İDRAK MƏKTƏBİ

Logical Integrity, Fuzzy Logic and Modeling Content of Education

Fatma khanim Bunyatova, Aynur Bunyatova. Intellect School, Azadliq Pr.151A, 1106, Baku, Azerbaijan. fatmaxanum@rambler.ru and aynur_bunyatova@yahoo.com 

Abstract-This presentation is about building the model of language in a formal-logical way. The presentation is made of 3 parts. The first one is setting the language’s formal-logical-models on Piyajes integrity-logic. The second part is comparing Piyaje’s logic with Zade’s logic and how the Zade’s logic transforms this model. The last part is about what new innovations can be brought by this model. Key Words ; -Logical thought operations; -Nanostructure of knowlodge; -The integrity logic, FL, SC; — The comparative machine translatıon 

INTRODUCTION 

Two coryphaeus’s   of XX century Piyaje and Zade brought the big contribution to development of a modern science. One of them Piyaje in 40-s’ years has created the theory of intelligence, and another Zade–SC. In the theory of development of natural intelligence Piyaje marked, that to develop operational character of thinking it is necessary to consider, that in any area constructive  thinking the psychological reality consists of operational systems of the whole, instead of from the isolated operations. 

From the logic point of view it represents structure which has operational rules, and these rules form: «just that logic of integrity which expresses in the axiomatic or formal scheme actual work of reason on operational level of its development, i.e. in the final form of balance. ». [1]. 

Piajes’s logic of integrity or work of reason at an operational level, i.e. at a is formal-logic level, is work of a human brain. 

Zade has created SC which provided sharing such numerical new approaches as fussy logic, neural networks, evolutionary calculations and etc. [2]. These technologies are of great importance for compression of data and designing of system with high MIG and the best model SC is the brain of the person as marked Zade [2] 

Constructed by us at an operational level, i.e. on formal — logic I.Q. model . 

Language can become machine operational intelligence which is capable to understanding and  reasoning. The general in these theories, that they show work of a brain: natural – Piyaje, and artificial– Zade. 

Constructed by us at an operational level, i.e. on formal — logic I.Q. model language can become machine operational intelligence which is capable to understanding and a reasoning. Constructed by us at an operational level, i.e. on formal — logic I.Q. model language can become machine operational intelligence which is capable to understanding and a reasoning. 

II.ESTABLISHMENT OF FORMAL-LOGICAL  MODEL OF THE LANGUAGE   

Establishment of formal-logical model of the language is reviewed on examples of Russian language. 

Piaje determines the definite form of balance operation of intellect, with the terms “groups” and “grouping”, i.e., the activities which integrated and organized in the structure of whole. 

For this, he draw 4 conclusions for “groups”, and 5 conclusions  “grouping”. 

The term “groups” is considered as a word determining object, its indication, quantity, action, sign of action and word describing the object. These groups have been determined as parts of speech and their six groups, i.e. six parts of speech. Consequently, operational groups will be six: a 1-noun. A 2-adjective; the 3-numeral; 4-pronoun; 5 — a verb; 6 an adverb. [3] 

«Groupings» will be considered by us as groups of the words incorporated by general by an attribute. For example: 1, 2, 3, 4, 5, 6 — are grouped as the words concerning a subject. 

Rules of «grouping»: 

a) Any two elements of «grouping» can be connected among themselves and as a result to generate a new element or new unit of «grouping». For example: words beautiful; the boy; (красивый; мальчик) can be united and this association generates a new element – a word-combination «a handsome boy». (красивый мальчик) 

b) Two attitudes А > В > С can be А > С, in which they include. If under  A, we understand  I, under В – 5, and under С- 6, the attitude А>В in the syntaxes of Russian will govern the attitude 1 with  А > С -1 will be also dependent. 

For example: яйцо варить — А > В, to cook an egg- А > В;  В > С boil an egg lightly (В > С варить всмятку)  А > С яйцо всмятку; 

c) any transformation  is reversible. 

For example: a handsome boy-красивый мальчик. 

These two elements incorporated in a word-combination can be disconnected. 

e)Composition of operations. 

The thinking always keeps ability separation to deviations, the result received in two various ways in both cases remains to the same. 

For example: the word combination «пишу письмо»- I write a letter. From morphological point of view-it is object expressed in accusative case; and from syntactical point of view –it is government where, the word «пишу» write  require that the word «письмо» -a letter .should be Accusative case. 

d) The operation, related to reversible operation is annulled. For example: день +день= дни. ( a day + a day=days  Дни –Days in  plural form, but  in singular form will be a day. 

е) Identical operation: А +А = А 

In the language it is understood as a simple sentence which related  with other simple sentence and  formed complex sentence. 

Piaje numerating  “grouping” said that, he described  the finite structure of intellect and explained the formation process of these “grouping”. 

Formation of grouping 

The system of “grouping”  is formed, so-called logic operations, i.e. operations, which starting point are individual elements considered as invariant. Under individual elements we understand parts of speech. At realization of such operations they are classified and subject  to serialization. For example: the set of words is given: the book- книга, a table- стол, the house- дом, the ground- земля, the girl- девочка, a writing-book- тетрадь, the pupil- ученик, the young man- юноша, a banner- знамя, соня-, a horse- лошадь, a field- поле, a window- окно, time- время- день, day- день, a horse- конь 

1) First operation on these words is operation of classification. 

TABLE I .CLASSIFICATION OF WORDS. 

To I to a class or to «group» concern 1 feminine gender; to II class-1 a masculine gender; to III 

To class of 1- neutral gender; 

The words given in IV class have a double output. Definition of gender goes through transformation, i.e, declination according to cases – нет коня-there is not a horse (masculine gender) нет лошади – there are not horses-feminine gender-(женский род).The words relating to V grade-—мя, which declination happens as  1 neutral gender. Operation of classification in language is understood as division of nouns on gender classification. 

2) Second «grouping» spends operation serialization by the existing  endings. Feminine gender and some words of a masculine gender are equally declined i.e. they concern to I to declination Feminine gender and some words of a masculine gender with the endings —а,-я,  are equally declined i.e. they concern to I  declination; Words II, III class and some words from IV class are declined equally and in Russian these nouns concern to II declination, etc. Operation of serialization in Russian language is distribution of words on declinations or declination of nouns. 

3) The third basic operation is an operation of replacement. In grammar of Russian it is equivalent to concepts of the synonym, the antonym and the homonym.. 

4) The fourth operation is the attitudes uniting elements of same classes, i.e. equivalence. For example: 1 (школа) school; 

новая школа-new school; одна школа-one school; моя школа-my school; школа строится-the school is built;  cтроится  быстро-the school is built  fast. 

5)  Multiplicate operations » i.e. the operations concerning simultaneously to more than to one system of attitudes. As we have mentioned, all this work of thinking presented by us on an example of Russian, according to Piaje, is the final structure of intelligence expressed by formal logic. On an example of «logic of Russian”, activity of natural intelligence  has been shown as a human brain. 

Overlapping of logic of integrity with linguistic logic. Replacing formal logic of integrity of Z.Piaje with Zade’s Linguistic logic, we receive following model of the language: [4] 

Let’s admit, concept of «group» it is compatible concept « elements of set » then under «set», we shall understand «groupings» i.e. all are parts of speech then, Х-« the universal set », will be a lexicon of language, and «elements» are parts of speech which we shall designate through х. In this case X-it all words of language, and х1-is 1; х2-it is 2; х3 is 3; х4 is 4; х5 is 5; х5–it is 6 and they are marked through 0,1 as estimations of set, i.e. 0,1 words which designate a subject; About, 2-attribute of a subject; 0,3 – the quantity of a subject, 0,4 specifies for, 0,5 – designates action of a subject; 0,6 designates an attribute of action. 

«The fuzzy set» can be presented in the form of a lexicon of language. 

Under function of fuzzy set then it will be understood words in direct lexical value. For example:– дом-the house, стол— a table, берег -coast, океан— ocean, etc. 

Proceeding, from concepts of Zade’s linguistic variable -the category of possession has two rules: 

1) Syntactical, which is set in the form of the grammar generating the name of values of a variable in the form of categories of language. 

2) Semantic which defines algorithmic procedure for calculation of sense of each value. 

Then У–will designate grammar rules of language, and X will designate parts of speech which too have the internal rules. Rules X will submit to rules Y how rules Y submit to rules X. 

 As it has been told  Y is all rules of a category of language, X is all parts of speech with the internal rules. 

Then in this function the category of possession х1 is   1;  х2 is   2  ;  х3 is 3  ;.х4is   4  ;  х5is  5  ;   х5 is 6. 

У is the category of the language: 

У1 is the category of the number-singular and plural; 

у2 is the category of the gender-feminine gender (1), masculine gender (2), neutral gender(3); 

у3 is the category of case (1-6); 

у4 is the category of the person; 1-3´ 

On the basis of it, the sentence « Recently I have received the letter from the close friend» will be symbolically described as у3 is a category of a case (1-6); 

у4 is the category of the person; 1-3 ´ 

х 6    х4     х5у/1      х4у2/2     x 2 у2/2     x1y2     x1 у/3/4       

qrafically (Scheme.1.)   

This model of a natural language, being exposed to transformation by the conceptual tool of linguistic logic of Zade  gets a following kind: 

1) The fuzzy set can be final and infinite; in language it  is endings X = (х1 – х5) of only six parts of speech 

2) The fuzzy set  А can be characterized with the  formula (composition according to the Piaje’s logic). А= Е х 

For example: х3 х1 (один мальчик-a boy), х2 х1 высокий мальчик- a tall boy and etc. 

3) The fussy set А can be described in the following form: 

a noun can be described as А =0,1 – игра— game: 0,1+ 0,2-сильная игра-strong game;  0,1+ 0,3;-одна игра-one game ;  0,1+ 0,4;- моя игра-my game; and etc.. 

4) Operation of integrity. 

Integrity of two fussy set, А and В is determined as the following: if А –1 ,  В —  2 then, the function of category of possession у1 and у2 is related  for A and B. 

5) А is the a real number which close to 8; 

If А-will be understood as a word большой (big), and — as a word дом -the house then the word большой— big will be really close to a word дом— the house as it defines number 8: a of the house; quantity, an attribute of the house; it will be coordinated with all category of possession  of the house, etc. The category of the language –(y) 

  III. WHAT INNOVATIONS CAN BRING THESE MODELS IN PEDAGOGICS, PSYCHOLOGY AND INFORMATION TECHNOLOGIES? 

1. Language is considered in the scheme of integrity. As language is means of dialogue and expression of ideas, that, naturally, conditions of the scheme of integrity and Zade’s logic  can be in any scientific knowledge and rules of Piaje’s logic  and  fussy  logic can be applicable to them.
2. Structures of knowledge will share on invariant and variable or on syntactic and semantic.
3. Operational thinking allows to unite structures of knowledge in «groups» and «groupings», to find out their interrelation and attitudes, to classify them, to enrich or replace with other structures.   
4. Cogitative activity of the individual in a type of operationality allows it to build structures of the thinking adequately.
5. Piaje’s logic of integrity  destroys traditional vertical construction of structures of knowledge and builds them in horizontal structure [5]. Here by means of the conceptual tool of Zade’s fuzzy logic structure of knowledge are understood as nanostructure of knowledge;»groups»and «groupings» as « fuzzy set » and « elements of set » [6].
6. Zade’ linguistic variable  and a combination  of logic allows to model the maintenance of subject knowledge by definition of optimum quantity of variables and constant rules of a subject. This logic model in a combination to educational technologies in study will reduce terms of learning on 20-30 %.]..
7.  Machine translation.

If through And ху-we shall designate is formal-logic model of the Azerbaijani language, Е ху – English language, Р ху-Russian, etc. then it is possible to create comparative formal-Logic model of Аzerbaijani-English language (And ху-Еху), English-Russian language (Еху-Рху), etc. This comparative model will approach language of machine translation much more to human translation. 

REFERENCE 

1.  Жан Пиаже, «Генетическая психология», Москва, 2001
2. Р. А. Алиев, «Soft computiring», АзДНА, Баку, 1999 г
3. Ф.Д..Бунятова, «Пиаже в школе»,. Elmi axtarislar.(Scientific researches) Baki 2001
4.  Ф.Д.Бунятова, «Применение нечётной логики в образовательных технологиях», Copyright Agency of the Azerbaijan Republiс, № 328, 01.07.02,  Baku.
5. Ф.Д.Бунятова, «Логический способ обучения. Альтернативное образование», Баку, 1991
6. F.Bunyatova, «Structural Teaching Technology and perspectives nano Psycopedagogy», IETC-2009, May 2009, Ankara, Turkey

The works approved AICT2009 for the    publication include an engineering index (Engineering Index — EI), EI Compendex and IEEE Explore TM. 

Number IEEE of the catalogue: CFP0956H, ISBN: 978-1-4244-4740-4 and library of the Congress of the USA: 

Статья напечатана в www.ieeexplore.iee.org

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