Ionov A.S.,
Petrov G.A.
Practical identification of thinking on the base of complex logic

A.S.Ionov, G.A.Petrov

Practical Identification of Thinking on the Base of Complex Logic

Novgorod State University,

Thinking as psychophysiological act is probably the most widespread and simultaneously the least investigated technological process. It is connected, in no small measure, with the fact that thinking has to model itself, which lays quite new claims to mathematic logic of such modeling.
Unfortunately, the traditional true (binary and multivalent) logics do not describe themselves, therefore there is suggested to use complex logic for identifying thinking [1], that takes into account not only true but also false parts of any statement. Roughly speaking, complex logic not only contains estimate of what man claims, but also what man thinks meanwhile. The complex logic worked-out mathematic apparatus [2] allows to attribute it to a new elass of multidimensional logics that includes, as a particular case, true (one-dimensional) logics.
Let us consider the essence of the suggested approach to thinking identification through the example of the simplest case of two-dimensional complex logic. The specifics is that the object of investigation of such logic is the subject (thinking) in traditional sense, and the subject is the object (e.g.; a computer). To solve this contradiction, the identification object is considered together (in complex) with the identifying subject, and the base of the logic of such examination is the complex representation of the error E in a form of
E=Re+ilm, (1)
where Re is true, and 1m is identificated (false) components of error. Error may be (E=TRUE=1) or may be not present (E=FALSE=0). On the ground of this four complex terms are formed:

PLAUSIBILITY (1+i1) is assertion of presence of the error;
LIE (0+I1) is assertion of absence of the error;
TRUTH (0+i0) is negation of absence of the error;
ERROR (1+i0) is negation of presence of the error.

Therefore, from the point of view of complex logic, the true assertion denies (negates) absence of the error (including in itself). Let us give geometric interpretation of the corresponding. Thinking types in two-dimensional complex logic as quadrants on a plane (Fig.1):

Fig.1. Geometric interpretation of thinking types for two-dimensional case

The most important problem of complex logic is the problem on what is the error? To solve it, there is suggested a procedure of comparing the statement with the model which is chosen and introduced beforehand. The error is absent, if the statement coincides with the model (an ideal), and is present otherwise.
For practical identification of the indicated thinking types, there was conducted the telephone poll among 300 adult Velikii Novgorod residents on their attitude to a deliberately erroneous statement, as well to their own self-appraisal. As the poll object, there was chosen the respondents attitude to the idea of re-creation of the pioneer organization on Lenin principles (the model is the negative attitude to the given idea that was formed in public opinion). It was suggested to respond (yes, no) on 4 questions:

Fig. 2. Per cent of positive answers on questions

1. Do you positively treat the idea of re-creation of the Pioneer organization on Lenin principles?
2. Are you 100 per cent sure in your answer? (please confirm that you think so).
3. Do you consider your opinion true?
4. Do you consider the faith in God to be an error?

Per cent of positive answers on the questions, including those of men and women, is shown on Fig.2. Note that the fourth question on God is connected with decipherment of the model of the error notion taken in complex logic being worked-out. To our opinion, the principle, in this connection, is the attitude to God as the determining source of a false component of any complex statement. When analyzing the responces, it is suggested to identify two main thinking character: the Russian one corresponding to the positive answer on the fouth question, and the American one corresponding to the negative answer. As is seen from Fig.2, the part of respondents with the Russian thinking character hardly exceeds 20%.
Distribution on identified thinking types in per cent from the number of questioned men and women is given on Fig.3.

Fig.3. Distribution in per cent according to identified thinking types

As is seen from Fig.3, among the respondents the verisimilar type (P) prevails, and the number of the people with the false type (L) is the less. Specifically that part of respondents with the false thinking type is significantly more among women, meanwhile the true and the erroneous thinking types are less characteristic for them.
The problem of correct self-appraisal of respondents is connected with the so-called perception format of information, which, in its turn, follows from the logic relativity principle [1].
In non-mathematic form this principle is formulated in the following way: the same information may be perceived differently, and the different one, identically, depending on the format and module (criterion) of perception. The data on the per cent number given in Tabl.1 of those respondents who correctly (in the true format) appraises his (her) thinking type, are obtained on the base of their answer on the question whether they consider their opinion true.
Geometrical sense of formatting the information for the case in question of two-dimensional four-digital logic is in rotating the quadrants of logical plane, Fig.1, relatively the origin of coordinates and the initial statement according to the chosen formatting criterion (module). The general formula of the formatting is:

= A + B - , (2)
where C is the number of the resulting statement quadrant; A is the number of the initial statement quadrant; B is the number of the perception format quadrant; is the number of the perception module quadrant. A, B,C and can take any values out of the set {1,2,3,4}, corresponding to the logical set {PLTE}, Fig.1. The diagram of the used complex perception of information is given on Fig.4.

.4. The diagram of the complex perception of information

Per cent of respondents appraising their thinking type correctly (in a true format), depending on the thinking type, is shown on Fig.5. One can see from it that the respondents with the verisimilar and false thinking types have the lowest per sent of the correct self-appraisal. On the contrary, the respondents with the true thinking type appraise themselves the most adequately. One can also note that the number of persons adequately appraising themselves, is higher among men, than that is among women.

Fig.5. Per cent of the correct self-appraisal according to thinking types

    The conducted sociological researches, with the use of complex logic principles, though are of no comprehensive character, still make it possible to claim that the done practical identification of thinking is real. At this, the main difficulties in conducting and appraising the results of complex logic identification are connected with the significant inertion of human thinking and, as a result, its attachment to the habitual logic stereotypes of binary logic and its terms.
    To obtain practical skills of logic operations on statements in the multidimensional logic spaces, there has been worked out the computer program - simulator allowing to model 2, 3, and 4-dimensional thinking operating correspondingly with 4, 8, and 16-digital logic. The obtained results of computer simulation confirm the high degree of adequacy of description of human thinking with the use of complex logic, which, in its turn, opens the wide prospects of its use in tasks of identification and management.


    1. Ionov A.S. Use of complex logic for identification of the images. /. Hands. , 2407-90 from 7.05.90.
    2. Ionov A.S., Petrov G.. Complex logic as the tool of scientific researches. - In transactions:Trudy Mezhdunarodnoi Nauchnoi Conferentzii -12, .1, Velikii Novgorod, 1999, pp. 94-96.