that the amendment strategy was induced, whereasin the third part, the problems were presented in an integrated manner. First, wewill discuss the general idea behind the three parts of the experiment and theirrespective methods.

A problem with Experiment 2 was that the participants could not produce theirown answers, but had to choose their answer(s) from several answer alternatives.In order to test more directly the hypothesis that some participants reasoned witheach premise separately, we repeated the experiment as a production task(Experiment 3.1), which gives participants the opportunity to formulate answersas:

She will study late in the library, unless the library is closed.

Experiment 3.2 induced a line of reasoning that is based on the amendmentstrategy. In order to achieve this, we conducted this experiment on a computer,whereby we presented the two conditionals in two stages. First, the participantssaw one conditional and one categorical premise:

If it is raining, then she will get wet.It is raining.

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They had to write down a conclusion based on these two premises. Next, wepresented the second conditional:

If it is snowing, then she will get wet.

We asked the participants if they thought they had to change their previousconclusion in the light of this new premise. If they thought so, they could writedown the new conclusion or adapt the first conclusion.

With this procedure, we predicted mainly answers that are in accordance withthe amendment strategy. Moreover, we expected more amendment answers inthis experiment than in Experiment 3.1.

Experiment 3.3 induced a line of reasoning based on an integrated conditional.Byrne (1989, 1991) proposed that the alternative antecedent be integrated as adisjunctive antecedent to the consequent. Consider for instance the followingconditional with an alternative antecedent from the previous experiment:

If she has an essay to write, then she will study late in the library.If she has some textbooks to read, then she will study late in the library.

These premises would be integrated in a conditional like:

If she has an essay to write or has some textbooks to read, then she will study latein the library.

Similarly, the integration strategy proposes that additional antecedents be in-corporated in a conjunctive antecedent. Hence, the following premises:

If she has an essay to write, then she will study late in the library.If the library remains open, then she will study late in the library.

would be integrated in a conditional like:

If she has an essay to write and the library remains open, then she will study late inthe library.

In Experiment 3.3, we presented our participants with such integratedconditionals. When they received such integrated conditionals, we predictedmainly answers that are in accordance with the integration strategy. Moreover,we expected more integration answers in this experiment than in Experiment 3.1.In Table 3, we indicate the predicted integration and amendment answers.Categories without an index are answers that could follow from bothstrategies.

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Method

Design. The design of Experiment 3.1 was the same as in Experiment 1. Theonly difference was that the participants were asked to produce their ownconclusions, instead of selecting the conclusion that resulted from the premises.Answers in the baseline condition will not be discussed further, because they didnot significantly differ from the answers in the baseline condition (simpleanswers) in Experiment 1.

In Experiments 3.2 and 3.3, the participants served as their own control withrespect to the presented conditional problems accompanied by either a con-ditional containing an alternative antecedent or a conditional containing anadditional antecedent. In both conditions, the participants received two versionsof the four sorts of conditional problems: Modus Ponens, Modus Tollens, denialof the antecedent, and affirmation of the consequent.

Materials. The materials used in Experiment 3.1 were the same as the onesused in Experiment 1 (see Appendix A). We decided to use more diverse contentsin Experiment 3.2 than in the previous experiments, in order to minimise theinfluence of previous sentences and inferences on the subsequent ones. In a pilotstudy with 18 participants, we tested seven different problem contents on thestrength of their alternative and additional premises. In one of the seven differentcontents, the additional premise was not rated as very additional and thealternative premise was not rated as very alternative. Although we presented all14 problems in the experiment, we did not include this problematical contentin the statistical analysis (see Appendix B; un-analysed contents are notmentioned). Appendix C represents the different contents of the conditionals thatwere used to construct the four types of conditional problems for Experiment 3.2.

Procedure. The procedure of Experiment 3.1 was the same as the procedureof Experiment 1. Experiment 3.2 differed from the previous experiments, as theparticipants were tested on a computer. At the beginning of each trial, the screensignalled “press space bar for the next problem”. When participants pressed thespace bar, the first premise appeared together with the categorical premise andthe question “what follows?”. At this point, the participants typed their firstanswer. When they had entered their answer, we presented the followingquestion under the first two premises:

Do you have to change your conclusion: [and then the conclusion of the participantwas repeated] in the light of the following information: [and then the secondconditional premise appeared on the screen].If you think so, how would you change your conclusion (if not, press “enter”)?

The computer recorded their first answer and the second answer (if theychanged their first answer). The instructions were presented on the screen. They

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explained the participants’ task. None of the participants had any difficulty withthe procedure.

Experiment 3.3 was a paper and pencil test. The participants received twobooklets: The first booklet contained the instructions and the second onepresented the 16 problems, each on a separate page. As in Experiments 3.1 and3.2, the participants had to produce their own conclusion to the problems.

Participants. A total of 178 participants took part in the three parts of theexperiment. In Experiment 3.1, we tested 111 participants, of whom 22 solvedsimple problems that are not discussed further. In the alternative condition, wetested 43 participants; in the additional condition, we tested 46 participants. Allparticipants were students of a secondary school, between 16 and 19 years old. InExperiment 3.2, 21 students at the University of Leuven, who had not taken partin previous reasoning experiments, participated. They had not yet received aformal introduction to logic. In Experiment 3.3, 46 first-year psychologystudents at the University of Leuven who had not taken part in previousreasoning experiments, participated. They received credit points towards acourse requirement and had not yet received a formal introduction to logic.

Results and discussion

The three parts of Experiment 3 have a different design. This manipulation wasnecessary to induce the use of the amendment (3.2) and the integration strategy(3.3). It is as well to note, however, that the difference in design implies lesspower in the statistical analysis.

In Table 3, we present all the answers and the corresponding percentages ofthe three parts of the experiment. We did not restrict the different answers byputting them into categories. The diversity of different answers given by theparticipants is in itself already an important finding. As is immediately observed,almost all answers given in 3.1 are given in 3.2 or 3.3, or in both 3.2 and 3.3. Thetheoretically predicted integration and amendment answers are indicated. Wedistinguish four kinds of answers: theoretically predicted pure amendmentanswers, theoretically predicted pure integration answers, answers that areexpected from both theories, and finally answers that are not specificallypredicted (not indicated). Very few answers are pure integration answers. Theamendment hypothesis, being more general, can account for a larger set ofpossible answers than the integration hypothesis.

Of all given answers, 72.6% were theoretically predicted. Overall, the purelypredicted integration answers account for 1.7%, 0%, and 2.7% of all answers,respectively. Also in line with expectations, the purely predicted amendmentanswers account for 32.2%, 34.9% and 8.0% of all answers, respectively. Thestatistical comparisons of the pure amendment answers in Experiment 3mentioned in Table 4. These comparisons are consistent with the idea that

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amendment is encouraged in Experiment 3.2. Finally, the answers predicted fromboth hypotheses account for 42.9%, 36.9%, and 58.7% of all answers,respectively. Table 5 shows the statistical comparisons of the mixed amendmentand integration responses in Experiment 3. These findings together with thecomparisons of Table 4 are consistent with the idea that Experiment 3.3encourages integration. As shown in Table 3, most answers given in 3.2 are inline with the amendment strategy (71.8%), and most answers given in 3.3 are inline with the integration strategy (61.4%).

Our hypothesis for the two existing strategies is largely confirmed. There are,nevertheless, a minority of answers that we did not predict. We want to focus onthese answers now, showing that even some of these answers fit in the proposedstrategies.

One example in this category is the “maybe p” (alt: 4.8%; add: 11.9%) answerfor the Modus Tollens problem (alternative and additional condition). It isexplainable when one uses the amendment strategy. The putative “not p”conclusion is put into question when the second premise is brought to theattention of the participant. One can express his/her doubt about the putativeconclusion in a way that is more (not p … or not q, not p … and not q) or less (notp … or maybe still p) specific. This latter answer is difficult to explain with theintegration strategy, because one would expect an answer containing the two(disjunctive or conjunctive) related propositions of the antecedent in that case.Indeed, this answer is not given in 3.3 (alt: 1.1%; add: 0%). Another possibleexplanation of the “maybe p” answer is that participants start doubting theoriginal premise when an extra premise is added (David Over, personal com-munication, May 1999). We can agree with this point of view. It might be thecase that this answer and some and of the other, are given because the participantsconsider a stronger answer (e.g., not-r) too strong or improbable bearing in mindthe doubt they have about the major premise. However, this viewpoint cannotexplain all observed answers. Indeed, the “maybe p” answers represent only7.7% of the Modus Tollens answers of Experiment 3, but most answers for theseproblems as well as some others are clearly predicted by the amendment orintegration strategies. Also and most importantly, some of these answers (e.g.,not-r unless q) cannot be explained by means of doubt about the premises.

Another group of unpredicted answers that we observed are “both, r if qadd andnot r if not qadd” for the Modus Ponens problem and “both, r if qalt, and not r if notqalt” for the denial of the antecedent problem. It is easy to see why these answersonly appear in Experiment 3.1 and 3.3. Because the latter answer is a specifi-cation of the predicted “r if qadd” (Modus Ponens) and “not r if not qalt” (ModusTollens), which stresses the “if and only if” meaning of the expected answers, itfits perfectly the line of thinking of the integration strategy. However, it does notfit with the amendment strategy. Indeed, why should participants, when they

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TABLE 4Pure amendment answers in Experiment 3

Modus Ponensr if (also) qalt 3.1 (0%) 3.2 (19.0%) 3.3 (0%)radd: 3.1 > 3.2: 61.6% vs. 28.6%; U = 275.5, p <.005

3.2 > 3.3 28.6% vs. 8.7%; U = 386, p < .05

Modus Tollensnot palt: 3.2 > 3. 1: 35.7% vs. 7.7%; U = 309, p < .005

3.1 > 3.3: 7.7% vs. 1.1, U = 851, p < .05not padd: 3.1 > 3.3: 36.2% vs. 10.9, U = 670, p < .0005

3.2 > 3.3: 31.0% vs. 10.9; U = 183, p < .0001

Denial of the antecedentnot ralt: 3.1 > 3.3: 42.6% vs. 18.4%, U = 641.5, p < .00 1

3.2 > 3.3: 33.3% vs. 18.4%, U = 380, p < .05r if qadd 3.1 (7.9%) 3.2 (21.9%) 3.3 (0%)

Affirmation of the consequentpalt 3.1 (10.0%) 3.2(28.6%) 3.3 (0%)p and qalt 3.1 (11.6%) 3.2 (11.9%) 3.3 (0%)p or qadd 3.1 (7.9%) 3.2 (7.1%) 3.3 (0%)padd: 3.1 > 3.3: 31.1 % vs. 6.5%, U = 586, p < .000 1

3.3 > 3.2: 27.0% vs. 6.5%, U = 309.5, p < .0005

TABLE 5Mixed amendment and integration answers in Experiment 3

Modus Ponensralt: 3.1 > 3.2: 93.8% vs. 76.2%; U = 348, p < .05

3.3 > 3.2: 96.7% vs. 76.2%; U = 349, p < .005

Modus Tollensnot p and not qalt: 3.3 > 3.1: 83.7% vs. 71.3%, U = 749.5, p < .05

3.1 > 3.2: 71.3% vs. 31.0; U = 309, p < .005not p or not qadd: 3.3 > 3.2: 69.6% vs. 31.0, U = 264, p < .001

3.3 > 3. 1: 69.6% vs. 29.7%, U = 483, p < .0001

Denial of the antecedentnot ralt +: 3.1 > 3.2: 36.4% vs. 14.3%, U = 312, p < .05

3.3 > 3.2: 35.9% vs. 14.3%, U = 337.5, p <.05

Affirmation of the consequentp or qalt: 3.3 > 3.2: 82.6% vs. 38.1%, U = 250.5, p < .0001

3.1 > 3.2: 66.0% vs. 38.1%, U = 301, p < .05p and qadd: 3.3 > 3. 1: 78.3% vs. 55.0%, U = 681, p < .001

3.3 > 3.2: 78.3% vs. 45.2%, U = 287, p < .005

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want to express a revision of the putative conclusion in Stage 2, work out therelation between the propositions that far?

A related category of observed answers are “not r if not qadd” for the ModusPonens problem and “r if qalt”/“not r unless qalt” for the denial of the antecedentproblem. These answers appear in all parts of Experiment 3, and should thereforebe explainable from both strategies. If one reasons in two stages, one mayconditionally conclude from the first premise “if p, then r” and the categoricalpremise “not p” that “not r” is the case. This putative conclusion may bereconsidered in Stage 2 when one takes into account the premise “if q, then r”, to“(not r, but still) r if qalt”/“not r, unless (when) qalt (then r)”. When one follows theintegration strategy, on the contrary, the following models may be made explicit:

not-p qalt rnot-q not qalt r

This leads to the same “r if qalt” answer.An intriguing finding is the “r” answer that appears in 8.7% of the cases in

Experiment 3.3 for the Modus Ponens problem. We presented the problems in theadditional condition of Experiment 3.3 as follows:

If p and qadd, then r. / p

The logically correct answer therefore is not “r”, but “one can’t know” (13.1%),“maybe r” (0%), or “r if qadd” (68.4%). This answer is neither a simple con-ditional answer nor an integration answer. Given the following model, we cannotsee how the “r” answer would be inferred:

p q r…

Hence, we think that people used the amendment strategy even in Experiment3.3. Indeed, the disjunctive or conjunctive combined answers may still be quiteeasy to solve for the Modus Ponens problem, but they are far more difficult forthe other problems. This is an example of why we suppose that some people,even when forced to use the integration strategy, split up the problems andhandled them in two stages. As the problems were randomised, participants mayhave developed the amendment strategy for the more complex problems and usedit to solve the less complex ones. This explanation might also account for thefollowing answer categories: “not p/not q”, “not p and not qadd”, “not p or not qalt”for the Modus Tollens problem; “not r”, “not r unless qalt” for the denial of theantecedent problem; “not p/not qadd” for the affirmation of the consequentproblem. An alternative explanation that can account for the strange “not p or notqalt” and “not p and not qadd” answers for the Modus Tollens problem is that this

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problem is difficult to solve: Including a conjunction, disjunction that has to benegated makes the problem even more complex (De Morgan rule).

We end the discussion of Experiment 3 with three general conclusions. First,the existence of the two strategies is well confirmed. More than 70% of all givenanswers are predicted by at least one of the proposed strategies. Second, inducingthe amendment like the integration strategy worked very well: Most answersgiven in 3.2 are predicted or (ad hoc) explained by the amendment strategy, andmost answers given in 3.3 are predicted or (ad hoc) explained by the integrationstrategy. Third, the amendment strategy seems to be preferred over theintegration strategy, which we attribute to the lesser load on working memory.

GENERAL DISCUSSION

In Experiment 1, we found that conditional inferences can be suppressed, repeat-ing the findings of Byrne (1989). Indeed, reasoners made fewer denial of theantecedent and fewer affirmation of the consequent inferences (which are invalidinferences) when the major premise was accompanied by an alternativeantecedent. Reasoners also made fewer Modus Ponens and Modus Tollensinferences (which are valid inferences) when an additional antecedent ac-companied the major premise. However, we revealed a serious shortcoming inthe design of both our replication Experiment 1 and Byrne’s Experiment 1(1989): The answer alternatives only deal with the inferences that can be madewith respect to the first conditional.

In Experiment 2, reasoners could choose their answers among many answeralternatives. Because of this procedure, many reasoners gave a complex answer.Indeed, they did not only give information about the first conditional, they alsotried to give information about both conditional premises. It even seems asthough they attempted to reason conditionally. Indeed, in a somewhat broaderdefinition, we can describe a “conditional” answer as one in which at least onepart of the answer coordinates with the normal conditional pattern. This meansthat the single conditional answer is extended with another element mentioned inone conditional premise which enlarges the scope of that single conditionalanswer or makes it smaller. For example, given an affirmation of the consequentproblem such as:

If it rains, then Marianne gets wet.If she takes a walk, then Marianne gets wet.Marianne gets wet.

This example clearly illustrates how the conclusion “it rains” may be extendedwith “and she takes a walk”, which makes the scope smaller in this case. It isnecessary to consider also that if we take into account such a broader definition,we did not find suppression in Experiment 2. Conditional reasoning with two

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conditionals is not the same as reasoning with one conditional. Consider thedouble conditionals in Experiments 1 and 2. Making the Modus Ponens argumentmeans confirming the consequent (and doing something with the antecedent ofthe second conditional premise). Similarly, making the Modus Tollens argumentmeans denying the antecedent (and doing something with the antecedent of thesecond conditional premise); making the denial of the antecedent argumentmeans denying the consequent (and doing something with the antecedent of thesecond conditional premise); and making the affirmation of the consequent argu-ment means confirming the antecedent (and doing something with the antecedentof the second premise). If reasoners are given a less arbitrary set of choices in aforced choice paradigm (as in Experiment 2), the suppression phenomenon dis-appears. Indeed, reasoners choose or provide answers that show clear signs ofconditional reasoning.

Our results indicate that it is not the case that the first premise of the argumentwas rendered false by the additional premise, so that people simply refuse to useit in reasoning, as Savion (1993) claimed. The results also show that reasonersdid not reject the first premise of the argument (see Bach, 1993). Reasoners takeinto account the first premise and they reason with this premise. However, someof them change their conclusion in the light of the second (additional oralternative) premise, while some others may combine the two premises, as Byrne(1989) proposed. Politzer and Braine (1991) also responded to the experiments ofByrne (1989) by stating that the procedure caused the participants to doubt thetruth of one of the premises due to its perceived inconsistency with otherpremises. However, Byrne (1991) did show data that falsified this account. Mostof our data confirmed Byrne (1991), although a few of the answers (but clearlynot all) observed in our experiments can be explained by means of thismechanism of doubt (see e.g., the “maybe p” answer in Experiment 3.1).

With Experiment 3, we tried to solve some questions about the underlyingreasoning processes by taking into account the broad palette of answers. InExperiment 3.1, we did this by changing the task of Experiment 1 into aproduction task. In Experiment 3.2, we presented the conditionals in two stages.The first conditional was presented together with a categorical premise and theparticipants were asked to give a conclusion. Next, we gave the second con-ditional and asked the participants if they wanted to change their putativeconclusion, and if so, how. In Experiment 3.3, we presented the participantsintegrated conditionals, like:

If she has an essay to write and the library stays open, then she will study late in thelibrary.

We hypothesised that such a presentation would elicit reasoning from integratedconditionals. Most of the answers in Experiment 3.2 were amendment answersand most of the answers in Experiment 3.3 were integration answers, consistent

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with our predictions. Moreover, neither the answer categories of Experiment 3.2alone nor those of Experiment 3.3 alone can account for all answer categories inExperiment 3.1 (i.e. both strategies are used in Experiment 3.1). Thus far, theresults confirm our predictions. However, we must admit that some of ourpredictions were not confirmed: in Experiment 3.3 we observed answers that weclassified as amendment answers. Only if the reasoning progresses in two stageswould these answers be explainable. What is brought to light by this is that, at themoment, we do not yet know enough of the strategic and interpretive componentsthat play a crucial role in reasoning. What we do know, however, is that itrequires a lot from working memory to take into account more than two models atthe same time, especially when they each contain three atomic propositions(Schaeken & Johnson-Laird, 2000).

We conclude with some theoretical points of view. Some other researchershave reported suppression effects. Chan and Chua (1994) interpreted theirfindings in terms of the relative salience model. According to them, thecritical component is the relative salience of the two antecedents, with respectto the consequent as interpreted by the reasoners. Consider the followingproblem:

If p then r.If qadd then r.

Chan and Chua predict that suppression of the valid inferences (Modus Ponensand Modus Tollens) would occur only if “qadd” was more salient relative to “p”for the occurrence of “r”, and that the probability of suppression would increasewith an increase of relative salience. The results, which are not predicted directlyby the mental model theory, confirmed their hypothesis. We agree with them thatthis finding shows that the mental model theory fails to give a principled accountof the critical interpretative component involved in reasoning (see alsoFillenbaum, 1993). However, we do not agree with their proposed implemen-tation of the principle of salience. They suggest a production system (seeAnderson, 1983) comprising two fairly simple production rules:

Prodl: IF qadd or not-qadd is unknown,THEN scale qadd according to the assertion p (i.e., qadd/P)

Prod2: IF (qadd/P)<1,THEN respond “r”OTHERWISE respond “don’t know”.

This production system divides the reasoning process into two stages, as weproposed. In one stage, reasoners make the Modus Ponens inference (i.e., Prod2)and in the other stage, reasoners take into account the relevance of the additionalpremise. One difference between their proposal and ours is the order of the two

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stages. Based on our results, we believe that reasoners first make the ModusPonens inference and next consider if they have to amend this putativeconclusion. The major problem we have with their production system is the lastpart of the second production rule, because this model predicts “don’t know”answers. When reasoners rate the salience of the additional premise higher thanthe salience of the first premise, this cannot predict the more complex answers weobserved in our last two experiments. The participants in the experiment of Chanand Chua (1994) were not able to give a more complex answer, because they hadto choose between the same possibilities as the participants in the experiment ofByrne (1989).

Stevenson and Over (1995) report four experiments in which theymanipulated the uncertainty of the conditional (see also George, 1997). In one oftheir experiments, they presented the participants problems such as:

If John goes fishing, he will have a fish supper.If John catches a fish, he will have a fish supper.John is always lucky when he goes fishing.John goes fishing.

The result of adding the third premise turned out to be that reasoners made moreModus Ponens inferences than when the third premise was absent, meaning thatthe third premise cancelled the pragmatic suggestion of the second premiseconcerning the uncertainty of the first. If the third premise is changed to:

John is very rarely lucky when he goes fishing.

then reasoners make the Modus Ponens inference less often. Stevenson and Over(1995) explain their data in terms of the mental models theory. They argue (seealso Johnson-Laird, 1994) that proportions of representative cases might be usedto represent some probability judgements. In our opinion, their approach has twoproblems. First, in their experiments participants were not able to concludeanything about the additional premise (as in the experiments of Byrne, 1989;Chan & Chua, 1994) and, as we have shown, this aspect influences the reasoners.

Second, Stevenson and Over (1995) argue that reasoners integrate theinformation of the major premise, the additional premise, and the qualifyingstatement in a mental model. We propose an alternative that at least somereasoners need two separate reasoning stages in order to come up with their finalconclusion.

The study of Cummins, Lubart, Alksnis, & Rist (1991; see also Cummins,1995) shows that logically valid causal inferences are suppressed when it is easyfor reasoners to find possible “disabling conditions” that could prevent the effectfrom occurring despite the presence of a cause. Similarly, nonvalid causalinferences are also suppressed when it is easy to find possible “alternativecauses” that could produce the effect in question.

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In our view, the results of this study can be interpreted as evidence that somepeople solve these problems in two stages. Cummins et al. asked a first group ofparticipants to find as many disabling conditions/alternative causes as possible.Problems were then categorised (many–few disabling conditions/alternativecauses). Another group of participants was asked to answer problems such as thefollowing Modus Ponens argument with many disabling conditions:

Rule: If I eat candy often, then I have cavities.Fact: I eat candy often. Therefore, I have cavities.Given the this rule and this fact, place a mark on the scale below that best reflectsyour evaluation of the conclusion

Very sure sure somewhat sure somewhat sure sure very sure

That I cannot draw this conclusion That I can draw this conclusion

How are these kind of valid inferences suppressed? As there is no explicitinformation about a disabling condition, reasoners have to come up with it ontheir own. It seems implausible to us that people include these disablingconditions when they read the first rule. Rather, it seems that they read theargument, form a conclusion, and when they have to quote how sure they are,they may come up with disabling conditions that make them less sure. Of course,we acknowledge this is a post hoc interpretation, and we do not have experi-mental evidence for it. But the idea of holding all kinds of disabling conditions/alternative causes in your mind would mean a heavy load on working memory,especially if you are not sure that you will need them anyway after reading thefirst rule.

What are the consequences of our results for the current reasoning theories? Afirst lesson is that the kind of answer procedure strongly influences the answersthat are given by the participants. The difference between Experiment 1 (onlythree answer alternatives) and Experiments 2 and 3 makes this clear. In bothExperiment 2 and Experiment 3, participants had a lot of freedom; in Experiment2, they could choose their answers among more than 10 alternatives and inExperiment 3, they could produce their own answer. Still, there were someremarkable differences between the answers given in these last two experiments.Table 3 shows the wide variety of answers given in Experiment 3. More than20% of the answers given in Experiment 3 could not be chosen from the answerpalette in Experiment 2 (e.g. “she did not get wet if it did not snow”). Given thisfinding, we must emphasise the importance of careful consideration about thisaspect of setting up experiments (for a similar view, see e.g., Dugan & Revlin,1990; Hardman & Payne, 1995). Likewise, the diversity and richness of answersgiven by our participants in Experiments 3.1, 3.2, and 3.3 should not beneglected.

A second lesson is that of Byrne (1989, p. 79): “The moral of these

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experiments is that in order to explain how people reason, we need to explainhow premises of the same apparent logical form can be interpreted in quitedifferent ways.” It is important that both current reasoning theories must offer abetter account of the interpretive processes in reasoning, if they want to explainhow human beings make inferences. It is only after this account is given that onecan decide decisively between the two theories. Hence, we do not agree with laterwritings of Byrne (e.g., 1991) in which she argues that her experiments aredecisive evidence for mental models over mental logic. In the same vein, we wantto emphasise that our experiments are not decisive evidence for the sole existenceof these two strategies in solving complex conditional problems. Although thesetwo strategies can explain the majority of the answers, some of the findingsremain problematic. Consider for instance the DA problems in Experiment 2.More participants chose an “impossible to tell” response with an additionalconditional than with an alternative conditional. As we pointed out, these resultsare problematic for the integration account of the suppression effect. However,even under an amendment strategy, this result remains surprising. As Fillenbaum(1993) argued, the extension of our knowledge about the interpretive processes inreasoning is a prerequisite for a more detailed account of all responses.

A third lesson is that reasoning researchers must pay more attention todifferent strategies that are used. Indeed, research (see e.g., Roberts, 1993;Roberts, Gilmore, & Wood, 1997) shows that reasoners use different strategies intackling a deductive reasoning problem. This aspect sometimes makes it difficultto distinguish between the actual basic reasoning process and the strategies thatoverlie and obscure them. Our experiments revealed that at least two differentstrategies are used by the participants: the integration strategy, which wasproposed by Byrne (1989, 1991) and Rumain et al. (1983) and the amendmentstrategy. The mental model theory can incorporate this new strategy. One canargue that the amendment strategy resembles the basic principle of the mentalmodel theory. People reason by constructing one or more mental models, theyformulate a putative conclusion, and test this conclusion by searching foralternative models that falsify the putative conclusion. Furthermore, if reasonersreason with each of the two major premises separately, then they minimise thenumber of atomic propositions they have to consider simultaneously, which is inaccordance with the claim that reasoners try to minimise the load on workingmemory. Of course, the mere fact that a strategy can be easily integrated withinone theory (the mental model theory), does not imply that it cannot be integratedwithin another theory. We will not go deeper into this topic; for a review ofrelevant research and theorising about strategies in deductive reasoning, seeSchaeken, Vandierendonck, d’Ydewalle, and De Vooght, (2000).

In conclusion, additional premises do not lead to fewer valid inferences, andalternative premises do not lead to fewer nonvalid inferences. In all conditionsreasoners tried to reason conditionally. Thus, there is neither suppression of validinferences or invalid inferences. As a consequence, the argument of rule theorists

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(e.g., Rumain et al., 1983; see also Politzer & Braine, 1991) that there are no rulesfor invalid inferences because they can be suppressed does not hold. In addition,the results show that many reasoners do not combine the premises, but that theyinstead perform the task in two stages. More notably however, is the fact that thecurrent reasoning theories have not yet offered a principled account of theinterpretative processes in reasoning that are very important, as our experimentsshow (see also Dieussaert, Schaeken, Schroyens, & d’Ydewalle, 1999).

NOTE 1The fully explicit model is:

p not-qalt rnot-p not-qalt rnot-p not-qalt not-rnot-p qalt rp qalt r

NOTE 2Stage 1 Stage 2p r q rnot-p rnot-p not-r

… leads to (conditional) conclusion which will be revised in the light of

Manuscript received 25 August 1998Revised manuscript received 23 August 1999

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APPENDIX AMaterials used in Experiments 1–3.

Antecedent type Conditional

Simple If she meets her friend, then she goes to a pub for a drink.Alternative If she meets her family, then she goes to a pub for a drink.Additional If she has enough money, then she goes to a pub for a drink.

Simple If she has an essay to write, then she will stay late in the library.Alternative If she has some books to read, then she will stay late in the library.Additional If the library stays open, then she will stay late in the library.

Simple If it is raining, then she will get wet.Alternative If it is snowing, then she will get wet.Additional If she goes out for a walk, then she will get wet.

Each initial conditional was presented in a simple argument to one group of participants,accompanied by an alternative to a second group of participants, and by an additional antecedent toa third group.D

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APPENDIX BMaterials used in Experiment 3.2.


Alternative If the sun is shining, then Eric will make a trip to the beach with the car.If he is feeling well, then Eric will make a trip to the beach with the car.

Additional If his father will let him use it, then Eric will make a trip to the beach withthe car.

If she meets her friend, then An goes to a pub for a drink.Alternative If she meets her family, then An goes to a pub for a drink.Additional If she has enough money, then An goes to a pub for a drink.

If it is raining, then Marianne will get wet.Alternative If it is snowing, then Marianne will get wet.Additional If she goes out for a walk, then Marianne will get wet.

If it is dark in the house, then the thief will break into the house.Alternative If there is no car near the house, then the thief will break into the house.Additional If he can force the lock, then the thief will break into the house.

If Jan goes out fishing, then there is fish on the menu tonight.Alternative If Jan buys a fish in the store, then there is fish on the menu tonight.Additional If Jan catches a fish, then there is fish on the menu tonight.

If she goes out working, then the woman next door takes a housekeeper.Alternative If she will have a child, then the woman next door takes a housekeeper.Additional If she earns enough money, then the woman next door takes a housekeeper.

APPENDIX CMaterials used in Experiment 3.3.


Alternative If she meets her friend or she meets her family, then she goes to a pub for adrink.

Additional If she meets her friend and she has enough money, then she goes to a pub fora drink.

Alternative If it is raining or it is snowing, then she will get wet.Additional If it is raining and she goes out for a walk, then she will get wet.

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Strategies during complex conditional inferences

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