Activation of end-terms in syllogistic reasoning

ACTIVATION AND REASONING 67

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

THINKING AND REASONING, 2000, 6 (1), 67–89

Activation of end-terms insyllogistic reasoning

Orlando Espino and Carlos SantamariaUniversidad de La Laguna, Tenerife, Spain

Juan A. Garcia-MadrugaUNED, Madrid, Spain

We report five experiments showing that the activation of the end-terms of asyllogism is determined by their position in the composite model of the premises. Weshow that it is not determined by the position of the terms in the rule being applied(Ford, 1994), by the syntactic role of the terms in the premises (Polk & Newell, 1995;Wetherick & Gilhooly, 1990), by the type of conclusion (Chater & Oaksford, 1999),or by the terms from the source premise (Stenning & Yule, 1997). In our firstexperiment we found that after reading a categorical premise, the most active term isthe last term in the premise. In Experiments 2, 3, and 4 we demonstrated that thispattern of activity is due to the position of the concepts in the model of the premises,regardless of the delay after reading the premises (150 or 2000 msec) or the quantityof the quantifiers (universal or existential). The fifth experiment showed that thepattern switches around after participants evaluate a conclusion. We propose that thelast element in the model maintains a higher level of activity during thecomprehension process because it is generally used to attach the incominginformation. After this process, the first term becomes more active because it is theconcept to which the whole representation is referred. These results are predicted bythe mental model theory (Johnson-Laird & Byrne, 1991), but not by the verbalreasoning theory (Polk & Newell, 1995), the graphical methods theory (Yule &Stenning, 1992), the attachment-heuristic theory (Chater & Oaksford, 1999), or themental rules theory (Ford, 1994).

Address correspondence to Orlando Espino, Departamento de Psicologia Cognitiva,Universidad de La Laguna. Campus de Guajara, 38205–Tenerife, Spain.Email: [email protected]

We wish to thank Clare Walsh and Alice McEleney for their helpful comments on thisresearch. The authors thank J. Evans and two anonymous reviewers for comments on anearlier version of the manuscript.

68 ESPINO, SANTAMARIA, GARCIA-MADRUGA

INTRODUCTIONA categorical syllogism consists of two premises and a conclusion. Forexample:

premise 1: All of the A are Bpremise 2: All of the B are C

conclusion: All of the A are C

The premises contain three terms (A, B, and C), one of which, the middle term (B)occurs in both premises. The conclusion connects the other two terms (end-terms). The premises and conclusion each contain one of the quantifiers: all,none, some, and some not.

The arrangement of the middle terms in each of the premises of a syllogismgives rise to a four-way classification, known as the figure of the syllogism.

Figure 1 Figure 2 Figure 3 Figure 4A–B B–A A–B B–AB–C C–B C–B B–C

The figure affects syllogistic reasoning. This effect is particularly clear in figures1 and 2.1 In figure 1 there is a preference to build conclusions in the order A–C,while in figure 2 the opposite preference is observed. Although thisphenomenon has been known for a long time (Dickstein, 1978; Ford, 1994;Garcia-Madruga, 1982; Johnson-Laird & Bara, 1984), there is no clear consensusabout its actual nature (Evans, Newstead, & Byrne, 1993). Although severalexplanations of this phenomenon have been provided to date, some authors(Rips, 1994) consider that this effect is specific to one particular type of task.

Wetherick and Gilhooly (1990), consider that the figural bias stems from arhetorical principle. These authors argue that the effect arises from the tendencyto use as the first term in the conclusion, a term that has appeared as the subjectof one of the premises. In figure 1, “A” is the subject of the first premise, so thepreferred order of the end-terms in the conclusion will be: A–C. In figure 2, “C”is the subject of the second premise, so C–A will be more frequent.

In a similar way, Polk and Newell (1995) argue that the figural effect is basedon the special availability of proposition topics in the annotated model. Theproperties in the annotated model that correspond to the premise topics (i.e.,their grammatical subjects) are more available than other properties. If only oneend-term appears as the topic of a premise, the reasoner will tend to produce

1As we are going to refer to only two of the four syllogistic figures, we prefer to numberthis figure as 2, although it is numbered as figure 4 in Johnson-Laird and Bara (1984) and asfigure 1 in classical syllogisms.


conclusions referred to it. In figure 1, “A” is the topic in the annotated model,consequently the preferred order of the end-terms in the conclusion will be:A–C. In figure 2, “C” is the topic in the annotated model, so the conclusionsC–A will be more frequent.

Chater and Oaksford (1999) postulate that conclusion order is determined bythe attachment-heuristic. This heuristic fixes conclusion order using thefollowing procedure: if the min-premise has an end-term as its subject, use this asthe subject of the conclusion. Otherwise, use the end-term of the max-premise asthe subject of the conclusion. The attachment-heuristic operates after otherheuristics (min-heuristic, max-heuristic, and P-entailments) have selected thequantifier of the conclusion. For all figure 1 and 2 syllogisms the predictions ofthe attachement-heuristic are in agreement with the figural effect. In figure 1, “A”is the subject, consequently the preferred order of the end-terms in theconclusion will be A–C. In figure 2, “C” is the subject, so the conclusions C–Awill be more frequent.

Yule and Stenning (1992; see also, Stenning & Oberlander, 1995; Stenning &Yule, 1997) suggest an explanation in terms of the logical properties of thesyllogism. They explain this effect by the “Source-Founding Hypothesis” whichstates that “the terms from the source premise will tend to precede the other end-term in conclusions and will tend to retain the order in which they appear in thesource premise” (Stenning & Yule, 1997, p. 128). The source premise is thepremise that provides the necessary individuals (individuals whose existence isentailed by the premises) which are not bisected during the formation of theregistration diagram. More specifically, they suggest that the figural effect is theconsequence of starting the construction of the individual description from thesource premise. For example, in a syllogism of figure 1 such as: all the of A areB / all the of B are C, “A” is the end-term of the source premise, and this end-termwill tend to precede to the other end-term (“C”) in the conclusion. On thecontrary, in a syllogism of figure 2, (e.g. all of the B are A / all of the C are B) “C”is the end-term of the source premise, and this end-term will tend to precede theother end-term (“A”) in the conclusion.

Ford (1994) has proposed that some individuals (verbal reasoners) use formalrules whereas others reasoners use Euler circles (spatial reasoners) when solvingsyllogisms. She found that in both groups that there was an effect of the figure innon-symmetric syllogisms (figure 1 and figure 2). She concluded that for thespatial reasoner, “it seems that whether there is a position effect or not may besomewhat dependent on whether the syllogism is symmetrical or not… Morework needs to be carried out to reveal subtle factors affecting the order of terms inconclusions” (Ford, 1994, p.69). Her predictions are more precise for the verbalreasoner. She proposes an explanation of the figural effect in terms of formalrules of inference (in fact, it could be considered the only current formal-ruletheory providing a detailed account of this phenomenon). She argues that theparticipants manipulate the verbal form of the syllogism as an algebraic


problem, by taking one premise as having a term that needs to be substitutedwith another term, and the other premise as providing a value for thatsubstitution. The premise that provides the values for substitution acts as a rulerelating membership of class C to a property P, while the premise containing theterm that needs to be substituted acts as a case of specific objects, O, whose statuswith regard to either C or P is known. She proposed four principles that aresupposed to govern substitutions (Ford, 1994, p. 21):

A. If a rule exists affirming of every member of the class C the property P then(i) whenever a specific object, O, that is a member of C is encountered it can

be O has the property P and(ii) whenever a specific object, O, that lacks property P is encountered it can

be inferred that O is not a member of C

B. If a rule exists denying of every member of the class C the property P then(i) whenever a specific object, 0, that is a member of C is encountered it can

be O does not have the property P and(ii) whenever a specific object, O, that possesses the property P is

encountered it can be inferred that O is not a member of C

In relation to the figural effect, Ford postulates that occurrence of a positioneffect may be dependent on which part of the rule is being applied. For example,consider the syllogism of figure 2:

All of the lawyers (C) are vegetarians (P)All of the stamp collectors (O) are lawyers (C)

To solve it we need to apply rule Ai. The first premise affirms that every memberof the class of lawyers (C) has the property of being vegetarian (P). This premiseprovides the value for the substitution (vegetarians). The second premiseidentifies “all of the stamp collectors” as specific objects O whose status withregard to C (lawyers) is known. Then, this premise contains the term that needs tobe substituted (lawyers). Now, we can infer that O (all of the stamp collectors)have the property P (the property of being lawyers) and we can conclude that:“all of the stamp collectors are vegetarians”.

Solving a figure 1 syllogism is more complex. Consider the syllogism:

All of the vegetarians (O) are lawyers (C)All of the lawyers (O) are stamp collectors (P)

In order to solve it we need to apply rule Ai, but we should start applying this ruleto the second premise. The second premise affirms that every member of the classof lawyers (C) has the property of being a stamp collector (P). This is the premise


that contains the term that needs to be substituted (lawyers). The first premiseidentifies “all of the vegetarians” as specific objects O whose status with regardto C, lawyers, is known. So this premise is the premise that provides the value forthe substitution (vegetarians). Now, we can infer that O (all of the vegetarians)have the property P (the property of being lawyers) and we can conclude that:“all of the vegetarians are stamp collectors”.

Johnson-Laird and Bara (1984) suggest that figural effects in syllogisticreasoning stem from the difficulty of constructing composite mental models ofthe two premises in working memory. In order to build this composite model, theparticipants should bring the two middle terms into contiguity. In the syllogismsof figure 1 (A–B/B–C), the composite model is attained directly because themiddle terms (“B”) are adjacent. In this case, the first term that enters workingmemory is “A” and the last term is “C”. Consequently, the most frequentconclusion will be in the direction A–C. In the syllogism of figure 2 (B–A/C–B),the participants cannot build the integrated mental model directly, as the middleterms are not adjacent. In this case, it is necessary to carry out additional mentaloperations in order to bring the two middle terms into contiguity. The simplestway is to discard the first encoding of the first premise and reread it following thesecond premise. Now, the first term that enters working memory is “C” and thelast term is “A”, for this reason the more likely conclusion will be in thedirection: C–A.

The aim of this paper is to explore the activation of end-terms of premisesduring the comprehension and deduction phase of categorical syllogisms.Measurement of the level of activation of concepts in texts has been frequentlyused in the field of text comprehension (Chang, 1980; Corbett & Chang, 1983;Gernsbacher, 1990; Gernsbacher, Hargreaves, & Beeman, 1989; Stevenson,1986). Gernsbacher and her colleagues analysed two seemingly contradictoryphenomena: the Advantage of the First-Mentioned Participant (the conceptmentioned first in a sentence is more accessible than the concept mentionedsecond), and the Advantage of the Most Recent Clause (concepts mentioned inthe most recent clause are more accessible than concepts mentioned in an earlierclause). Within her Structure Building framework Gernsbacher considers thatpeople build mental structures while reading. In a multiple-clause text,participants would represent the information from each clause in a separatesubstructure. Consequently, they would have greatest access to the informationfrom the substructure they are currently processing (the most recent clause).However, the first clause will gain activation as it serves as a foundation for thewhole sentence representation. In this paper, we take the time taken by theparticipants to test whether a word was present in the problem as a measure of theactivation of the corresponding term (see, Gernsbacher, 1990; Gernsbacher et al.,1989). It is hypothesised that the most active word (the most active end-term inour case) will be involved in laying a foundation and mapping subsequentinformation into that foundation.


Whether the first or the second term in a quantified (syllogism-like) sentenceis the most active is an empirical question. In this paper, we will use measures ofthe level of activation of the end-term of a syllogism to explore the currenttheories about syllogistic reasoning and, particularly, about the figural effect.We now describe predictions derived from different theories of the figural effectand the rationale for these. Our predictions based on model theory (Johnson-Laird & Byrne, 1991) are that the activation of the terms is affected by theposition of the tokens representing the terms in the model. During thecomprehension process the last element in the model maintains a higher level ofactivity because it is generally used to attach the incoming information. In figure1, “C” is the last term of the model, consequently this term will hold the highestactivation. In figure 2, “A” is the last term of the model, and consequently themost active term. After this process, the first term becomes more active because itis the concept to which the whole representation is referred. In figure 1, “A” is thefirst term that enters working memory in the composite model, and,consequently this term will hold the highest activation. In figure 2, “C” is thefirst term that enters working memory in the composite model, and consequentlythe most active term.

Our prediction based on Polk and Newell’s theory (1995) is that the highestlevel of activation will correspond to the end-term that is the topic of the premise(the grammatical subject). Polk and Newell (1995, p.536) postulate that theirmodel to solve categorical syllogism (Verbal Reasoning) “uses an annotatedmodel representation in which properties can be annotated… Identifyingproperties are distinguished from other, secondary properties by being moreeasily accessible… The identifying properties simply correspond to the topics ofthe propositions being encoded.” In figure 1, “A” is the topic in the annotatedmodel, and, consequently, this term will hold the highest activation. In figure 2,“C” is the topic in the annotated model, and the most active term. Similarly, ourprediction based on Wetherick and Gilhooly’s theory (1990) is that the highestlevel of activation will correspond to the end-term that is the grammaticalsubject of the premise (“A” in figure 1, and “C” in figure 2). Wetherick andGilhooly (1990) postulate that the end-term that appears as subject of thepremises is what the argument is then it is about. If the subject of the premises iswhat the argument is about, then it is probable that this term is the focus in themental representation. As some authors suggest “that which is readily accessibleand available in a mental representation may be said to be in focus” (Moxey,Sanford, & Barston, 1990, p.111).

Our prediction based on Chater and Oaksford’s theory (1999) is that thehighest level of activation will correspond to the end-term that is the subject ofthe min-premise or the subject of the max-premise. These predictions are basedon Chater and Oaksford’s (1999) claim that the attachment-heuristic selects theend-term that is the subject of the min-premise or of the max-premise as first end-term of the conclusion. If this heuristic acts only when it identifies the term that


is the subject in the premise, this term will be more active than the other end-term. Gernsbacher has found that the first word that the participant uses in his orher representation is more active than others (Gernsbacher, 1990). In figure 1,“A” is the end-term that is the subject (in the max-premise or in the min-premise)and this term will hold the highest activation. In figure 2, “C” is the end-term thatis the subject (in the max-premise or in the min-premise) and this term will holdthe highest activation.

Our prediction based on the “Source-Founding Hypothesis” (Stenning &Yule, 1997) is that the highest level of activation will correspond to the term thatcomes from the source premise. Yule and Stenning (1997) postulate thatparticipants use the strategy of beginning the construction of the individualdescription from the source premise. Some research has suggested that the firstelement in the construction of the model is more active (Gernsbacher, 1990). Inthe syllogism of the form “all of the A are B / All of the B are C”, “A” is the termfrom the source premise, and this term will be the most active. In the syllogism ofthe form “all of the B are A / All of the C are B”, “C” is the term from the sourcepremise, and will be the most active.

Our prediction based on Ford’s theory (1994), at least for verbal reasoners, isthat the highest level of activation will correspond to the first end-term of thepremise that the rule identifies. In the syllogism of the form “all of the A are B /All of the B are C”, “C” is the first end-term of the premise that the rule identifies,and so this term will be the most active. In the syllogism of the form “all of the Bare A / All of the C are B”, “A” is the first end-term of the premise that the ruleidentifies, and so this term will be the most active. Gernsbacher (1990) hassuggested that the first term that the participants use in their mentalrepresentation is more activated.

In short, each of these approaches can make particular predictions about theactivation of end-terms in a syllogism. Our prediction based on the model theory(Johnson-Laird & Byrne, 1991) is that the activation of the terms is affected bythe position of the tokens representing the terms in the model. Our predictionbased on Ford’s rule theory (1994) is that the first end-term that the rule identifiesis the main determinant of activation. Our prediction based on Wetherick andGilhooly’s (1990) and Polk and Newell’s (1995) theory is that the syntactic roleof the terms is the main determinant of their activation, while our predictionbased on Chater and Oaksford’s theory (1999) is that the syntactic role of end-terms in the more or less informative premise is the main determinant of theiractivation. Finally, our prediction based on Stenning and Yule’s theory (1997) isthat the activation depends on whether or not the terms come from the sourcepremise. In Table 1, we show our predictions in relation to the activation of theend-term and the more active end-term in syllogism AA1 and AA2 for differentreasoning theories.

These predictions could be tested by measuring the activation of end-terms infigures l and 2. In some cases the position of the tokens cannot be distinguished


from the position of the terms in the problem, as is the case in figure 1 syllogisms(A–B/B–C). In this case, the token(s) corresponding to the end-term of the firstpremise (“A”) occupies the first position, while the token(s) corresponding to theend-term of the second premise (“C”) holds the last position. However, in figure2 syllogisms (B–A/C–B) the token(s) corresponding to the end-term of the firstpremise (“A”) occupies the last position, while the token(s) corresponding to theend-term of the second premises (“C”) holds the first position.

Our first experiment tests the level of activation of each term after reading aquantified statement similar to a syllogistic premise. The aim of this experimentwas to explore whether our experimental paradigm would be able to detectdifferences between the terms after reading a premise.

EXPERIMENT 1The first experiment was designed to test the level of activation of the terms (Aand B) in a single quantified statement (e.g. All of the A are B). The participantshad to decide whether or not a test word had been present in the statement. Theirresponse times to this question were taken as indicators of the level of activation.If the response time was low then the level of activation was high, and if theresponse time was high then the level of activation was low.

MethodParticipants. A total of 35 students from La Laguna University acted as

participants and received course credit for their participation.

Design and materials. We constructed 24 quantified sentences with theuniversal affirmative quantifier (ALL). An example sentence appears in Table 2.The participants were presented with a test word and were asked if it appeared inthe previous sentences. We asked 24 questions (TEST WORD) about the same

TABLE 1Our predictions about the factors that are determinants of activation

level of the end-term, and the more active end-term in syllogismAA1 and AA2 for different reasoning theories.

FACTOR SYLLOGISM AA1 SYLLOGISM AA2

Wetherick and Gilhooly Syntactic role in the premise A CPolk and Newell Syntactic role in the premise A CChater and Oaksford Syntactic role in the premise A CStenning and Yule Source premise A CFord Rule C AJohnson-Laird and Byrne Position of the tokens in the

mental model C/A A/C


word presented in different positions. In half of the trials the test word was thefirst term in the quantified sentence, and in the other half the test word was thesecond term in the quantified sentence. We constructed 12 lure sentences withdifferent quantifiers (SOME, NONE, SOME… NOT). The test word presented forthese lure items had not occurred in their respective sentences, so the correctanswer was “no”.

To ensure adequate comprehension, and to encourage participants to attendto all aspects of the sentence (not just the terms), each sentence was followed bya comprehension question that the participants had to evaluate as true or false.The order of terms of the comprehension question was counterbalanced (A–B inhalf of the trials and B–A in the other half). This comprehension question waspresented immediately after the test word.

Procedure. Each trial began with a warning signal, which was a plus sign (+)appearing for 750 milliseconds in the centre of the screen. After the warningsignal disappeared, one quantified sentence appeared (also in the centre of thescreen) for 2000 msec. The interval between the quantified sentence and the testword was 150 msec. The test words appeared in capital letters at the top of thescreen and remained on the screen until participants responded or 3 secondselapsed. Participants responded by pressing one or two response keys; one waslabelled “yes”, the other “no”.

For each experimental sentence, after 250 msec, the word “PREGUNTA”(“QUESTION”) appeared towards the bottom of the screen to warn participantsof an upcoming comprehension question. This warning signal remained on thescreen for 750 msec, after which the comprehension question appeared and,below it, two answer choices. One answer was positioned towards the left side ofthe screen, and the other towards the right side. Participants pressed the left-mostresponse key to select the answer on the left or the right-most response key toselect the answer on the right. The correct answer choices appeared equally oftenon each side of the screen. The question and answer choices remained on thescreen until either the participants responded or 10 seconds elapsed.Immediately after responding, the participants were given feedback about theiraccuracy, the time of duration of feedback was 1500 msec. The participantspractised on three sentences before they began the experiment.

Three participants were excluded because they failed to meet the followingcriteria: 90% accuracy in responding to experimental test words (requiring a

TABLE 2Sentence-type used in Experiment 1

SENTENCE: All the Spanish are physiologistsTEST WORD: SPANISHCOMPREHENSION QUESTION Are some physiologists not Spanish?


“yes” response), 90% accuracy in responding to lure test words (requiring a “no”response), and 75% accuracy in answering the two-choice comprehensionquestions.

Results and discussionThe analyses were based on response times for correct responses to the test word.The repeated-measures ANOVA revealed a reliable effect, F(1,32) = 43.87, p <.0001 MSE = 3795, for the position of terms in the quantified sentence (first orsecond place). The terms presented in second place in the quantified sentencewere responded to 102 msec faster than the terms presented in first place (secondplace = 938 msec; first place 1040 msec.). The total percentage of correctresponses to the comprehension questions was 85%.

These results suggest the existence of a recency effect of the last word in thequantified sentence or the last element in the mental model. The results are notsurprising (and are not in opposition to the Advantage of the First Mentionhypothesis) because the second term in a sentence of this type is the final word ofthe sentence, to which greatest attention is paid during reading, as shown inreading time experiments (see Aaronson & Ferres, 1983). From the point of viewof mental models this effect could arise because people attempt to attachincoming information (in this case, the comprehension question) to the lastelement in the mental model.

EXPERIMENT 2Although we showed in Experiment 1 that the last term has a higher level ofactivation than the first term, this experiment cannot show any differencebetween the predictions of different reasoning theories. To do that, we need fullreasoning problems. In this experiment we use figure 1 and 2 syllogisms. Ourpredictions based on model theory are of an interaction between figure (1 and 2)and presentation (first end-term and second end-term) because the last element inthe model will be the most active irrespective of its original position in thephrasing of the problem (the last element in the composite model is the end-termof the second premise in figure 1, A–B/B–C, and the end-term of the first premisein figure 2, B–A/C–B).

Our prediction based on Ford’s theory (1994) is that the highest level ofactivation corresponds to the first end-term of the premise that the rule identifieswhen it is applied. In the syllogism of the form “all of the A are B / All of the B areC”, “C” is the first end-term of the premise that the rule identifies, so this termwill be the most active. In the syllogism of the form “all of the B are A / All of theC are B”, “A” is the first end-term of the premise that the rule identifies, and thisterm will be the most active.

On the contrary, our prediction based on Yule and Stenning (1992) is that thehighest level of activation corresponds to the term that comes from the source


premise. In the syllogism of the form “all of the A are B / All of the B are C”, “A”is the term from the source premise, and this term will be the most active. In thesyllogism of the form “all of the B are A / All of the C are B“, “C” is the term fromthe source premise, and this term will be the most active.

Our predictions based on Polk and Newell’s theory (1995) is that the highestlevel of activation will correspond to the end-term that is the topic (thegrammatical subject) of the premise. In figure 1, “A” is the topic in the annotatedmodel, and this term will be the most active term. In figure 2, “C” is the topic inthe annotated model, so this term will be the most active. In the same way, ourprediction based on Wetherick and Gilhooly’s theory (1990) is that the highestlevel of activation will correspond to the end-term that is the grammaticalsubject of the premise (“A” in figure 1, and “C” in figure 2). Likewise, ourprediction based on Chater and Oaksford’s theory (1999) is that the highest levelof activation will correspond to the end-term that is the grammatical subject ofthe minimal-premise or the maximal-premise. In figure 1, “A” is always thegrammatical subject (in both the minimal premise and the maximal premise), andthese terms will be the most active terms. In figure 2, “C” is always thegrammatical subject (in both the minimal-premise and the maximal-premise),and this term will be the most active.

We designed the second experiment to test the level of activation of the end-terms (A and C) after reading the premises and before evaluating the conclusionof figure 1 and 2 syllogisms. The participants had to decide whether or not a testword (A or C) had been present in the problem. The response time to this questionwas taken as an indicator of the level of activation.

MethodParticipants. A total of 33 students from La Laguna University acted as

participants and received course credit for their participation.

Design and materials. We constructed 24 syllogisms, 12 syllogisms of figure1 (A–B/B–C and 12 of figure 2 (B–A/C–B) with the universal affirmativequantifier (ALL) in both premises. The participants were presented with a testword and were asked if it appeared in the previous sentences. We asked 24questions (TEST WORD), 12 questions when the test word was the end-term inthe first premise (“A”) and 12 questions when the test word was the end-term inthe second premise (“C”). That is, when the test words appeared in contexts thatsome theories would predict to lead to the highest amount of activation, theyalso appeared in contexts that the same theories would predict to lead the lowestactivation. An example for each figure appears in Table 3 (all the materials in thispaper are translated from Spanish). We constructed 12 lure syllogisms, 6syllogisms of figure 3 (B–A/B–C) and 6 syllogism of figure 4 (A–B/C–B) withdifferent quantifiers (SOME, NONE, SOME ... NOT). In the lure syllogisms, thetest words had not occurred in the premises.


To ensure adequate comprehension, and to encourage participants to payattention to all aspects of the sentences (not just the terms), each pair of premiseswas followed by one candidate conclusion that the participants had to evaluateas true or false. The end-term of the candidate conclusion was counterbalanced(A–C in half of the trials and C–A in the other half). This candidate conclusionwas presented immediately after the test word. In each figure, we presented fiveuniversal affirmative conclusions, four universal negative conclusions, twoparticular affirmative conclusions, and one particular negative conclusion.

Procedure. A trial began with a warning signal, which was a plus signappearing for 750 milliseconds in the centre of the screen. After the warningsignal disappeared, two premises appeared (also in the centre of the screen) for5000 msec. The interval between the disappearance of the premises and the testwords was 150 msec. The test words appeared in capital letters at the top of thescreen and remained on the screen until participants responded or 3 secondselapsed. Participants responded by pressing one of two response keys; one waslabelled “yes”, the other “no”. 250 msec after the participants responded to thetest word, the word “PREGUNTA” (“QUESTION”) appeared towards the bottomof the screen to warn participants of an upcoming candidate conclusion. Thiswarning signal remained on the screen for 750 msec, after which the candidateconclusion appeared and, below it, two answer choices. One answer waspositioned towards the left side of the screen, and the other towards the right side.Participants pressed the left-most response key to select the answer on the left orthe right-most response key to select the answer on the right. The correct answerchoices appeared equally often on each side of the screen. The question andanswer choices remained on the screen until either the participants responded or10 seconds elapsed. Immediately after responding, the participants were givenfeedback about their accuracy. The time of duration of feedback was 1500 msec.The participants practised on three three problems before they began theexperiment.

The experiment had two sessions with 18 syllogisms each. Between sessionone and two, the participants had a break of five minutes. The order of sessionswas counterbalanced.

TABLE 3Problem-type used in Experiments 2, 3, and 4

SENTENCE: All the Spanish are physiologistsAll the physiologists arepolicemen

TEST WORD: SPANISHREASONING QUESTION Are all the Spanish policemen?

In Experiment 4 we used the particular affirmative quantifier(SOME) in the premises.


Four participants were replaced because they failed to meet the followingcriteria: 90% accuracy in responding to experimental test words (requiring a“yes” response), 90% accuracy in responding to lure test words (requiring a “no”response), and 65% accuracy in answering the reasoning questions.

Results and discussionThe analyses here are based on response times for correct responses to the testword. The repeated-measures ANOVA revealed an interaction effect, F(1,28) =15.08, p < .0001, MSE = 5984 between the place of the end-terms in thesyllogism (first or second premise) and figure (figure 1 or figure 2). In figure 1syllogisms, the end-terms of the second premise were responded to 56 msec fasterthan the end-terms of the first premise (end-terms of the second premise = 1083msec; end-terms of the first premise = 1139 msec). In figure 2 syllogisms, the end-terms of the first premise were responded to 56 msec faster than the end-terms ofthe second premise (end-terms of the first premise = 1134 msec; end-terms of thesecond premise = 1190 msec). We found main effects for the type of figure,F(1,28) = 13.40, p < .0001, MSE = 5656. The participants used less time torespond to the test word in the figure 1 syllogisms (1111 msec) than in the figure2 syllogisms (1162 msec). The total percentage of correct responses to thereasoning questions was 67%.

Post-hoc analyses showed that the differences in the response times to the testword were only reliable in the second premise, where the test words of figure 1problems were read faster than those of figure 2 (LSD = 74.61; p < .0005).

These results are consistent with our predictions based on the model theory.The first result suggests the existence of a recency effect of the last end-term ofthe composite mental model. In figure 1 syllogisms (A–B/B–C), the last term ofthe composite mental model is the end-term of the second premise (“C”). Infigure 2 syllogisms (B–A/C–B), the last term of the integrated mental model isthe end-term of the first premise (“A”). These effects of recency of the last end-term of the composite model could arise because until reasoners integrate theconclusion in the mental model of the premises, they have greatest access to thelast information that they are currently processing. They use the last element ofthe model to integrate the upcoming information in their representation. Theresults are in opposition to our predictions about activation based on Polk andNewell’s theory (1995), Wetherick and Gilhooly’s theory (1990), Yule andStenning’s theory (1992) and Chater and Oaksford’s theory (1999), but areconsistent with our predictions based on Ford’s theory (1994) for verbalreasoners.

The second result showed that the participants used less time to respond to thetest word in figure 1 syllogisms than in figure 2 syllogisms. This result suggeststhat the former syllogisms are easier than the latter, as predicted by the modeltheory, as a consequence of the process of switching around the premises to


create a composite model. This result contradicts the predictions of Ford (1994)and Chater and Oaksford (1999). Ford maintains that syllogisms of the forms“All of the B are A / All of the C are B” are easier than syllogisms of the form “Allof the A are B / All of the B are C”, while no Chater and Oaksford postulate thatthere are no differences in difficulty between syllogisms of different figures.

EXPERIMENT 3The results of the second experiment showed the interaction that we predictedfrom the model theory and Ford’s theory. However, there could be anotherexplanation for these results. These recency effects could be a consequence ofthe short time between the last premise and the test word. It could be thatparticipants were caught at different stages in their cycles of rehearsing the twoend-terms (see Gernsbacher, 1990). This would explain the greater accessibilityof the last term. To rule out this explanation, we conducted a third experiment inwhich we delayed the test point for a total of 2000 msec. In this experiment, weinvestigated whether lengthening the time between the presentation of thepremises and the test word would give participants greater access to theinformation in the last position in the model. To test this hypothesis we used thesame procedure as in Experiment 2, but we presented the test word 2000 msecafter the second premise.

MethodParticants. These were 33 from La Laguna University who received course

credit for their participation. Five participants were replaced because they failedto meet the criteria described in Experiment 2.

Design and materials. We used the same design and materials as inExperiment 2.

Procedure. The same as in Experiment 2 was used, except that the test wordappeared 2000 msec after the premises disappeared.

Results and discussionOnly the RTs for correct responses to the test word were used in the analyses. Therepeated-measures ANOVA revealed an interaction effect, F(1,27) = 43.22, p <.0001, MSE = 7611, between the place of the end-terms in the syllogism (first orsecond premise) and figure (figure 1 or figure 2). In figure 1 syllogisms, the end-terms of the second premise were responded to 120 msec faster than the end-terms of the first premise (end-terms of the second premise = 1041 msec;end-terms of the first premise = 1161 msec). In figure 2 syllogisms, the end-termsof the first premise were responded to 90 msec faster than the end-termspresented in the second premise (end-terms of the first premise = 1098 msec; end-


terms of the second premise = 1194 msec). We again found main effects for thetype of figure, F(1,27) = 8.06, p < .01, MSE = 6970. The participants used lesstime to respond to the test word in the figure 1 syllogisms (1101 msec) than infigure 2 syllogisms (1146 msec). The total percentage of correct responses to thereasoning questions was 68%.

In this experiment, a post-hoc analysis showed that the difference in theresponse time to the test word was reliable both in the second premise (LSD85.64; p < .0005) and in the first premise (LSD = 57.50; p < .01).

These results confirm the existence of a recency effect of the last end-term ofthe composite mental model that continued until 2000 msec after presenting thepremises. This result supports the idea that the recency effect is a relatively long-lived feature of there presentation of the syllogism. The results of thisexperiment confirm the hypothesis that participants build different mentalmodels in solving figure 1 and figure 2 syllogisms. As in Experiment 2, theresults oppose our predictions about activation derived from Polk and Newell’stheory (1995), Wetherick and Gilhooly theory’s (1990), Yule and Stenningtheory’s (1992) and Chater, and Oaksford theory’s (1999), but they areconsistent with our predictions based on Ford’s (1994) hypothesis for verbalreasoners.

The result that the participants used less time to respond to the test word infigure 1 syllogisms than in figure 2 syllogisms opposes Ford’s and Chater andOaksford’s predictions. According to Ford’s model, the verbal reasoners wouldfind figure 2 easier than figure 1. Chater and Oaksford (1999) postulate that thereare no differences between the different figures. However, the result is consistentwith the predictions of the model theory.

EXPERIMENT 4The previous experiments give clear support to the mental models theory ofreasoning by showing an interaction predicted by us based on this theory thatcannot be accounted for by the theories of Polk and Newell (1995), Wetherickand Gilhooly (1990), Yule and Stenning (1992) or Chater and Oaksford (1999).We explained these results as an advantage of the last element in the compositemodel. However, within the model theory there could be another explanation forthe interaction. It could be that the terms that attain greater activation within amodel are those that are not exhaustively represented in the model. For example,the following pair of premises:

All of the athletes are bakersAll of the bakers are canoeists

yields the composite mental model:

[[athlete] baker] canoeist[[athlete] baker] canoeist…


Where, as indicated by the absence of square brackets, “canoeist” is the onlyterm that is not exhausted. This means that this term could occur anywhere in theimplicit individuals (signified by the three dots). In contrast, in figure 2 the end-term in the first premise is the term that is not exhaustively represented. It couldbe that the participants focus their attention on the non-exhausted terms of theproblem because they are of central importance if the implicit models are to befleshed-out.

Experiment 4 tested this possibility by using the existential quantifier“SOME” instead of the universal “ALL” in both premises. Consider, forexample, the premises:

Some of the athletes are bakersSome of the bakers are canoeists

They support the composite initial model:

athletes bakers canoeistsathletes bakers canoeists

…

In these cases, none of the terms is exhaustively represented, and so nodifferences would be expected if the exhaustivity hypothesis were true.

MethodParticipants. These were 31 students from La Laguna University who

received course credit for their participation. Two participants were replacedbefore data analysis because they failed to meet the criteria described inExperiment 2.

Design and materials. The same design and materials were used as inExperiment 3, used figure 1 and figure 2 premises with the particular affirmativequantifier (SOME) in both premises. For each figure we presented four universalaffirmative conclusions, four universal negative conclusions and four particularaffirmative conclusions.

Procedure. The same procedure as in Experiment 3 was used.

Results and discussionWe only used the correct response times to the test word in the analyses. Therepeated-measures ANOVA revealed an interaction effect, F(1,28) = 23.84, p <.0001, MSE = 15800, between the place of the end-terms in the syllogism (first or


second premise) and figure (figure 1 or figure 2). In figure 1 syllogisms, the end-terms in the second premise were responded to 70 msec faster than the end-termsin the first premise (end-terms in the second premise = 935 msec; end-terms in thefirst premise = 1005 msec). In figure 2 syllogisms, the end-terms in the firstpremise were responded to 158 msec faster than the end-terms in the secondpremise (end-terms in the first premise = 951 msec; end-terms in the secondpremise = 1109 msec). We found main effects for the type of figure, F(1,28 =10.37, p < .005, MSE = 10024. The participants used less time to respond to thetest word in figure 1 syllogisms (970 msec) than in figure 2 syllogisms (1030msec). Moreover, in this experiment we found main effects for the place of theend-terms in the premise, F(1,28) = 5.68, p < .05, MSE = 10108. The participantsused less time to respond to the test word (end-term) from the first premise (978msec) than to that from the second premise (1022 msec ). The total percentage ofcorrect responses to the reasoning questions was 84%.

A post-hoc analysis showed that the difference in response time to the testword was only reliable for the second premise (LSD = 120.78, p < .0005).

These results permitted us to reject the exhaustivity hypothesis by confirm-ing that the interaction arises because the participants pay more attention to theinformation holding the last position in the model. This could be a generalpreference because the last term in the model is normally where new informationwould be attached. In the type of problems we have used, this new information isincluded in the conclusion proposed to the participants. As in the previousexperiments, these results are very difficult to explain by the theories of Polk andNewell (1995), Wetherick and Gilhooly (1990), Yule and Stenning (1992), andChater and Oaksford (1999).

EXPERIMENT 5

If the interaction found in Experiments 2, 3, and 4 is due to a preference to attachnew information to the last element in the model, then this effect shoulddisappear when the participants know that no additional information ispresented after the test word. Moreover, the structure-building framework(Gernsbacher, 1990) would predict the opposite interaction in this case.Gernsbacher et al. (1989) have shown that an advantage of the first-mentionedterm arises after a two-clause sentence is comprehended. If this effect depends onthe position of the concepts in the model of the problem, then the end-term in thefirst premise should be more active than the end-term in the second premise infigure 1; whereas the opposite pattern would be expected in figure 2. But, if thiseffect depends on which part of the rule is being applied (Ford, 1994), then themore active end-term will be the term of the premise the rule identifies when it isapplied.

Experiment 5 was designed to test the level of activation of the end-terms (Aand C) after evaluating the conclusion.


MethodParticipants. These were 33 students from La Laguna University who

received course credit for their participation. Five participants were replacedbecause they failed to meet the criteria described in Experiment 2.

Design and materials. The same design and materials were used as inExperiment 2. An example for each figure appears in Table 4 (all the materials inthis paper are translated from Spanish).

Procedure. This was as in Experiment 2, except that the test word appeared150 msec after the candidate conclusion. Afterwards participants judgedwhether the test word had appeared in the candidate conclusion.

Results and discussionWe only used the correct response times to the test word in the analyses. Therepeated-measures ANOVA revealed an interaction effect, F(1,27) = 5.19, p < .03,MSE = 6900, between the position of the end-terms in the syllogism (first orsecond premise) and figure (figure 1 or figure 2). In figure 1 syllogisms, the end-terms in the first premise were responded to 24 msec faster than the end-terms inthe second premise (end-terms in the first premise = 950 msec; end-terms in thesecond premise = 974 msec). In figure 2 syllogisms, the end-terms in the secondpremise were responded to 48 msec faster than the end-terms in the first premise(end-terms in the second premise = 989 msec; end-terms in first premise = 1037msec). We also found main effects for the type of figure, F(1,27) = 16.72, p < .001,MSE = 4334. As in the previous experiments, the participants took less time torespond to the test word in figure 1 syllogisms (962 msec) than in figure 2syllogisms (1013 msec). The total percentage of correct responses to thereasoning questions was 79%.

A post-hoc analysis showed that the difference in the response times to thetest word was only reliable for the first premise (LSD 81.56; p < .0005).

In this experiment, we obtained clear support for the hypothesis that theactivation of the terms is a consequence of their position in the composite model.Once participants had finished the problem, greatest activation was maintainedin the first element of the model. The reason could be that this term is thereference point to which all the information in the model is referred.

TABLE 4Problem-type used in Experiment 5

SENTENCE: All the Spanish are physiologistsAll the physiologists are policemen

REASONING QUESTION: Are all the Spanish policemen?TEST WORD: SPANISH


The results oppose the predictions about activation that we derived fromFord’s theory (1994). As we have previously mentioned, our prediction based onFord’s theory is that the highest level of activation will correspond to the firstend-term of the premise that the rule identifies when it is applied. In thesyllogism of the form “All of the A are B / All of the B are C”, “C” is the first end-term of the premise that the rule identifies when it is applied, and so this termshould be the most active. In the syllogism of the form “All of the B are A / All ofthe C are B”, A is the first end-term of the premise that the rule identifies when itis applied, and so this term should be the most active.

GENERAL DISCUSSIONThe experiments reported in this paper confirm the main assumption of themodel theory of reasoning: while comprehending a reasoning problem peoplebuild a representation that goes beyond the superficial structure of the phrasingof the problem. Furthermore, our experiments present new evidence on theprocess of adding information to an existing model.

Evidence of model buildingIn the field of syllogistic reasoning, there are a number of theories that explainthe conclusions that people reach depending on the mode and figure of theproblem (Begg & Denny, 1969; Garcia-Madruga, 1989; Johnson-Laird & Bara,1984; Johnson-Laird & Steedman. 1978; Wetherick & Gilhooly, 1990;Woodworth & Sells, 1935; Yule & Stenning, 1992). A large database ofpercentages of errors and correct responses to the different syllogisms has beenaccumulated from several decades of research.

Consequently, any of the current theories could quite accurately explain thetypical results of traditional syllogistic reasoning experiments. This could leadto the erroneous idea that these theories are quite similar to each other. On thecontrary, the processes assumed by the model theory of reasoning and othertheories are strikingly different (Chater & Oaksford, 1999; Ford, 1994; Polk &Newell, 1995; Wetherick & Gilhooly, 1990; Yule & Stenning, 1992). If theseprocesses depended on the construction of a mental model of the state of affairsdescribed in the problem, not only would responses conform to the predictionsof the theory, but other measures taken during the reasoning and comprehensionprocesses would provide evidence for a representation in the form of a model.

For the theories that consider reasoning a result of the direct application ofrules to the prepositional structure of the premises (Ford, 1994), there is no wayto explain why, as found in Experiment 5, the activation of the terms in thesyllogism is not determined by which part of the rule is being applied. Sometheorists could appeal to a scholastic argument: in figure 1, the subject of theconclusion comes from the first premise and the predicate from the secondpremise, whereas in figure 2, the subject of the conclusion comes from the second


premise and the predicate from the first premise. This could exert some influenceon the activation of the terms because it could be argued that the subject is moreactive than the predicate (see Wetherick & Gilhooly, 1990, for an account of thefigural effect based on this assumption). Similarly, Polk and Newell (1995) haveargued that the subject (or “topic”) of a premise is more accessible and is triedfirst in generating putative conclusions. However, this sort of explanation hasbeen discarded in the field of language comprehension by Gernsbacher andHargreaves (1988) who demonstrated that the advantage of first mention doesnot depend on the first-mentioned term being the semantic agent of the sentence.Moreover, Carreiras, Gernsbacher, and Villa (1995) have shown that this effectdoes not depend on whether the term is the subject or the object of the sentence(there is also an advantage of first mention in Spanish sentences with nonpassiveobject–verb–subject constructions). Furthermore, Espino, Santamaria, Garcia-Madruga, and Carreiras (1997) extended this finding to quantified sentences.With regard to this paper, an explanation based on the subject being more activethan the predicate would fail to explain the results of Experiments 2, 3, and 4where the opposite pattern was found.

Our results cannot be explained by the attachment-heuristic (Chater &Oaksford, 1999). We have found that the activation of the terms does not dependon whether the end-term is the subject of the min-premise or of the max-premise(Experiments 2, 3, and 4). Likewise our results cannot be explained in terms ofthe logical properties of the syllogism (Yule & Stenning, 1992). If the figuraleffect is a consequence of starting the construction of the individual descriptionfrom the source premise, then the end-term that is in the source premise would bemore active than the other end-term. Our results in the Experiment 2, 3, and 4 arein the opposite direction.

One noteworthy finding from our data is to confirm the predictions of thefigural effect in an evaluation task, whereas this effect is not observed with paperand pencil tasks. This results is important because some authors has consider thatthis effect is specific to construction tasks. In this sense, Rips postulates that the“figure effects might be more prominent in experiments in which subjectsproduce their own conclusions…” (Rips, 1994, p.237).

Our results confirm the hypothesis that the activation of concepts involved ina syllogism is determined by their position in the mental model. One of the mainadvantages of this finding for the current state of the art in the psychology ofreasoning is that it directly implies that people build a model of the premises inorder to solve syllogisms. An additional benefit is that it permits us to explorethe time-course of the modelling process.

Attaching information to an existing modelBesides giving support to the model theory of reasoning, our experimentsprovide some general evidence on human thought processes. In particular, we


have investigated the time course of attaching information to the model of thepremises. According to our data (see Experiments 1–4), people seem to bind theincoming information to the last element Experiments l of the model. Thisfinding could reflect a general preference in human cognition which frequentlyaccesses sequential information. When reading a text or watching a sequence ofactions the incoming information is generally more easily ascribable to theimmediately previous information. However, after completion of the compre-hension process, the first information, which served as a foundation for themodel, becomes more relevant (Experiment 5). This time course is consistentwith the classic findings of primacy and recency effects in memory which goback to Ebbinghaus (1885). Our contribution to this topic is its extension to thefield of comprehension of reasoning problems and the finding that it is theposition in the mental model and not in the superficial structure of the materialsthat is responsible for these effects. In the field of language comprehension theorder of the constituents is normally the same as the order of the elements in themodel. However, the same pattern of results would be expected if the appropriatemanipulation were made.

Another noteworthy finding from our data is that reasoners maintain a similarpattern of activation (a dominance of the last element of the composite model)until they finish reading information related to the problem, when the pattern ofactivation is reversed. The recency pattern observed during comprehension israther stable and can be found not only immediately after reading the premises,but also 2000 milliseconds later (Experiment 3), and seems to depend on generalprinciples because it also occurs in problems with non-exhaustive terms(Experiment 4). However, the pattern is reversed when the conclusion has beenread. This suggests that reasoners use the proposed conclusion of an evaluationtask as additional information that they have to append to their current model.

In conclusion, this paper provides evidence for the modelling process andadvances some suggestions concerning its time course. Moreover, our data giveevidence for the figural effect to be regarded as a semantic rather than asuperficial factor, which depends on the position of the concepts in the modelrather than the phrasing of the problem itself.

Manuscript received 14 October 1998.Revised manuscript received 26 August 1999.

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Activation of end-terms in syllogistic reasoning

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