Elsevier

Cognitive Brain Research

Volume 18, Issue 2, January 2004, Pages 130-141
Cognitive Brain Research

Research report
P600 related to rule violation in an arithmetic task

https://doi.org/10.1016/j.cogbrainres.2003.09.010Get rights and content

Abstract

The goal of the present paper was to study if a similar neurophysiological process is required for treating violations of both arithmetical rules and linguistic syntactic structures. It has been shown that syntactic violations elicit the P600/syntactic positive shift (SPS) component, reflecting secondary parsing processes or repairing of an incorrect syntactic structure. However, late positivities, similar to the P600/SPS component, are also elicited by other types of violations (e.g. harmonic anomalies or violations in non-linguistic abstract rules), so this component is thought to be an index of detection for any anomaly in rule-governed sequences. We carried out an experiment where violations of arithmetic rules were presented. These violations were evident to a greater or lesser degree (a number very different or very similar to that which correctly completed a series of seven numbers). The type of rule was also manipulated, and increasing and decreasing series were presented. Results showed a late centro-parietal positivity related to arithmetic violations, whose amplitude was larger, the more evident the violation presented was, in both addition and subtraction. It is concluded that a similar neurophysiological process could be required for the processing of violations in numerical sequences and in linguistic syntactic structures. When the rule was broken, another component was present for the adding operation: an early negativity peaking between 250- and 300-ms post-stimulus. Regarding this negative peak, although some possible explanations are drawn, further research needs to be carried out in order to gather more knowledge about it.

Introduction

In recent years, many researchers have studied the linguistic specificity of some components of event related potentials (ERPs) (for a review, see [14], [55], [56]). This interest is due to the fact that these linguistic components can be used to gather more knowledge about language processing. Psychophysiological research has so far reported a component that seems to be specific for semantic processing1, and other components related to syntactic processing. One of these syntactic components is the core of this paper.

Three ERP components have been associated with syntactic processing: the early left anterior negativity (ELAN), the left anterior negativity (LAN), and the syntactic positive shift (SPS)—this latter component was called P600 by Osterhout and Holcomb [46] and SPS by Hagoort et al. [21]. ELAN, LAN and P600/SPS components are elicited by a variety of syntactic and morphosyntactic violations. ELAN and LAN are two negative components that present similar scalp distribution but which differ in latency. ELAN is a negativity peaking approximately 150–200 ms after stimulus, which has its maximum amplitude in the left anterior region of the scalp, and that has been reported in phrase structure violations in both visual and auditory modalities [15], [42]. LAN is also a negative peak with a left anterior distribution, but differs from ELAN in latency—it presents its maximum amplitude at about 400-ms post-stimulus. This component has been reported in inflectional verb violation [48], [54]. The functional nature of these components is still unclear, although they are believed to reflect the first-pass parsing stage, which is said to operate quite quickly and automatically—these components have been found to be independent of attentional factors [16], [17], [19], [20], [22]. Gunter et al. [20] refer to LAN as a “more primary/automatic reflection of syntactic violation than the P600” ([20], p. 672). The LAN component has also been associated with aspects of working memory [30], [32] and with the processing of word class information [6], [57].

The most extensively studied component related to syntactic processing is P600/SPS, a late positive component, peaking around 600 ms after stimulus onset, which has a centro-parietal distribution. P600/SPS is elicited by syntactic violations, and is considered to be a reflection of secondary parsing processes including re-analysis or repair of an incorrect structure [17], [19], [22]. Moreover, P600/SPS has a more controlled nature than either LAN or ELAN. Gunter and Friederici [19] found that P600 amplitude was reduced when they presented verb inflection violations to subjects who were required to judge if a word in a sentence was printed in upper case.

Another characteristic of the P600/SPS component is that its amplitude is also sensitive to the severity of syntactic anomalies. Osterhout et al. [49] presented syntactically correct sentences, violations of verb subcategorization and subcategorization biases. Whereas the first violations produce an irreversible ungrammaticality (thus making the sentence uninterpretable), violations of subcategorization biases merely require a structural re-analysis of the sentence (in this case, the subject is forced to re-analyze the sentence to turn to the less-preferred syntactic analysis for the sentence). In other words, sentences were manipulated in such a way that they were easy, difficult or impossible to integrate within the prior context. P600/SPS amplitude was modulated by integration difficulty, it being largest for the strongest violation. Osterhout et al. ([49], p. 798) concluded that the larger the P600/SPS, the more difficult it is to construct a grammatical representation. Two specific explanations were given for this finding. First, that the “P600 amplitude is sensitive to the syntactic fit between a sentence constituent and preceding sentence structure in a manner analogous to the way that N400 amplitude is a function of the semantic fit between a word and preceding context”. Second, that “the amplitude variation in the P600 reintroduces the notion of cost of reprocessing” ([49] p. 798). The first explanation accounts for the P600/SPS amplitude as a function of the syntactic expectations, whereas the second explanation claims that P600/SPS amplitude depends on the ease with which an alternative analysis can be constructed.

Although P600/SPS could be considered to be a specific linguistic component, some authors question this. Firstly, it has been said that P600/SPS could be a P3b component. P3b is a centro-parietal component which is thought to reflect the resolution of prior uncertainty and the task-relevant surprise value of the stimulus: its amplitude is proportional to the probability of the stimulus and its latency varies with the difficulty of the task [52], [53]. Some years ago, there was an interesting debate about P600/SPS-P3b similarities between Coulson et al. [9], [10] and Osterhout and Haggort [45]. The question as to whether P600 is a specific syntactic index or a reflection of a more general mechanism is still unresolved.

A second group of authors argues against the language specificity of P600/SPS and claims that this component, rather than being syntactic, is related to any anomaly in rule-governed sequences. Patel, Gibson, Ratner, Besson and Holcomb [51] compared ERP patterns elicited by syntactic anomalies in sentences and harmonic anomalies in music. A positive peak similar in latency, polarity, amplitude and scalp distribution was found whenever an anomaly, syntactic or harmonic, was presented (late positivities to deviant notes in musical melodies have also been reported by Besson and Faı̈ta [3] and Janata [25]). Patel et al. [51] also manipulated the integration difficulty in music and language and found similar results to those reported by Osterhout et al. [49]: the amplitude of the positive peak increased when the stimulus was more difficult to integrate. This amplitude variation was present in both language and music. Consequently, Patel et al. ([51], p. 726) stated that “the positivities to structurally incongruous elements in language and music do not appear to be distinguishable”. Similarly, a late positivity comparable to the P600/SPS component has been reported when presenting orthographic anomalies (mis-spelled words) [41] or violations in non-linguistic abstract sequences [4], [39], [40]. These results once again question the syntactic specificity of the P600/SPS component.

Studies with arithmetical tasks have also reported late positive components (LPC) when an arithmetic rule is broken [43], [44]. Niedeggen and Rösler [43] used an arithmetic task consisting of multiplication problems (a×b=c). The solution to the product—number c—was manipulated by presenting the correct number or an incorrect number that differed either by a small, medium, or large numerical distance from the correct product. An LPC was elicited whenever an incorrect number was presented. This component peaked around 600-ms post-stimulus and had a posterior distribution; moreover, the amplitude of this component increased monotonically with increasing numerical distance from the correct solution. Nieddegen and Rösler [43] stated that “this pattern suggests that the LPC amplitude is a function of the implausibility of a presented solution, a possibility that fits with the well-established interpretation that the LPC amplitude is always inversely proportional to the subjective probability of its evoking event” ([43], p. 274). Although these authors related this LPC to the P3b, it is also similar to the component reported by Osterhout et al. [49] in syntactic violations, and that reported by Patel et al. [51] in musical violations. All three components match in terms of polarity, topography, latency, and sensitivity of the same experimental manipulation. As for this last point, reaction time studies have described the split effect: the more distant the proposed results from the correct result in an arithmetic operation, the faster subjects classify the result as incorrect [1], [2]. The split effect is thought to reflect the comparison of the result computed by the subject with that proposed by the experimenter—in other words, it reflects the calculation verification. In this sense, split effect reflects a process similar to the syntactic verification reported in sentences [49], [51] or the harmonic verification reported in music [51]. Recently, El Yagoubi, Lemaire and Besson [13] have reported differences in the ERP pattern when subjects have to verify small and large-split problems. It has been found that small-split problems are associated with less positivity than large-split problems.

Although the arithmetic LPC reported by Niedeggen and Rösler could be considered to be a general index of anomaly detection in rule-governed sequences, the number processing model proposed by Dehaene and Cohen [11] enables us to relate the arithmetic LPC to linguistic processing. Dehaene and Cohen's triple-code model postulates that arithmetic facts, such as multiplication and addition tables, are stored in a verbal word frame “in which numbers are represented as syntactically organized sequences of words” ([11], p. 85). This model also proposes that complex operations with numbers, such as subtraction problems or number comparison—which are not learnt by rote verbal learning—need to pass through the magnitude representation of the quantity in order to be solved. This magnitude representation is thought to be stored in a preverbal system of arithmetic reasoning. Single-case studies performed with brain-damaged patients supported the triple-code model (see, for example, Ref. [8]): “Some patients with left parietal lesions exhibit a loss of the sense of numerical quantity with a relative preservation of rote language-based arithmetic such as multiplication tables. Conversely, aphasia following left-hemispheric brain damage can be associated with a selective impairment of rote arithmetic and a preserved sense of quantity” ([12], p. 973). According to the Dehaene and Cohen model, the LPC reported by Niedeggen and Rösler [43] could be explained in terms of the linguistic P600/SPS component, because arithmetical fact retrieval depends on the general language processing system.

The aim of the present study was to find out if P600/SPS is a language-specific component or if it could be elicited by other violations of rule-governed sequences. We worked with series of seven numbers where a simple arithmetic rule could be easily discovered. The last number of the series could end it in three different ways: the correct number, an incorrect number very similar to the correct one, or an incorrect number very different from the correct one. Thus, we wanted to manipulate the integration difficulty of the number with the previous series. The arithmetic rule was also manipulated and consisted of adding or subtracting a constant number. Addition and subtraction were selected because evidence about some processing dissociation for these two arithmetical rules could be investigated. Moreover, neither processing increasing series nor processing decreasing series seem to rely on memorized syntactically organized sentences, according to Dehaene and Cohen's model [11]. As it has been mentioned before, this model argues that only addition and multiplication tables are stored as syntactically organized sequences of words. Therefore, increasing and decreasing series of seven numbers can be considered non-linguistic sequences governed by arithmetical rules.

According to the previous reasoning, if a violation of an arithmetical rule elicits a positivity peaking around 600 ms, with maximum amplitude at centro-parietal regions and whose amplitude varies depending on the difficulty of integration of the number in the previous series, it can be concluded that this positivity is functionally similar to the P600/SPS component. Consequently, similar neurophysiological processes could be required for the processing of numerical sequences and linguistic syntactic structures.

Section snippets

Participants

Fourteen volunteers (11 women; age 20–33 years, mean=22.1, standard deviation=3.4; 12 right-handed) took part in the experiment. All participants were university students and had normal or corrected-to-normal visual acuity. Written informed consent was obtained from all participants prior to the start of the experiment.

Stimulus materials

The stimuli were series of seven Arabic numbers: the first six digits constituted the series and the seventh was the ending. Series were constructed in the following way: the

Results

Figs. 2 and 3 show the grand average ERPs for the different final numbers in increasing and decreasing series, respectively. As for the increasing series—those consisting of adding a number—the presence of an early negativity, peaking between 250 and 300 ms, should be noted, followed by a positive wave (peaking around 600 ms) of large amplitude when a clear incorrect ending was presented. A similar pattern can be seen in confusing incorrect endings, but, in this case, the late positivity was

Discussion

The main goal of the present study was to examine whether the P600/SPS component is a specific linguistic component or if, conversely, it could be considered to be a more general index related to violations in any rule-governed sequence. To this end, we presented anomalies in increasing and decreasing series, whose difficulty of integration was manipulated. We hypothesized that P600/SPS specificity would be brought into question if a late positivity, similar to this component, was elicited by

Acknowledgements

This research was supported by grant FI-PG/95-1.191 from the Generalitat de Catalunya. The authors thank Antonio Solanas, Carles Escera and Nuria Sebastian for their helpful comments on an previous draft of this paper. The authors also thank two anonymous reviewers for their helpful suggestions on an earlier version of this manuscript. A special acknowledgment to Isabel Palmerı́n, who gave us time to finish this paper.

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