The modelling of some intelligence functions Текст научной статьи по специальности «Физика»

THE MODELLING OF SOME INTELLIGENCE FUNCTIONS

DUDAR Z.K, CHIKINA V.A., SHABANOV-KUSHNARENKOS. Y.

Kharkov National University of Radio Electronics, Lenin ave,14, Kharkov, 61166, Ukraine. Tel.: +380-57-7021446. E-mail: vchikina@hotmail .com

Abstract. General tasks ofintelligence function modeling connected with a language text form, color sight, sound signal coding are considered in this article. The methods and concepts necessary for intelligence processes are described; theory fundamentals as mathematical concept description within a correspondence with the studied information processes are introduced.

Introduction

Artificial intelligence as a scientific trend connected with an attempt to formalize humanthinking has quite a long prehistory. The first steps of cybernetics were aimed at new concepts studying and understanding of processes taken place in complex and live systems including intellectual ones. This trend has taken shape of an independent field, which develops the artificial intelligence tasks. At further artificial intelligence research development their division has taken place. It is connected with two points of view of how the artificial intelligence systems are to be built. The supporters of one point of view are convinced that the result is of the greatest importance, i.e. the coincidence of artificially built and natural intellectual systems behaviour. As to inner mechanisms of behaviour at forming the artificial intelligence creator is not to copy or bear in mind the features of natural live analogues.

Another point of view is that the study of natural thinking mechanisms and analysis of methods of logical human behaviour forming data may build the basis for artificial intelligence systems construction, such as modeling, principle and biological objects concrete features reproduction with the help of technical means.

Thus, the first trend considers the product of human intellectual activity, studies the structure, and tends to reproduce this product by modern technology means.

The results of this trend of artificial intelligence, characterized by machine intelligence term, are appeared to be connected with computer potential development, art of programming, and computer science.

The second trend considers data of neurophysiological and psychological mechanisms of intellectual activity and human logical behaviour. It tends to reproduce these mechanisms with the help of some technical facilities in order such facilities “behaviour” to coincide with human behaviour in defined and a beforehand set range. The development of this trend, characterized by “artificial intellect” term, tightly bounds with the results in human sciences. The tendency to reproduction of wider than in computer intelligence human logical activity spectrum is typical for it.

Both main artificial intelligence trends tightly bound with modelling. The construction of very complex processes models connected with humanbrain activity is entailed while

intellectual systems designing. This is the perception, thinking, and memory modelling, and modelling of mental functions, etc. Two sides of human intelligence may be studied: the material one - as brain, nervous system, human body, as well as non material one - as intelligence activity, its functions expressed in human behaviour and actions.

The fact that constructed models, which imitate brain activity, are suitable and essential for computer systems construction do not give rise to any doubts. Human intelligence is similar to computer in functioning, and as any computer system it is subjected to the same limitations.

Any computer can be used for perception, transformation and information forming; it also characterizes the activity of human brain. Information, operated by human brain, has a word form, represented by texts, conversations, perceptible object images. Human information input is carried out by senses; the output is carried out by movement and speech organs. Obtained reactions are designated by external influence (by information received from senses, as well as by genetic information). All above mentioned let us consider the opportunity of intelligence model construction and its use while designing human brain simulating computer systems .

1. Identification

The identification as a mathematical description of human intellectual activity is a very important task of intelligence physics [1]. At direct identification the signals x, which are chosen from some set A, are given to the identifiable process r input, and reciprocal signals y, which form a set B, are registered at the process output (fig. 1).

f

X p J

A B

/M=y

Figure 1. Process identification

The identification purpose is a mathematical description of function r(x)=y, which reflects a set A into set B. Function r is a process characteristicfunction. At a direct identification the input and output signals of a studied process are accessible for direct physical observation and measuring. Only the observed from the outside examinee behaviour (a man, whose intellectual activity is under consideration) can be studied with the help of the direct identification method.

The indirect identification method is required for studying of examinee inner condition inaccessible from outside. At the indirect identification along with process itself the unknown input and output signals are to be described mathematically.

Comparator circuit identification. One of the indirect

identification forms is a comparator circuit identification. Comparator circuit Kis a device with m inputs yp y2,..., ym and one output t (fig. 2).

ym ——►

Figure 2. Comparator circuit identification

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166

where t is a binary comparator circuit (te£, £ = {01})

reaction; y p y2,..ym are information system inner conditions; Bp B2,..., Bm are sets of any kind inner conditions (y1 g Bp

y2G ym^ Bm).

Comparator circuit K determines whether its inner signals y p y2,..., ym are in a given ratio K. If they are, then it produces a signal t=1, at negative answer - a signal t=0. The examples of such a comparator circuit are: for a man these are a colour equity comparison; sound volume comparison, a determination of a given statement correspondence with the situation; for a computer - if there are spelling mistakes; whether it is a Russian text; or two given texts correspond; or two sentences express the same idea; or a given image corresponds with its verbal description.

By its behaviour the comparator circuit realizes comparator circuit K(y1, y2,..., ym)=t predicate, which corresponds to ratio K. Information processes f1,f2,_,fm are connected to comparator circuit K input with its output. Symbols x1, x2,..., xm stand for physical signals shown to examinee; A1, A2,., Am are different kind physical signal sets (x1 g A1, x2 g A2,., x g A ). Thus:

mm

P(x1, x2,., f2(X2), .,fm(xm))=t. (1)

Information processes along with connected comparator circuit are called an identifiable object. P is an object predicate.

signals Perception

mechanism

Figure 3. The realization scheme of comparator circuit

Signals yi, y2,..., ym are obj ect P inner conditions inaccessible for outer observation. Among comparator circuit identification tasks are: mathematical description of output signals y1, y2,..., ym of processes f1, f2,., fm as well as the description of the process itself by given comparator circuit and object P certain properties; the cases of simultaneous consideration of object P1, P2,., Pn system (n is an object number in a system).

2. Natural language text modeling

At Russian language mechanisms forming a morphological ratio P is described [2]; it connects a word-form fragment (for

instance, an ending) with its fragment (x!,x2,...,x T) P( x1,x2,...,x

\ [ 1, if (x1, x 2x J e P, [0,if (x1,x2,...,x Jg P, (2)

where L is all ration set on Um, M is all predicate Um set. The ratio P e L and the predicate P e M correspond if at any

x1,x2,...,xt e U.

Reverse transfer:

if P(x1>x2>- .,x J = 1, then(x1,x2,.. ,xt)e P;

fP(x1>x2v .,xT) = 0,then (x1,x2,. ..,x Jg P. (3)

All vectors set (x!,x2,...,x T) that satisfies an equality P(x1,x2,...,x T) = 1 ,forms a ratio P that is a verity range of predicate P. Predicate P e M, defined by principle (2), is a characteristic function of ratio P e L . Rational choice of all vector (x1, x2,..., x T ) set is defined by a certain language and its inner structure properties.

Cartesian predicate decomposition. Polyadic predicate P(x1, x2,., xn) is divided into two layers. On a upper layer the unary predicate P(y) is introduced, where y=(x1, x2,., xn); on the lower layer variable y is expanded into variables (x1, x2,..., xn) set. It is a basis of n-dimensional Cartesian co-ordinates introduction, and a pointy receives its coordinate presentation

(xV V- xn)- S(X1, V- xn)-

The predicate P(x1, x2,., xn) is given on a Cartesian product A=A1 x A2 x . x An. Each set (a1, a2,., an) e P is named. All names form a set B. Variable name y e B and functiony=S(x1, x2,., xn) (S: P ^ B) that defines the name of any set from P, are introduced.

Figure 4. Predicate P spatial presentation

Function y=S(x1, x2,., xn) correspond with some predicate S(x1, x2,..., xn, y) on A x B, which gives a space S in coordinates A. The space S is quasicartesian, i.e. predicate S is monosemantic, injective, surjective, but not everywhere defined.

As a result of Cartesian decomposition n+1-ary predicate S

is replaced by equipotent binary predicate system Gi(i= 1, n).

Cartesian composition of predicate P according to predicates G1, G2,..„ Gn is:

P(x1, x2,..., xn)= 3 yeBS(x1, x2,..., xn, y) (4)

Project predicate are found by formula:

Gi(y, xi) 3 x1 G A1 3 x2 6 A2 • • • 3 xi-1 G Ai-1

3xi+1 e Ai+1.3xneAnS(x1, x2,..., xn, y) (i=1,n). (5)

The polyadic predicate (ratio) substitution for equipotent binary predicate (ratio) system is called its binarization.

Cartesian decomposition of a full non-possessive adjective ending predicate is considered as an example (tab.):

1 2 3 4 5 6 7 8 9 10 11 12 13

IH oro oMy MM oM aa yro OH oro oe Me MX MMH

4 15 16 17 18 19 20 21 22 23 24 25 26

H ero eMy HM eM aa roro eH ero ee He HX HMH

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The complete disjunctive normal form of ending predicate has 26x3=78 predicates of object recognition:

P(xb x2, x3)= xjxfxj V x°x[x° V ... V xfxf xf .

Let us number all endings (all sets (xb x2, x3), for which P(xj, x2, x3)=1). Then the set B={1, 2,..., 26} is introduced. The

function y=S(xb x2, x3): y1=xjx2xj,..., y26=xfxMfxf is written down. The predicate S(x1, x2, x3, y) is:

S(xi, x2, x3, y)=( x j x 2x3 -y1)...( xf xMM xf ~y26).

The explicit concept of a projector predicate is received; vectors are found according to co-ordinates, projector predicates - according to formula (3), and proj ectors - according to projector predicates.

Xi X2

A A

B

A

Figure 6. Colour sight identification

The first projector: y1 v y4 v y11 v y12 v y13= x\l (only endings 1, 4, 11, 12, 13 have a first letter j);

y14 v y17 v y24 v y25 v y26= x1; y2 v y3 v y5 v y8 v y9 v y10= x10;

y15 v y16 v y18 v y21 v y22 v y23= xf; y6= xf ; y19= x*; y7= x{; y20= xf (y=g1(x1)).

The second projector:

y1 v y8 v y14 v y21=x2 ; y2 v y15=x2; y3 v y4 v y5 v y13 v y16 v y17 v y18 v y26= xMM; y6 v y19=x2; y7 v y9 v y20 v y22=x“; y10 v y11 v y23 v y24=x 2; y12 v y25=xf (y=g2(x2)). The third projector:

14 191417 25 —

y1 v y4 v ... vy12 v y14 v y v ... vy25=x3 ; y2 v y15=xO; y3 V y16=xy; y13 v y26=xf .

Ratio S, i.e. Cartesian equality system, broke up into many small equalities of the form ya1 v ya2 v ... v yak= xb, with two variables.

By his behaviour the examinee realizes the predicate

P(x1, x2)=D(f(x1), f(x2)), (6)

which is called colour predicate. Here D(y1, y2) is an colour equality predicate:

D(y1, y2)

1, if y1 = y2,

0, if y1 = y2.

(7)

The predicate D(y 1, y2) characterizes the operation of examinee consciousness mechanism, who analyzes the colour y1, y2 perception and defines their equality or non equality. Function f(x)=y represents a transformation ofphysical light radiation x to psychological colour y, performed by human sight system. Comparator circuit that realizes equality predicate is called null apparatus. The experiments with the examinee show that the predicate P is reflexive:

V xe A P(x, x)=1; (8)

is symmetrical

v x1, x2 e A P(x1, x2)=1 ^P(x2, x1)=1; (9)

is transitive

3. Colour sight theory

The null apparatus method is used for mathematical description of human colour sight. Light radiation

Figure 5. The null apparatus method affecting retina provokes a felling in a man’s consciousness called colour

The intellectual theory part that studies light radiation transformation f(x)=y into colour y made by human sight system is called colour sight theory. The examinee is shown light radiations x1 and x2 on a comparison fields, which he perceives as colours y1 and y2. If colours coincide then the examinee should answer t=1, if not - then answer t=0.

V x1, x2, x3e A P(x1, x2)=1 andP(x2, x3)=1 ^ P(x1, x2)=1.(10)

The colour predicate reflexive property means that identical radiation generate identical colours. The symmetric property means the colour equality is not upset at radiation shift. The transitive property means that if the colours of first and second radiation are equal, as well as the second and third radiation colours are also equal then the first and third radiation colours are also equal. Any binary predicate with reflexive, symmetric, and transitive properties is called the equivalence predicate.

The theorem of equivalence predicate general form. Any

equivalence predicate (and equivalence predicate only) can be presented in the following form:

P(x1, x2)=D(f(x1), f(x2)) (11)

at appropriate set B and function f: A ^B (x1, x2eA) selection.

Let us name the function f a generic equivalence function. Colour predicate generic function mathematically describes the transformation of light radiation to colour process made by human sight system.

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In colour sight theory function f form, i.e. the transformation principle of light radiation to colour, can be derived from analysis of examinee binary answers, i.e. from colour predicate properties. Additional predicate P properties are attracted for function f determination: its additivity, homogeneity, three-dimensionality, and continuity.

The colour predicate additivity:

v Xi, X2, Xi', X2' e A f(xi )=f(x2) and f(xi ')=f(x2')

^ f(Xi+Xi')=f(X2+X2'). (12)

The x+y addition of light radiation x and y is achieved by their superposition in space. The colour predicate additivity means that sums of equally coloured light radiations are equally coloured

The colour predicate homogeneity:

V Xi,X2 e A Vae R f(xi)=f(x2) ^f( a xi)=f( a X2). (i3)

Here 6 is any real number, ae R; R is a set of all real numbers. The aX multiplication of a number x=x( X) radiation is achieved by its capacity change in 6 times at frequency content maintenance.

Figure 7. Light radiation spectrum

The x( X) note stands for light radiation spectrum, i.e. light radiation intensity dependence on X wave-length of electromagnetic waves of a [Ai, X 2] light range; Ai=0,4 mcm - a low bound of wave-length (violet light radiation); X2=0,8 mcm - an upper bound (red light radiation). Multiplication 6x of light radiation x by positive number 6 is realized by its luminous flux intensity change due to masking or source of light approach (moving off) to illuminated surface. Radiation multiplication by negative number stands for its transfer to a neighbour field of comparison. Colour predicate homogenity means that equally coloured radiation will be equally coloured again after its multiplication by the same number.

The colour predicate three-dimensionality:

there will be such light radiations ai, a2, a3 e A, that y X e A

f(x)=f( aiai +a 2a2 + a 3a3) (i4)

at a unique numbers set ai,a2,a3 e R .

Light radiations ai, a2, a3 and their colours are called the main. They canbe chosen in different ways. The red, green and blue

colours are used as the main ones. The colour predicate three-dimensionality means that mixture aiai +a2a2 + a3a3 (in other words - a weighted total or linear combination) of the main radiation can be levelled by colour to colour of any radiationx, even at the only set oftheir intensities a i, a 2, a 3. Thus, the set of numbers ai(X), a 2(x), a 3(x) defines uniquely the colour oflight radiation x. Numbers ai,a2,a3 are called colour references oflight radiation x in colour space with a basis ai, a2, a3. They define uniquely the coloury=f(x)of light radiation x.

The colour predicate homogenity is accepted as A Hilbert space L2[Ai A 2] of all spectrums x( X) x eA; then at continuous light radiation x e L2[Ai, X 2] change the references of generated colour a i (x), a 2 (x), a 3 (x) will change continuously.

Any additive, homogeneous, three-dimensional, and continuous predicate P(xi, x2) is called three-dimensional linear predicate.

Theorem of three-dimensional linear equivalence predicate general form. The generic function f: L2[Ai, X 2 ] ^ R3 of any three-dimensional linear equivalence predicate can be presented as following: y=f(x)=( ai(x), a 2(x), a 3(x)), where

k2

ai(x) = J x(A)Ki(A)dA •

Li

k2

a2(x) = J x(A)K2(A)dA; (i5)

Li

k2

a3(x) = J x(A)K3(X)dA

Li

at appropriate functions Ki( X), K2( X), K3( X) choice.

Integrals of type (i5) are called colour ones. Functions Ki( X), K2( X), K3( X) are called spectrum sight perceptibility functions in basis ai, a2, a3. They are defined experimentally. One way of such a definition is called Maxwell method. It consists in the following. Monochromatic radiation of a unitary intensity xx with a wave-length X is considered; and the equally coloured mixture

ai(x L )ai + a 2(x L )a2 + «3(x L )a3

of main radiations ai, a2, a3 is found for every wave-length X on examinee experimentally.

In the colour sight theory it is proven that at Maxwell method Ki( X )= ai(xx) = ai (A), K2( X )= a2(xx) = a2(A),

K3( A )= a3(x x) = 03(A) (i6)

can be accepted.

Spectrum sight perceptibility functions Ki (X), K2( A), K3( X) found experimentally are averaged over several examinees. On this basis standard spectrum sight perceptib ilityfunctions (i.e. adding curves) are obtained.

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X, MCM

Figure 8. Spectrum sight perceptibility functions

Red, green, and blue monochromatic radiations (so called RGB system or the basic physiological system of adding curves) are used as the basis for depicted adding curves (fig. 8). Various adding curves choices are possible. Their type depends on basis ab a2, a3 choice. The necessary type of spectrum sight perceptibility functions is obtained from standard functions by linear calculations.

4. Frequent-pulse sound signal coding

Reinforced generalized Talbot principle. On the basis of some hearing property studies the method of economical discrete speech sound performance is developed, i.e. patterns, which are the basis of continuous ear perception of air fluctuation and their transformation into discrete form [9].

According to generalized Talbot principle [10] a sensation caused by a visual image BN (t), in a limit at N ^ <x> will be indistinguishable from visual sensation caused by an image B(t)

t2 t2

lim J BN(t)dt =JB(t)dt (17)

N^rc t1 t1

where {BN (t)} N=1 is an infinite sequence ofvisual stimulus; t1 and t2 are any fixed moments of time.

The generalized Talbot principle is applicable to hearing; it establishes a sufficient condition of any sound acoustical equality. Let us characterize any sound by its acoustic diagram given on an interval [0,T0]. Let us consider sounds A(t), whose diagrams smoothly vary in time. Let us use some artificially formed sounds B1(t), B2(t), ..., whose diagrams should be locally summable. The generalized Talbot principle can be written down in the following form. If at any t1 and t2

t2 t2

lim J Bro (t)dt =JA(t)dt (18)

ti ti

then in a limit at unlimited positive real number w increase the sound Bro (t) sensation will coincide with the sound A(t) sensation.

The reinforced generalized T albot principle canbe formulated as follows: if a sound A(t) and sound set {Bro (t)}roe(0,M), satisfy the condition (4), then there will be such a number ®0 > 0, that for any a > ^ the sound Bm (t) sensation will coincide with the sound A(t)sensation. Let us designate a set M low bound with a symbol a Kp and name it a critical value of parameter m .

Sound asynchronous frequency - pulse code. Let us construct frequency - pulse code family {Bro(t)}roe(0,M) for a sound A(t) that satisfies a condition (4). Let A(t) is a an arbitrary

chosen speech sound diagram, whose ordinates are limited on absolute fixed positive number a value on a whole interval [0, T0]

-a < A(t) < a, (0 < t < T0). (19)

Number a is accepted equal to

a = max |A(t)| (20)

• 0<t <T0 • (20)

Let us choose some real number a0 that satisfies the condition a0 >a.

Let us introduce positive real parameter s and related parameter m varied on an interval (0, <x>), and defined by the formula:

a0 — a 8

(21)

Let us build a moments of time 01,02,..., 0m sequence. As number m the greatest of integers that satisfies a condition

Qm ^ T0 (22)

is accepted.

At the moments of time 01,02,..., 0m short standard pulses are formed, each of them covers the area s . The received pulse sequence, after its downward bias on size ao, is accepted as the diagram of a sound Bro (t). The diagram Bro (t) can be presented in the following form:

m

B»(t) = “a0 + sZ5(t-6i), (23)

i=1

where 5(t-0i) is a delta function It sets a pulse of neglibly small duration that appears at the moment of time 0i and covers the unitary area. The acoustic diagram Bro (t) is called a sound A(t) asynchronous frequency - pulse code.

The physical sense of parameter is the minimal recurrence frequency of pulses in a sound A(t) asynchronous frequency

- pulse code Bro(t). The constructed set {Bro(t)}roe(0,M), of a sound A(t) asynchronous frequency - pulse codes satisfies the condition (18).

Critical frequency. According to the reinforced generalized Talbot principle, for a sound A(t) asynchronous frequency

- pulse codes family {Bro(t)}roe(0,M),there should be avalue a Kp (critical recurrence pulse frequency in a sound A(t) asynchronous frequency - pulse code Bro (t)) of parameter w. If on all sound interval [0, T0] the frequency of following of pulses in a sound Bro(t) exceeds critical, i.e. a > a Kp, then sounds Bro (t) and A(t) should sound equally. At the same time, the acoustical sensations of sounds Bro (t) and A(t) at a = a Kp should differ.

The experiments of frequency a Kp determination for various sounds A(t) and their asynchronous frequency-pulse codes Bro(t) are carried out on experimental device, i.e. a sound signal quantizer. Its block circuit is shown on a fig. 9. A continuous sound

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Figure 9. The sound signal quantizer block circuit

A(t) is perceived by a microphone 1, which transforms it into voltage fluctuations U(t) (k1 is a microphone transfer factor). The voltage U(t), after p times amplification and upward displacement on size b by the block 2, enters as a voltage V (t) on a threshold element 3. The threshold element develops some sequence of standard pulses; each of them covers the area g. The received sequence of pulses P(t) is amplified q times and is displaced downwards on a size with the block 4. As a result the signal Q(t) is formed that enters through the switch 5 on the telephone 6 and is listened by the examinee as a sound B(t). Through the same switch on the telephone the signal W(t) enters, which is a signal U(t) amplified r times by the block 7. The signal W(t) after passing through the telephone with transfer factor k2, is listened by the examinee as a sound A(t).

The critical frequency is defined by the formula:

1V

®KP = VKp (24)

g

where VKp is greatest bottom level of a sound A(t) voltage, when the sensations of sounds B(t) and A(t) still differ. This level is defined with the help of electronic oscillograph, whose screen visually observes a voltage V(t) fluctuation in time.

It was revealed that the critical frequency m K practically does not depend on a sound A(t) kind, it is slightly influenced by an auditor’s choice. It precisely coincides with the maximal frequency of sinusoidal signal heard by ear, and is 16-20 kilohertz. The critical frequency is strictly correlated with the top limit of audible frequency. Apparently, as soon as the

pulse recurrence frequency in a signal Bro (t) is reduced so, that it gets in audible range; it starts to be perceived by ear. When the minimal pulse recurrence frequency in a signal Bro (t) even on small time intervals is reduced up to size a Kp and sounds A(t) and Bro (t) can be orally differed; this difference consists in the fact that at a sound Bro (t) sensation a high-frequency squeak on a sound A(t) background occurs.

Sound code synchronization. As a result of a sound asynchronous frequency - pulse coding the real values of time qi, q2,..., qm moments have appeared. For a sound code pulse synchronization the discrete time is necessary to introduce and detain each of code pulses, in order its forward front to coincide with the nearest discrete moment of time (fig. 10). On the diagram a) the sound A(t) asynchronous code B (t) is shown. By hyphens on an abscissa axis discrete moments of time are marked.

tB(t

T

To t

>T

T

o. t

Figure 10. Sound code pulse synchronization diagram

0

0

The duration TH of each pulse canbe less or more than a clock interval Tt. The figure depicts the situation, when Th>Tt. On the diagram a) the synchronous code C^ (t) received as a result of a code B(t) synchronization is shown. The index y stands for synchronization frequency equal to

_ 1

T- . (25)

tt

During synchronization I-pulse is shifted in time towards a delay on an interval A9;. Due to unequal code B(t) pulses shift in time at its synchronization there is a case, when, despite identical sound A(t) and B(t) perception, the sounds A(t) and C^ (t) will cause different acoustical sensations. On the other hand, it is clear that at a frequency synchronization y increase the time position of synchronous code C^ (t) pulses will approximate to asynchronous pulses of a synchronizationB(t) code. Hence, in a limit at synchronization frequency directing to infinity both codes will coincide:

lim C^ (t) =B(t). (26)

T

Let B(t) is a diagram of any sound and (C^(t)}^e(0,M) is one-parametrical family of arbitrary sound diagrams. Functions B(t) n C^ (t) are only supposed to be locally summed on a given interval [0, T0]. If a sound B(t) and a set

of sounds (Cv (t)}ye(0,o,) satisfy the condition

T0, I

0 lCf(t) - B(t)ldt = °- (27)

then there is such a number y 0 >0 that for any y > y0 a sound C^ (t) sensation will coincide with a sound B(t) sensation.

The sense of the formulated hearing property (let us name it a threshold existence principle) is that any two sounds, whose diagrams differ from each other, will be orally indistinguishable. The threshold existence principle cannot be logically deduced from the reinforced generalized Talbot principle, and vice versa. This is the powerful tool of an acoustical analyzer functioning study and effective means of the decision for technical acoustics tasks.

Synchronization frequency. Based on dependence (26) and applying threshold existence principle, we shall receive synchronization frequency y0 ; at its excess (i.e. at a choice y > y0 ) sounds B(t) and C^(t) will be orally

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indistinguishable. The bottom border of all numbers set, which can be used as a number y0 , let us designate with a symbol V Kp and name critical synchronization frequency. Thus, if on a whole sound interval [0, T0] the synchronization frequency in a sound C^(t) exceeds the critical one, i.e. ra > ra Kp, then the sounds C^ (t) and B(t) should be orally perceived equally. At the same time, the acoustical sensations ofsounds C^ (t) and B(t) at V = V Kp should differ. Actually the value V Kp essentially depends only on one function B(t) numerical parameter.

The experiments are carried out on a special device called a continuous sound digitizer. In the beginning they were performed on sinusoidal signals U’(t) that correspond to a continuous sound with frequency of 1 kilohertz.

A(t)=asin2 n nt+a0. (28)

Sound parameters a and a0 are adjusted. The maximal interval Tmax between the next pulses at an asynchronous signal for a sound (48) is defined:

T ="

-1 max

a0 — a

the minimal interval Tmin :

(29)

T =

-1- min

a0 + a

(30)

After value s determination the choice of sinusoidal signal parameters a and ao is unequivocally defined by Tmax and Tmin

The experiment purpose was to observe the critical synchronization frequency V Kp variation according to sinusoidal signal parameters Tmax and Tmin. Instead of V Kp the inverse value TKp is used, i.e. critical clock interval. The task is to find a function form experimentally

Tkp=F (Tmax, Tmin).

(31)

As a result it is received that at an increase of fluctuation amplitude of a sampled sinusoidal signal the sound purity is deteriorated. At an increase of average recurrence frequency pulses in a signal B(t) a sound quality is also deteriorated. Thus, the less often pulses in a sound code follow, the better will be the sound quality.

The Weber principle [15] was experimentally confirmed in a course of research: the stimulus differences, hardly perceptible by a sense organ, are proportional to this stimulus value. The value TKp is defined by the minimal interval between pulses, as the absolute ear sensitivity is the highest on the shortest interval. It is also defined that pulse breadth change does not affect synchronization critical value.

Conclusion

The formalism of some human intelligence function modelling as some logic mechanism is considered. The suggested methods are used for studying and formal description of natural language, colour sight, sounding speech mechanisms. The research basis is the intelligence model construction with its appliance at construction of imitating human brain activity technical systems.

The research results of some aspects of natural language written form algebra-logical modelling are presented. Modelling process compact representation as a Cartesian system of logical equations is of great importance. The theory of human colour sight is considered. The experimentally checked conditions of colour sight predicate model linearity are studied and formalized. The experimental procedure for linear predicate determination is offered.

The theory of frequency-pulse sound coding, which provides the hearing perception of natural and coded sounds, is stated. The generalized Talbot principle is reinforced; numerical values of sound code parameters, which provide the sound naturalness, are experimentally determined. The critical clock interval linear dependence on minimal interval between neighbouring pulses of synchronized frequent-pulse sound code is determined.

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