Pages: 244-264
Published: 30.01.2024
Abstract: A system of 6 semantic equations with 6 unknown y-senses has been developed. The model cognitively models the meaning of the calculated new uncorrelated y-variables. Calculated (not modeled) values ??of y-variables, calculating meters ckj=corr(zk,yj), k ({1,…,6}, j({1,…,6} quantitative connections of manifestations of properties. 6 semantic solutions were found: meaning(y1), meaning(y2), meaning(y3),..., meaning(y6), significantly complementing the initial knowledge. Numerical y-variables are not mathematically correlated with each other: corr(y1,y2)=corr(y2,y3)=corr(y1,y3)=…=corr (y5,y6)=0, since the eigenvalue matrix ?66= (1/m)YTm6Ym6 is diagonal: ?66=I66. .These equalities are a consequence of the initial hypothesis of the model: the y-variables are independent in meaning from each other. The z-variabilities of 20 measurements of each of the 6 correlated indicators are calculated. The matrix of z-variability values ??Zm6={zi}, zi=(z1j,z2j,…,zmj)T, j=1,…,6, is transformed into the matrix Ym6=Zm6C66={yi}, yi=(y1j,…, ymj)T, uncorrelated y-variability values. 2 matrices (C66,?66) were calculated using the correlation matrix R66, where R66=(1/m)ZTm6Zm6, Ym6=Zm6C66, R66C66=C66?66, C66CT66=I66, CT66C66=I66, ?66=diag(3.6235,1.3922,0.5762,0.2936,0.0731,0.0415), tr(?66)=?1+…+?6=6. The initial semantic equality is a semantic matrix equality of the form: meaning (Ym6)=meaning(Zm6C66). We found 6 semantic solutions to the semantic multidimensional equation meaning(y1)(… (meaning(y6)=meaning(Zm6c1)(…(meaning(Zm6c6), where cj=(c1j,c2j…,c6j)T is the j-th eigenvector from jth column of the C66 matrix. The semantic and formulaic justification of knowledge from 6 semantic equations is given. The variables introduced into the model are endowed with mathematical and statistical properties, and the parameters are constant. The meanings of the explanatory factors change their degrees of variability (Table 4) from constant to highly random (6 gradations). In Tables 4, 5, the primary evidentiary phrases of knowledge are rewritten in more compact forms of the semantic format of information from the matrices C66?66,Y m6,Zm6: semantic format of information from the matrices C66?66,Ym6,Z m6: about the factors of schoolchildren's learning and about the controlled values ??of the model parameters that influence the status of the family and the grades of schoolchildren in 20 public schools in the United States. Each set of parameters determines its own type of family, which includes its own set of factors. The status of parents influences the success of the student - type No. 1 (0.0415/6 = 0.69% - an almost constantly present factor). The socio-economic status of the family and the status of parents have little influence on the success of schoolchildren - type No. 2 (0.0731/6=1.2% - an almost constantly present factor). The socio-economic status of the family and the status of parents have an even weaker influence on the success of schoolchildren K-type No. 3 (0.2936/6=4.89% - an almost constantly present factor). The socio-economic status of the family has a greater influence than the status of the parents on the success of the student - type No. 4 (0.5762/6=9.6% - a random factor that did not appear by chance). With a noticeable level of payment for school staff and with a low level of socio-economic status of the family and the status of parents, the current grades of schoolchildren are higher than grades for 6 classes - type No. 5 (1.3922/6=23.20% - a random factor that did not appear by chance). With an imperceptible level of payment for school staff and with a noticeable level of socio-economic status of the family and the status of parents, the current grades of schoolchildren are higher than grades for 6 classes - type No. 6 (Table 5). This factor has the greatest information content: 3.6235/6=60.39% is a non-random factor, manifested by chance, because it depends on 5 z-factors, manifested with equal strength c((-0.48)2. With the least dispersion of y-factors y6,y5,y4,y3,y2,y1 (from 0.0415 to 0.5762 - “constant facts”, then (with a slightly larger dispersion) - “other facts”. Next - “noticeable random facts” , "highly noticeable random facts that require regulation by departments of municipal government structures. The greatest degree of variability in the explanatory y-factor y1 ((1=3.6235) corresponds to highly noticeable random facts from the “parent-students-school” system.”
Key words: semantic information format, semantic variables, matrix semantic equality, multi-semantic equation with known and unknown semantic variables, cognitive model.
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