Early and late processes in syllogistic reasoning: Evidence from eye-movements

Abstract

An eye-movement monitoring experiment was carried out to examine the effects of the difficulty of the problem (simple versus complex problems) and the type of figure (figure 1 or figure 4) on the time course of processing categorical syllogisms. The results showed that the course of influence for these two factors is different. We found early processing effects for the figure but not for the difficulty of the syllogism and later processing effects for both the figure and the difficulty. These results lend support to the Model Theory (Johnson-Laird, P. N., Byrne, R. M. J. (1991). Deduction. Hillsdale, New Jersey: LEA.) as opposed to other theories of reasoning (Chater, N., Oaksford, M. (1999). The probability heuristics model of syllogistic reasoning. Cognitive Psychology, 38, 191–258; Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press; Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press).

Introduction

This paper examines the time-course of processing during syllogistic reasoning. This kind of reasoning is produced from pairs of categorical premises such as:

• All Athletes are Brokers

• All Brokers are Catalans

where a valid conclusion is “All Athletes are Catalans”. Depending on the quantifier used, there are four kinds of premise and conclusion:

• All A are B (A)

• Some A are B (I)

• No A are B (E)

• Some A are not B (O)

The letters in parentheses are the traditional abbreviations for each kind of proposition. The arrangement of terms in the pair of premises determines the figure of the syllogism. There are four figures:

A is the extreme-term in the first premise (e.g. Athletes); B is the middle-term, that appears repeated in both premises (e.g. Brokers), and C is the extreme-term in the second premise (e.g. Catalans). Previous research (Bucciarelli and Johnson-Laird, 1999, Chater and Oaksford, 1999, Dickstein, 1978, Espino et al., 2000a, Espino et al., 2000b, Ford, 1995, Johnson-Laird and Bara, 1984, Polk and Newell, 1995, Wetherick and Gilhooly, 1990) has shown that the figure produces a response bias (figural effect). This effect is particularly clear in figures 1 and 4, and shows that in figure 1 there is a preference to build conclusions in the order C-A, while in figure 4 the preference is to build conclusions in the order A-C. Furthermore, the figure of the syllogism affects the processing time. Espino et al. (2000a) found that figure 4 syllogisms are processed faster than figure 1 syllogisms. Although the figural effect has been known for a long time there is no clear consensus about its actual nature.

Chater and Oaksford (1999) proposed the probability heuristic model (PHM) of syllogistic reasoning in which probability-based heuristics allow the generation of the most informative conclusion. The most relevant heuristics in PHM to explain the “response bias” are the min-heuristic and the attachment heuristic. The min-heuristic chooses the quantifier of the conclusion while the attachment heuristic specifies the order of end terms in the conclusion. Two predictions from PHM are important for our present research. First, PHM predicts that the conclusion order is determined by the conclusion type. In other words, “the order of the end term is decided after conclusion type is selected” (Chater & Oaksford, 1999, p. 212). Second, PHM predicts that the figure does not affect the difficulty of the task.

In contrast, for the Mental Model theory (Johnson-Laird & Bara, 1984) the figure affects the task difficulty. The difficulty arises when the separate models of the two premises are combined to form a composite model. This integrated model is obtained by temporally matching the middle terms of the premises. In the syllogisms of figure 4 (A-B/B-C) the composite model is attained directly because the middle terms (the Bs) are adjacent. In the syllogisms of figure 1 (B-A/C-B), the participants cannot build the integrated mental model directly, since the middle terms are not adjacent. In this case, Johnson-Laird and Bara (1984) propose two different procedures. First, the order of the terms within the first premise (B-A) and the second premise (C-B) could be swapped around. The second strategy to build the composite model consists in reversing the order of the two models of the two premises. For figure 1 syllogisms, the simplest way is to use the second strategy. This reversing process leads to more frequent C-A conclusions in figure 1 syllogisms. Therefore, Mental Model Theory predicts that the syllogism figure affects the difficulty of the task (for example, figure 4 syllogisms should be processed in less time than figure 1 syllogisms. Also, a greater number of A-C conclusions should be found with figure 4, while more C-A should be observed with figure 1).

Syllogisms vary widely in difficulty. While some syllogisms are easy and others are so difficult that typically only a few participants give the correct conclusion. There is disagreement about the origin of this divergence. Some authors, such as Braine and O'Brien, 1998, Rips, 1994, postulate that the difficulty of the syllogism depends on the number of inferential steps needed to find proof, and the nature of the rules involved. Mental Model theory (Johnson-Laird & Byrne, 1991) proposes that syllogism difficulty correlates with the number of models that need to be constructed: one-model problems are easier than multiple-model problems. Chater and Oaksford (1999) argue that the difficulty depends on the type of conclusion of the syllogism. If the syllogism has an informative conclusion then it is an easy problem, but if it has an uninformative conclusion, then it is complex.

We carried out an experiment to study the relevance of the figure and the difficulty on the time course of the resolution of syllogisms. This kind of research has implications for current theories of syllogistic reasoning, which predict that these factors could have different temporal courses. Mental-Model theory (Johnson-Laird & Byrne, 1991) proposes that the influence of the figure starts acting before the main factor which determines difficulty (i.e. the number of models), as the figure affects the construction of the composite model/s of both premises. On the other hand, PSYCOP (Rips, 1994) and Mental Logic (Braine & O'Brien, 1998) make no specific predictions about the temporal course of these factors. For the Probability-Heuristic Model (Chater & Oaksford, 1999) the figural effect is an end-result of the attachment heuristic, meaning that the figure has an effect on the construction of the response after other factors have determined the mode or the quantifier. Consequently, the figure should have a late effect, according to this theory.

Early and late effects of the variables we have manipulated in the syllogisms will be detected using a methodology that is new in this field: eye-movement monitoring, or eye-tracking. This technique is based on the assumption that the direction of our eyes can tell us something about the processing that is being carried out by our mind (e.g. Rayner & Pollatsek, 1989). Variations in eye fixation in terms of duration and position reflect variations in the difficulty of the words being looked at. The eye-tracking technique provides information about what is happening during both early and late processes of reading. To study these processes, we have chosen to analyse the eye-tracker measures of First Pass Time and Total Reading Time. First Pass time is defined as the sum of the durations of the fixations the reader makes in a given part of a sentence (a word or a group of words) from the time he/she enters in it until he/she leaves it forwards or backwards for the first time. It is generally assumed that this measure is sensitive to early processes in the comprehension of a sentence, such as syntactic parsing and the early integration of information. On the other hand, Total Reading time is defined as the sum of the duration of all the fixations made in a given part (a word or a group of words) of a sentence. It is assumed that this measure is sensitive to the later processes involved in the comprehension of sentences, such as re-analysis and discourse integration (e.g. Paterson et al., 1999, Rayner et al., 1989).