CLASSIFYING EVENT RELATED POTENTIALS FOR VALID
AND PARADOX REASONING
Solomon Zannos
3
, Fotios Giannopoulos
3
, Dimitrios Arabadjis
3
, Panayiotis Rousopoulos
3
,
Panos Papageorgiou
4
, Elias Koukoutsis
3
, Constantin Papaodysseus
3
and Charalabos Papageorgiou
1, 2
1
University Mental Health Research Institute (UMHRI), Athens, Greece
2
1st Department of Psychiatry, National University of Athens, Medical School, Eginition Hospital, Athens, Greece
3
School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece
4
Department of Electrical and Computer Engineering, University of Patras, Patras, Greece
Keywords: Event related potentials (ERPs), Curve fitting, Valid reasoning, Paradox syllogism, Aristotle’s reasoning,
Zeno’s paradoxes.
Abstract: In this paper, a new methodology is presented for comparing the ERPs of Aristotle's "valid reasoning" and
Zeno's "paradoxes". To achieve that, the ERPs of each such syllogism are grouped, by means of a new care-
fitting approach. This consists of a) application of time-domain and amplitude scaling to one ERP and b)
optimal fit of two ERPs via minimization of a properly defined error function. Next, the optimally fit ERPs,
which form a group, are averaged to obtain an ideal representative for the valid and paradoxes reasoning
separately. These ideal representatives manifest essential statistical differences per subject for a
considerable number of electrodes (18 electrodes). The latter supports the assumption that the underlying
mental processes of the valid and paradoxes reasoning are, indeed, different and this difference reflects upon
the corresponding ERPs and, in particular, upon the introduced ideal representatives.
1 INTRODUCTION
One of the most advanced intellectual abilities of
humans is the capacity to reason. Following
Aristotle, the reasoning starts with a set of two
statements such as “All men are mortal”; “All
Athenians are men”. Aristotle argued that these
statements imply that “All Athenians are mortal”
with absolute certainty. A series of relationships
described by the predicative verb “are” and specified
by the quantifier “all”, constitute the inference and
insure its validity (The revised Oxford Translation of
Aristotle, 1995). Syllogistic reasoning has
historically been the subject of active philosophic
and psychological inquiry, but only recently,
specific models of encoding and elucidating the
underlying mechanisms have been proposed;
however, the underlying processes are poorly
understood (De Neys, 2006); (Rodriguez-Moreno
and Hirsch, 2009).
In juxtaposition to this, Zeno the Eleatic, about
2500 years ago, conceived a number of paradoxes,
based on the axiom of the unity and permanence of
being (a fundamental principal of the doctrine of his
teacher Parmenides). Zeno employed the method of
indirect proof in his paradoxes consisting of three
major steps: 1) a temporal assumption of a thesis
that he opposed, 2) an attempt to deduce an absurd
conclusion or a contradiction, thereby 3) the
undermining of the temporary assumption. These
paradoxes have always amazed philosophers and
mathematicians, highly influencing subsequent
research (Atmanspacher et al., 2004); (Caveing,
2000); (Simplicious. In Physica, 1882). Zeno’s
reasoning may be seen as akin to the cognitive
illusions, which appear to violate the norms of
rational thought only in philosophical speculation
(Atmanspacher et al., 2004); (Strumia, 2007).
The nature of the mental processes induced by
the paradoxes remains an open, very important
research subject. Such research is not only of
academic interest but also of great importance for
clinical practice. From a cognitive viewpoint, it
seems interesting to study the Zeno's paradoxes
versus the Aristotelian deductive reasoning, using
contemporary technology. The aforementioned,
seemingly unrelated, notions appear to reflect certain
deep, inherent cognitive mechanisms (Turner, 2007).
218
Zannos S., Giannopoulos F., Arabadjis D., Rousopoulos P., Papageorgiou P., Koukoutsis E., Papaodysseus C. and Papageorgiou C..
CLASSIFYING EVENT RELATED POTENTIALS FOR VALID AND PARADOX REASONING.
DOI: 10.5220/0003767702180225
In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 218-225
ISBN: 978-989-8425-89-8
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
Hence, the present research was designed to
study healthy subjects engaged into two reasoning
tasks, valid syllogisms versus paradoxes, adjusted to
induce working memory (WM).
Contemporary neuropsychological views define
WM as the capacity of the human subject to keep
information ‘on-line’ necessary for an ongoing task
(Baddeley, 1998); (Collette and Van der Linden,
2002). Accordingly, WM is not for ‘memorizing’
per se; it is rather in the service of complex
cognitive activities, such as reasoning, monitoring,
problem solving, decision making, planning and
searching/shifting the initiation or inhibition
response (Miyake and Shah, 1999); (Glassman,
2000). Thus, WM incorporates, among others, a
central executive system. Therefore, the present
study, dealing with a sample of healthy adults, aims
at determining if different patterns of electro-
physiological activity exist, as reflected by event
related potentials (ERPs). Each experimental
condition and setting is adjusted, so as to induce
working memory operation.
Event-related potential (ERP) techniques are
known to be useful tools in the investigation of
information processing and seem to be sensitive to
subtle neuropsychological changes (Kotchoubey,
2006); (Kotchoubey et al., 2002); (Papageorgiou and
Rabavilas, 2003); (Papageorgiou et al. 2004);
(Beratis et al. 2009). The main goal of the present
work is to provide direct evidence of association
and/or dissociation of Aristotelian syllogistic
reasoning and reasoning induced during the
exposition to paradoxes. A comparative study of
these activation patterns in Aristotelian and paradox-
related reasoning could reveal critical aspects of
reasoning processing, associated with perception,
attention and cognitive behaviour. We note that
these aspects are unobservable with behavioural
methods alone.
2 METHODS
2.1 Participants
This study was approved by the Ethics committee of
University Mental Health Research Institute
(UMHRI). Thirty-one healthy subjects (aged 33.6
years on average, standard deviation: 9.1; 17 males)
participated in the experiment. All participants gave
written consent, after being extensively informed
about the procedure. They all had normal vision and
no one had neurological or psychiatric history.
2.2 Behavioural Procedures and the
Four Different Classes of Questions
The participants were seated comfortably 1m away
from a computer monitor in an electromagnetically
shielded room. First, proper instructions were given
to the participants together with a training test. The
participants entered the formal experimental session,
once they had fully comprehended the experimental
task. The experiment was designed to validate two
mental functions, one associated with “valid”
syllogisms and another with “paradox reasoning”.
Two indicative examples follow:
A) Concerning the class “valid”, the following
statements were shown to each participant: “All men
are animals. All animals are mortal. Hence, all men
are mortal.”
B) Concerning the class “paradox”, the following
statements were shown to each participant: “A
moving arrow occupies a certain space at each
instant. But, when an object occupies a specific
space, it is motionless. Therefore, the arrow cannot
simultaneously move and be motionless.” (The
revised Oxford Translation of Aristotle, 1995).
Every such sequence of statements, forming a
reasoning, appeared on the computer monitor
accompanied by the question “true or false”. The
duration of the presented sentence was directly
proportional to the letters involved in each sentence
as described in Table 1.
Table 1: Units for magnetic properties.
Sequence of actions Duration of actions
Valid or paradox sentence
(visual presentation)
Duration according to the
numbers of the letters in the
sentences e.g. a sentence
involving 92 letters presented
11,04sec
EEG recording 1000ms
Warning stimulus 100ms
ERP recording 1sec
Warning stimulus repetition 100ms
Response onset Within 5sec
Period between response
completion and onset of
next sentence presentation
4-9sec
Then, the monitor screen went blank for
1000ms. Next, a sound warning stimulus of 65dB,
500Hz and 100ms duration was given, followed by
the same warning stimulus after 900ms. Participants,
after the second warning stimulus, were asked to
judge each reasoning as either correct or incorrect.
In addition, his/hers estimated degree of confidence
CLASSIFYING EVENT RELATED POTENTIALS FOR VALID AND PARADOX REASONING
219
in each trial was recorded as a number varying from
100 (absolutely certain) to 0 (not at all certain). Each
class of the experiment contained 39 syllogisms.
To avoid habituation with the conditions of the
test, the onset of the next sentence presentation
varied from 4-9sec after completion of the previous
oral response. A complete sequence of events in
each experimental trial is shown in Table 1.
2.3 Experimental Setup and
Recordings
A Faraday cage has been used to eliminate any
electromagnetic interference that could affect the
measurements; the mean field attenuation was more
than 30dB. 30 scalp Ag/AgCl electrodes have been
employed to record the electroencephalographic
(EEG) activity in accordance with the International
10-20 system of electroencephalography (Jasper H.,
1958). These electrodes are shown in a form of map
in Figure 1. Two electrodes, attached to the two ear
lobes, served for obtaining the reference potential.
Recordings higher than 75μV were excluded.
Electrode resistance was kept constantly below 5kΩ.
The amplifiers’ bandwidth was 0.05-35Hz, to avoid
interference with the 50Hz power supply signal. The
evoked bio-potential signal was digitised at a
sampling rate of 1Khz. The signals were recorded
for 2000msec: 1000msec before the first warning
stimulus (EEG) and 1000msec after that (ERP).
2.4 First Stage Processing of the Data
For each question and for each electrode separately,
2000 samples (expressed in μV) have been recorded
in 2sec. We will employ for this subsequence of the
data the symbol
,,
where subscript k runs
through the electrodes, q through the 39 questions, j
through the subjects and X determines the class;
thus, ∈
,
where V stands for “Valid
reasoning” and P for “Paradoxes”. In order to
optimize the signal-to-noise-ratio (SNR) for each
subject, each channel and each class of questions we
have applied a rather standard method: a) For each
question separately, we have averaged the values of
the EEG, namely the data acquired in the 1000ms
before the first sound stimulus. Thus, we have
obtained quantities
,,
, b) We have subtracted
quantity
,,
from
,,
, thus obtaining a translated
version of
,,
for which we will employ the same
symbol, c) We averaged the translated
,,
overall
39 questions, thus obtaining a mean curve
,
, d)
We averaged the first 1000 values of
,
and we
have obtained quantity
,
, e) Finally, we have
calculated the sequence
,
=
,
−
,
.
Figure 1: Map showing the position of the ERPs'
electrodes.
3 A BRIEF DESCRIPTION OF
THE INTRODUCED
APPROACH
We have limited the obtained digital signal
,
to
the time interval (100,400]ms. We have decided to
start from this restricted sequence, since the interval
[1,100]ms refers to the EEG recordings previous to
the first sound stimulus, while in the interval
[301,1000]ms the Contingent Negative Variation
(CNV) (Tecce, 1972); (Neumann et al., 2003) is
dominant. The latter could obscure the analysis we
have developed. We will employ for this restricted
signal the symbol
,
, where, as always, ∈
,
indicating the class of questions, k indicates the
electrode number, except the ones attached on the
ear lobes, and j the subject’s cardinal number.
The basic notion behind the novel approach
introduced here may be described as follows:
Suppose there are causal functions, concerning the
mental processes in hand, common to a group of
persons. Then, one expects that this causality will
reflect in the form of the digital signal
,
. Thus,
we make the fundamental assumption that for each
group of persons sharing the same mental behavior
in “valid reasoning” and\or “paradoxes”, there is a
common underlying prototype curve
,
; in
addition, we assume that the various signals
,
BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing
220
corresponding to individuals belonging to this class,
are noisy versions of
,
. Consequently, we have
developed a method for classifying individuals
according to their “valid reasoning” or “paradox
understanding”, consisting of the following steps:
Step 1
– We have defined a class of transformations
applied to each signal
,
, in order to suppress
causal discrepancies among signals, corresponding
to specific differences in the various subjects’
mental functions.
Step 2
- We have defined an error function
indicating the similarity of two curves. This error
function takes into proper account the
transformations defined in step 1.
Step 3
– We have optimally fit curves
,
using the
results of step 1 and step 2, thus forming sub-groups
of similar curves.
Step 4
– In each such sub-group, we have calculated
a kind of “ideal representative”, by proper averaging
of the optimally fit curves
,
.
Step 5
– Finally, we have regrouped the individuals,
by letting their digital curve
,
fit the ideal
representative, having a fitting error with the curve
in hand, lower than a proper threshold.
4 THE NOTION OF THE ERPS'
IDEAL REPRESENTATIVE
FOR A CLASS OF SUBJECTS
In this section, we will give a more detailed analysis
of steps 1 to 4, introduced in section 3:
Step 1
– To account for latency in the human
response, we have performed time scaling in the
domain of
,
. This is achieved by applying to a
signal () the transformation given by (),
where t corresponds to time and λ is the scaling
factor. When () is a digital signal, say (
), then
the values of the signal in between the samples are
unknown. Thus, (
) in practice is unknown; to
circumvent this difficulty, we first interpolate the
signal by ensuring continuity of it and its first
derivative at the data points.
To account for differences in the ERPs amplitude,
we perform scaling along the y-axis, in which case
signal () yields signal ().
The combined action of these transformations to
a signal () yields signal ().
At this point, we will briefly describe a quite
standard approach used so far: a) One defines four
time intervals in the domain (100,400], namely, the
=
130,180
ms,
=
170,250
ms,
=
250,350
ms and
=
280,400
ms. b) One
computes the maximum of
,
in the interval
; its
value is often denoted by
and the point where
maximum occurs by
. c) One computes the
minimum of
,
in the interval
; its value is
often denoted by
and the point where minimum
occurs by
. d) One computes the minimum of
,
in
; its value is often denoted by
and
its position by
. e) One computes the maximum
of
,
in
; its value is often denoted by
and the point where maximum occurs by
. f)
One performs statistical tests for comparing i) the
peaks’ amplitudes and/or ii) the peaks’ positions,
among subjects, for each electrode separately.
The approach introduced in the present work is
that all these actions must take place on the
smoother and “normalized” curves we call ideal
representatives. The term “normalized” is used to
express the fact that curve fitting is performed after
application of the aforementioned transformations.
In addition, one can perform more statistical tests,
which take into account each ideal representative.
Step 2
- Suppose that a signal
(
)
is the reference
curve, while another signal () is subject to the
transformations described in step 1. Suppose,
moreover, that one wants to compare signals ()
and the transformed (). Then, one may define the
following fitting error ε:
(,)=
1
2
(
(
)
−()
)
(1)
Evidently, when the signals are digital, then the
integral is transformed to summation.
Step 3
- We optimally fit curves
(
)
and the
transformed (), by evaluating those scaling factors
λ and α which minimize the aforementioned error
function (,). Fortunately, this error
minimization has an analytic solution obtained by
setting the gradient of (,) equal to zero:
∗
=0⇒
∗
=
(
+
)
(
+
)
(
+
)
(2)
By substituting
∗
to
(
∗
,
)
, we obtain:
(
∗
,
)
=
1
2
(
+
)
−
∗
(
+
)
(3)
CLASSIFYING EVENT RELATED POTENTIALS FOR VALID AND PARADOX REASONING
221
(
∗
,
∗
)
=0⇒
(
+
)
=0
(4)
But, expanding the above integral we obtain:
(
+
)
=
−
(
)
−
1
(
+
)
(
)
(5)
and finally:
(
∗
,
∗
)
=0⇒
∗
=
(
+
)
(
)
(
−
)
(
)
(6)
Beginning from a point
=
of the - signal
time domain optimal time-scaling
∗
and amplitude
– scaling
∗
are computed via:
∗
=
2
−
,
(7)
∶
1
(
+
−
)
=
(
+
)
(8)
∗
=
∗
(
+
)
(
+
)
∗
(
+
)
(9)
Step 4
- Consider anyone of the digital curves
,
and let it be the reference curve as in steps 2 and 3.
Moreover, consider all other sequences
,
for the
same class X and the same electrode k. We let all
these curves be transformed and optimally fit to the
reference sequence, by the methods described in
steps 1, 2 and 3 above. The corresponding fitting
error is expected to follow a chi-square distribution
, a fact not rejected by the performed related
Kolmogorov-Smirnoff test (α=0.01). If two ERP
curves are noisy versions of the same ideal curve,
then one expects that, statistically, the related error
will be pretty close to zero. Therefore, we choose the
upper point ε
Τ
of the 5% left tail of the above
distribution to be an acceptable threshold for this
error. In other words, if a transformed curve
,
optimally fits to the reference curve with a fitting
error smaller than ε
Τ
, then we may reasonably
assume that these curves belong to the same group.
In this way, to each reference curve
,
, we have
associated a group of corresponding data sequences.
Next, we choose the group with the greater
number of optimally fit curves and we use, for the
corresponding reference curve, the symbol
,
(subscript k is the electrode number and subscript 1
stands for the group’s cardinal number). For the
transformed curves, optimally fit to
,
, we employ
the symbol
,,
, where the additional subscript i
indicates the corresponding transformed curve.
We repeat this process for all groups having
more members than 10% of the individuals sample
size, thus obtaining corresponding reference curve
,
and transformed
,,
.
Consider any reference curve
,
and the
transformed curves
,,
optimally fit to
,
, where,
superscript V stands for “valid reasoning”. Then, for
each sample point in (100,400]ms, we average the
values of
,,
and
,
simultaneously, obtaining a
mean curve denoted by
,
. If the assumption that
there is a causal underlying process for all members
of this group is correct, then one expects that the
averaging process will reduce the overall noise.
Hence, digital curve
,
is a better representative of
the mental process of “valid reasoning” for all
members of the group in hand (Figure 2).
We repeat this process for all groups of the
paradox reasoning, thus obtaining a class of
corresponding “ideal representatives”
,
.
Figure 2: An ERP’s ideal representatives with very low
error, supporting the authors’ assumption about an
underlying common mental behavior per group.
5 STATISTICALLY
SIGNIFICANT DIFFERENCES
IN “VALID REASONING” AND
“PARADOXES” IDEAL
REPRESENTATIVES
We have applied the approach introduced in Section
BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing
222
4 to the data sequences
,
corresponding to the
subjects’ responses to the valid syllogism questions
in one hand and to the subjects’ responses to
paradoxes questions
,
, on the other. In this way,
we have divided the entire class of sequences
,
into, occasionally overlapping, sub-groups, for each
electrode separately. The same was achieved for the
sequences
,
. From each such sub-group, we have
evaluated a representative curve which, we have
called “ideal representative” of the group in hand.
Then, we proceeded to step 5, described below:
Step 5
– We let
,
play the role of the reference
curve of group 1 and we optimally fit all data
sequences
,
to it by application of steps 1 to 4. In
this way, we obtain the final group of subjects,
whose ERPs associated with “valid reasoning”, are
similar to the ideal representative (Figure 3). We
would like to emphasize that this action offered a
larger group of well fitting curves than that in Step 4
for each electrode, when the same error threshold
was used. Equivalently, the number of subjects with
similar “valid reasoning” ERPs is, as a rule,
increased, when the smoother curve
,
is used as a
reference curve instead of the corresponding
,
.
This further supports the assumption that there is a
common underlying brain behavior among all
members of each group.
We have repeated the same process for all sub-
groups of valid reasoning ERPs with analogous
results. Namely, we have considered curve
,
, i.e.
the ideal representative of the second group, and we
let it play the role of the reference curve of the
second group. Subsequently, we have considered all
ERPs not belonging to the first group and we let it
optimally fit
,
with the same method, error
function and error value as in the previous steps.
Keeping the error threshold fixed, we have attributed
to the second group with ideal representative
,
a
specific curve, as far as “valid reasoning” is
concerned. After completing the attribution of ERPs
to the second group of individuals, always for the
same electrode k, we have proceeded in forming the
representative
,
and so on. In this way, finally,
we have selected the smaller class of disjoint groups
covering the entire set of
,
for each electrode
separately. Thus, to each individual who performed
the test and for each electrode separately, we have
attributed a unique ideal representative
,
, namely
the ideal representative of the group to which his/her
“valid reasoning” ERP has been attributed.
The same procedure has been applied to the class
of “paradoxes” ERPs
,
for each electrode
separately. Thus, we have obtained a minimum class
of paradox ideal representatives
,
, together with
a maximal set of
,
optimally fit to it, covering the
entire set of paradox ERPs. Consequently, each
individual, for each electrode k separately, has been
attributed to a specific sub-group, having a concrete
ideal representative
,
, where n is the cardinal
number of the specific distinct sub-group.
Eventually, statistical tests have been applied for
each electrode separately, in order to check possible
statistical differences between the brain functions
that take place during “valid” and “paradox”
reasoning. These statistical tests have been
performed in a subject-wise manner as follows:
We have considered an arbitrary subject, say A
1
and
let us suppose that his/her ERP, captured by the
electrode k, associated with “valid reasoning” has
been classified to the m
th
group with ideal
representative
,
; let us, also, assume that the
same subject and in connection with the same
electrode, has been classified to the n
th
group of
“paradoxes” having ideal representative of the
related ERPs, the digital curve
,
.
Figure 3: Ideal representatives manifest essential statistical
differences, supporting the assumption that corresponding
differences exist in the underlying mental processes of
“valid syllogism” and “paradox reasoning”.
II) We define a measure of difference of the two
brain functions (V and P) for subject A
1
, a properly
selected distance of the two digital curves
,
and
,
. In fact, for any point (i) of the common
domain of the curves
,
and
,
, we compute
the signed difference d
i
of the value of the two
curves at this point. Then, if N
1
is the number of
points of the common domain of curves
,
and
,
, we define quantities
=
∑
(10)
CLASSIFYING EVENT RELATED POTENTIALS FOR VALID AND PARADOX REASONING
223
=
∑(
−
)
(
−1
)
(11)
and
=
−
,
(12)
where
,
is the theoretical mean value of the
difference of the representative curves of groups m
(for “valid reasoning”) and n (for “paradoxes”),
where subject A
1
belongs for the electrode in hand.
III) We make the plausible assumption that if the
ideal representatives
,
and
,
differ
significantly, one may assume that the underlying
brain functions associated with “valid reasoning”
and “paradoxes”, do indeed differ. On the other
hand, if the two digital curves
,
and
,
do
not manifest essential differences, one must deduce
that the ERPs do not reflect differences of these
mental processes, as far as electrode k is concerned.
IV) To quantify the analysis stated in (III) above,
we have proceeded as follows:
First, we have stated the assumption that the
signed differences d
i
defined in (II), belong to a
normal distribution, an assumption verified by the
Kolmogorov-Smirnoff test (α=0.01). Then, quantity
t
1
, defined in step (III), follows a Student
distribution with (Ν
1
-1) degrees of freedom.
Moreover, if we make the hypothesis H
0
that the
two brain functions (V and P) do not generate
differences in the corresponding ideal
representatives, then,
,
=0. Thus, the value of t
1
is well defined and, hence, the validity of H
0
can be
tested, for subject A
1
and electrode k.
V) We repeat the aforementioned procedure
for all subjects and all electrodes. For each electrode
separately, we apply either Bonferoni test or
geometric distribution methods to decide if the ideal
representatives of the various groups manifest
statistically significant diversification of the two
mental processes (V and P).
Application of the method in 31 subjects to which
both the tests of “valid reasoning” and “paradox
syllogism” have been applied, indicated that
essential statistical differences exist in 18 electrodes,
as shown in the map of the Figure 4.
6 CONCLUSIONS
In the previous analysis, the ERPs of “valid
reasoning” on one hand and of “paradox syllogism”
on the other have been grouped by optimally fitting
the corresponding digital curves. The related new
curve fitting method accomplishes: a) time domain
and amplitude scaling to one of the two curves and
b) optimal determination of these scale parameters,
so as an introduced error function is minimized.
After grouping the various subjects’ ERPs, for each
electrode separately, the authors have evaluated a
kind of a mean curve, assumed to be a good
representative of the corresponding “ideal” mental
process’ ERPs. Next, the subjects' ERPs have been
regrouped by letting each ERP’s curve optimally fit
the proper ideal representative with the minimum
fitting error. Finally, statistical tests per electrode
and per subject’s ideal representative have been
performed, indicating statistically significant
differences in 18 electrodes.
The fact that “valid reasoning” ERPs in one hand
and “paradoxes” on the other, optimally fit the
corresponding ideal representatives with very low
error, supports the authors’ assumption about an
underlying common mental behavior per group, well
expressed via the ideal representatives (Figure 2). At
the same time, the fact that, per subject, there is a
considerable number of electrodes, for which the
ideal representatives manifest essential statistical
differences, supports the assumption that differences
do exist in the underlying mental processes of “valid
syllogism” and “paradox reasoning” (Figure 3).
Thus, future research will aim at more precise
determination of these causal behavioral functions
and the relation of the ERPs valid and paradox ideal
representatives with each subject’s mental state.
Figure 4: Map showing the 18 electrodes in red, for which
the introduced method offered statistically significant
differences between the mental processes of “valid
reasoning” and “paradox syllogism”.
BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing
224
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