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Методы и методология формализации принятия решения в строительстве.

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1/2011
ВЕСТНИК
МГСУ
ɆȿɌɈȾɕ ɂ ɆȿɌɈȾɈɅɈȽɂə ɎɈɊɆȺɅɂɁȺɐɂɂ ɉɊɂɇəɌɂə
Ɋȿɒȿɇɂə ȼ ɋɌɊɈɂɌȿɅɖɋɌȼȿ
METHODS AND METHODOLOGY TO FORMALIZATIONS
DECISION MAKING IN CONSTRUCTION
Ɏ. Ʉ. Ʉɥɚɲɚɧɨɜ
F. Klashanov
ȽɈɍ ȼɉɈ ɆȽɋɍ
Ɏɨɪɦɚɥɢɡɚɰɢɹ ɦɟɬɨɞɨɜ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɩɪɢ ɜɵɪɚɛɨɬɤɟ ɩɪɢɧɹɬɢɹ ɪɟɲɟɧɢɹ ɜ
ɫɬɪɨɢɬɟɥɶɫɬɜɟ, ɩɨɡɜɨɥɢɬ ɪɚɰɢɨɧɚɥɢɡɢɪɨɜɚɬɶ ɭɩɪɚɜɥɟɧɢɟ ɢ ɮɨɪɦɢɪɨɜɚɬɶ ɟɝɨ ɫ ɭɱɟɬɨɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɢ ɥɨɝɢɱɟɫɤɨɣ ɚɪɝɭɦɟɧɬɚɰɢɢ. ɂɧɬɭɢɬɢɜɧɵɣ ɩɨɞɯɨɞ ɧɟ ɩɨɡɜɨɥɹɟɬ ɜɫɟɰɟɥɨ ɩɪɨɫɥɟɞɢɬɶ ɡɚ ɜɧɟɲɧɢɦɢ ɢ ɜɧɭɬɪɟɧɧɢɦɢ ɮɚɤɬɨɪɚɦɢ, ɜɥɢɹɸɳɢɦɢ ɧɚ
ɫɬɪɨɢɬɟɥɶɫɬɜɨ. Ʌɨɝɢɤɨ-ɥɢɧɝɜɢɫɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɫɩɨɫɨɛɫɬɜɭɸɬ ɥɢɤɜɢɞɚɰɢɢ ɷɬɨɝɨ
ɧɟɞɨɫɬɚɬɤɚ.
The formalization of the methods, used at production decision making in construction
will allow to rationalize management and form it with provision for mathematical and logical argumentation. The intuitive approach does not allow completely track for external and
internal factor, influencing upon construction. The logician-linguistically methods promote
the liquidations of this defect.
Ⱦɥɹ ɩɨɜɵɲɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫɭɳɟɫɬɜɭɸɳɟɝɨ ɢɧɬɭɢɬɢɜɧɨɝɨ ɩɨɞɯɨɞɚ ɜ ɫɢɫɬɟɦɟ ɭɩɪɚɜɥɟɧɢɢ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɪɚɡɪɚɛɨɬɚɬɶ ɢ ɞɚɬɶ ɦɟɬɨɞɨɥɨɝɢɸ ɩɨɫɬɪɨɟɧɢɹ ɮɨɪɦɚɥɢɡɨɜɚɧɧɵɯ ɦɟɬɨɞɨɜ ɭɩɪɚɜɥɟɧɢɹ, ɛɚɡɢɪɭɸɳɢɯɫɹ ɧɚ ɥɨɝɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɛɚɡɟ. ɗɬɨ
ɨɛɴɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɮɨɪɦɚɥɢɡɦ, ɹɜɥɹɟɬɫɹ ɬɨɣ ɨɫɧɨɜɧɨɣ ɛɚɡɨɣ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɹɟɬ ɟɫɬɟɫɬɜɟɧɧɵɦ ɫɩɨɫɨɛɨɦ ɪɚɡɨɛɪɚɬɶɫɹ ɜɨ ɜɫɟɯ ɯɢɬɪɨɫɩɥɟɬɟɧɢɹɯ ɜɡɚɢɦɨɫɜɹɡɟɣ ɦɟɠɞɭ ɪɚɡɥɢɱɧɵɦɢ ɮɚɤɬɨɪɚɦɢ /6/, ɤɨɬɨɪɵɯ ɛɨɥɶɲɟ, ɱɟɦ ɞɨɫɬɚɬɨɱɧɨ ɜ ɭɩɪɚɜɥɟɧɢɢ ɫɬɪɨɢɬɟɥɶɫɬɜɨɦ. Ɍɚɤɨɣ ɩɨɞɯɨɞ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɫɨɫɪɟɞɨɬɨɱɢɬɶ ɜɧɢɦɚɧɢɟ ɧɚ ɮɨɪɦɚɥɶɧɨɣ ɫɬɪɭɤɬɭɪɟ, ɚ ɧɟ ɧɚ ɢɧɬɭɢɬɢɜɧɨɦ ɫɦɵɫɥɟ ɩɨɧɹɬɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɫɬɪɨɢɬɟɥɶɫɬɜɟ, ɚ ɷɬɨ ɜ
ɫɜɨɸ ɨɱɟɪɟɞɶ ɨɛɥɟɝɱɚɟɬ ɨɬɵɫɤɚɧɢɟ ɨɛɨɛɳɟɧɢɣ ɜ ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɛɵɥɨ ɭɩɭɫɬɢɬɶ ɩɪɢ ɱɢɫɬɨ ɢɧɬɭɢɬɢɜɧɨɦ ɩɨɞɯɨɞɟ ɤ ɭɩɪɚɜɥɟɧɢɸ. ɇɨ ɧɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɢɫɬɢɧɧɵɦ ɢɫɬɨɱɧɢɤɨɦ ɪɚɡɜɢɬɢɹ ɬɟɨɪɢɢ ɭɩɪɚɜɥɟɧɢɹ ɹɜɥɹɟɬɫɹ
ɬɜɨɪɱɟɫɤɚɹ ɦɵɫɥɶ, ɩɨɞɞɟɪɠɢɜɚɟɦɚɹ ɢɧɬɭɢɰɢɟɣ. Ʉɚɤ ɷɬɨ ɨɬɦɟɱɟɧɨ ɜ /6, ɫɬɪ.243/ «Ɍɜɨɪɱɟɫɤɚɹ, ɤɨɧɫɬɪɭɤɬɢɜɧɚɹ ɢɧɬɭɢɰɢɹ ɦɚɬɟɦɚɬɢɤɚ ɩɪɢɜɧɨɫɢɬ ɜ ɦɚɬɟɦɚɬɢɤɭ ɧɟ ɞɟɞɭɤɬɢɜɧɵɟ
ɢ ɢɪɪɚɰɢɨɧɚɥɶɧɵɟ ɦɨɦɟɧɬɵ, ɭɩɨɞɨɛɥɹɸɳɢɟ ɟɟ ɦɭɡɵɤɟ ɢɥɢ ɠɢɜɨɩɢɫɢ». ɗɬɨ ɩɨɥɧɨɫɬɶɸ ɨɬɧɨɫɢɬɫɹ ɢ ɤ ɢɧɠɟɧɟɪɭ-ɫɬɪɨɢɬɟɥɸ, ɪɚɡɪɚɛɚɬɵɜɚɸɳɟɦɭ ɩɪɨɟɤɬ ɭɩɪɚɜɥɟɧɢɹ
ɫɬɪɨɢɬɟɥɶɫɬɜɨɦ. ȼɪɟɦɟɧɧɨ ɨɬɤɚɡɚɬɶɫɹ ɨɬ ɫɦɵɫɥɨɜɨɝɨ ɬɨɥɤɨɜɚɧɢɹ ɨɛɴɟɤɬɨɜ, ɚ ɫɨɫɪɟɞɨɬɨɱɢɬɶɫɹ ɧɚ ɜɧɟɲɧɢɯ ɮɨɪɦɚɯ ɢ ɦɚɧɢɩɭɥɹɰɢɹɯ ɫ ɧɢɦɢ, ɬ. ɟ ɤɚɤ ɜ ɲɭɬɤɭ ɝɨɜɨɪɹɬ ɦɚɬɟɦɚɬɢɤɢ ɢɫɩɨɥɶɡɨɜɚɬɶ «ɫɩɨɫɨɛ ɧɚɧɟɫɟɧɢɹ ɧɚ ɛɭɦɚɝɭ ɛɟɫɫɦɵɫɥɟɧɧɵɯ ɡɧɚɤɨɜ». Ɂɞɟɫɶ ɬɚɤɠɟ
ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɧɟ ɜɫɟɝɞɚ ɜɨɡɦɨɠɧɨ ɨɛɨɫɧɨɜɚɬɶ ɜɧɭɬɪɟɧɧɸɸ ɫɨɝɥɚɫɨɜɚɧ-
331
ВЕСТНИК
МГСУ
1/2011
ɧɨɫɬɶ ɢ ɨɬɫɭɬɫɬɜɢɟ ɩɪɨɬɢɜɨɪɟɱɢɣ ɜ ɮɨɪɦɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ, ɨɫɧɨɜɚɧɧɵɯ ɧɚ ɚɤɫɢɨɦɚɯ
(Ƚɺɞɟɥɶ, 1931)
ɂɬɚɤ, ɟɫɬɟɫɬɜɟɧɧɵɣ ɹɡɵɤ ɢɦɟɟɬ ɪɹɞ ɨɫɨɛɟɧɧɨɫɬɟɣ, ɦɟɲɚɸɳɢɯ ɟɦɭ ɭɫɩɟɲɧɨ
ɫɩɪɚɜɥɹɬɶɫɹ ɫ ɪɟɲɟɧɢɟɦ ɡɚɞɚɱ. Ʉ ɷɬɢɦ ɨɫɨɛɟɧɧɨɫɬɹɦ ɩɪɟɠɞɟ ɜɫɟɝɨ ɫɥɟɞɭɟɬ ɨɬɧɟɫɬɢ
ɫɥɟɞɭɸɳɢɟ: ɩɪɚɜɢɥɚ ɩɨɫɬɪɨɟɧɢɹ ɫɥɨɠɧɵɯ ɜɵɪɚɠɟɧɢɣ ɢɡ ɩɪɨɫɬɵɯ ɪɚɫɩɥɵɜɱɚɬɵ; ɢɧɬɭɢɬɢɜɧɵɟ ɤɪɢɬɟɪɢɢ ɨɫɦɵɫɥɟɧɧɨɫɬɢ ɭɬɜɟɪɠɞɟɧɢɣ ɧɟɧɚɞɟɠɧɵ; ɫɬɪɭɤɬɭɪɚ ɮɪɚɡ ɫɤɪɵɜɚɟɬ ɪɟɚɥɶɧɭɸ ɥɨɝɢɱɟɫɤɭɸ ɮɨɪɦɭ; ɛɨɥɶɲɢɧɫɬɜɨ ɜɵɪɚɠɟɧɢɣ ɦɧɨɝɨɡɧɚɱɧɨ; ɦɧɨɝɨɟ ɨɫɬɚɟɬɫɹ ɧɟɜɵɹɜɥɟɧɧɵɦ, ɚ ɬɨɥɶɤɨ ɦɨɥɱɚɥɢɜɨ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ; ɧɟɬ ɜɨɡɦɨɠɧɨɫɬɢ ɬɨɱɧɨ ɩɟɪɟɞɚɬɶ ɮɨɪɦɭ ɦɵɫɥɢ. ɑɬɨɛɵ ɨɛɴɹɫɧɢɬɶ ɩɨɹɜɥɟɧɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɦɵɫɥɨɜ ɜɵɫɤɚɡɵɜɚɧɢɹ, ɝɥɭɛɠɟ ɩɪɨɧɢɤɧɭɬɶ ɜ ɡɧɚɱɟɧɢɹ ɫɥɨɜɚ, ɜɜɨɞɹɬɫɹ ɬɚɤɢɟ ɩɨɧɹɬɢɹ ɤɚɤ ɮɪɟɣɦɵ, ɫɰɟɧɵ
ɢɥɢ ɫɰɟɧɚɪɢɢ, ɤɨɬɨɪɵɟ ɩɪɟɞɨɩɪɟɞɟɥɹɸɬ ɪɟɱɟɜɵɟ ɜɵɫɤɚɡɵɜɚɧɢɹ.
Ⱦɥɹ ɤɨɧɤɪɟɬɧɨɣ ɤɨɥɢɱɟɫɬɜɟɧɧɨɣ ɨɰɟɧɤɢ ɭɬɜɟɪɠɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɫɬɢ
ɮɨɪɦɚɥɢɡɚɰɢɸ ɷɬɨɝɨ ɭɬɜɟɪɠɞɟɧɢɹ, ɬ. ɟ. ɧɟɨɛɯɨɞɢɦ ɢɫɤɭɫɫɬɜɟɧɧɵɣ ɹɡɵɤ, ɫɬɪɨɹɳɢɣɫɹ
ɩɨ ɫɬɪɨɝɨ ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɵɦ ɩɪɚɜɢɥɚɦ, ɢ ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɣ ɞɥɹ ɜɵɹɜɥɟɧɢɹ ɥɨɝɢɱɟɫɤɢɯ ɫɜɹɡɟɣ ɫ ɦɚɤɫɢɦɚɥɶɧɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɶɸ. Ʉɚɤ ɨɛɪɚɡɧɨ ɭɬɜɟɪɠɞɚɟɬ ɧɟɦɟɰɤɢɣ ɥɨɝɢɤ Ƚ. Ʉɥɚɭɫ «ɫɨɡɞɚɧɢɟ ɟɝɨ ɢɦɟɥɨ ɬɚɤɨɟ ɠɟ ɡɧɚɱɟɧɢɟ ɜ ɨɛɥɚɫɬɢ ɦɵɲɥɟɧɢɹ ɞɥɹ ɬɟɯɧɢɤɢ
ɥɨɝɢɱɟɫɤɨɝɨ ɜɵɜɨɞɚ, ɤɚɤɨɟ ɜ ɨɛɥɚɫɬɢ ɩɪɨɢɡɜɨɞɫɬɜɚ ɢɦɟɥ ɩɟɪɟɯɨɞ ɨɬ ɪɭɱɧɨɝɨ ɬɪɭɞɚ ɤ
ɬɪɭɞɭ ɦɟɯɚɧɢɡɢɪɨɜɚɧɧɨɦɭ»
ȼ ɮɨɪɦɚɥɢɡɨɜɚɧɧɨɦ ɹɡɵɤɟ ɮɨɪɦɚɥɶɧɚɹ ɥɨɝɢɤɚ ɫɜɨɟ ɝɥɚɜɧɨɟ ɜɧɢɦɚɧɢɟ ɧɚɩɪɚɜɥɹɟɬ ɧɚ ɜɵɹɫɧɟɧɢɟ ɫɬɪɭɤɬɭɪɵ ɡɧɚɧɢɹ, ɧɚ ɟɝɨ «ɚɧɚɬɨɦɢɪɨɜɚɧɢɟ» ɢ ɨɩɢɫɚɧɢɟ ɮɨɪɦɚɥɶɧɵɯ ɫɜɹɡɟɣ ɟɝɨ ɷɥɟɦɟɧɬɨɜ. Ɇɚɬɟɦɚɬɢɱɟɫɤɢɦ ɩɨɧɹɬɢɹɦ, ɜɜɟɞɟɧɧɵɦ ɩɪɢ ɮɨɪɦɚɥɢɡɚɰɢɢ,
ɧɢɤɚɤɨɣ ɢɧɬɭɢɬɢɜɧɨɣ ɪɟɚɥɶɧɨɫɬɢ ɧɟ ɩɪɢɩɢɫɵɜɚɟɬɫɹ, ɜ ɨɫɧɨɜɟ ɥɟɠɢɬ ɮɨɪɦɚɥɶɧɚɹ ɥɨɝɢɱɟɫɤɚɹ ɩɪɚɜɢɥɶɧɨɫɬɶ ɩɪɨɰɟɫɫɚ ɪɚɫɫɭɠɞɟɧɢɣ, ɛɚɡɢɪɭɸɳɚɹɫɹ ɧɚ ɩɨɫɬɭɥɚɬɚɯ. ɏɨɬɹ ɧɭɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɨɞɧɢɦ ɢɡ ɬɢɩɨɜ ɥɨɝɢɱɟɫɤɨɝɨ ɜɵɜɨɞɚ ɹɜɥɹɟɬɫɹ ɢɧɬɭɢɰɢɹ, ɤɨɬɨɪɚɹ ɨɫɧɨɜɚɧɚ ɧɚ ɩɪɨɜɟɪɟɧɧɨɣ ɬɟɨɪɢɢ. ȼɵɜɨɞɵ ɧɚ ɨɫɧɨɜɟ ɢɧɬɭɢɰɢɢ ɧɟ ɧɚɲɥɢ ɩɨɤɚ ɦɚɲɢɧɧɨɣ
ɪɟɚɥɢɡɚɰɢɢ, ɧɨ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɧɟɣɪɨɧɧɵɟ ɫɟɬɢ ɜɨɡɦɨɠɧɨ ɩɨɡɜɨɥɹɬ ɷɬɨ ɫɞɟɥɚɬɶ, ɩɨɫɤɨɥɶɤɭ ɧɟɣɪɨɧɧɚɹ ɫɟɬɶ ɜɫɟɝɞɚ ɜɵɪɚɛɚɬɵɜɚɟɬ ɫɜɨɟ ɜɨɡɦɨɠɧɨɟ ɧɚɢɥɭɱɲɟɟ ɩɪɟɞɩɨɥɨɠɟɧɢɟ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɤɨɦɨɝɨ ɪɟɲɟɧɢɹ. Ɍɟɪɦɢɧ ɮɨɪɦɚɥɶɧɵɣ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɥɨɝɢɤɚ, ɤ
ɤɨɬɨɪɨɣ ɨɧ ɨɬɧɨɫɢɬɫɹ, ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɬɨɥɶɤɨ ɧɚ ɮɨɪɦɭ ɥɨɝɢɱɟɫɤɢɯ ɭɬɜɟɪɠɞɟɧɢɣ,
ɧɨ ɧɟ ɭɱɢɬɵɜɚɟɬ ɢɯ ɡɧɚɱɟɧɢɹ, ɬ.ɟ. ɜ ɮɨɪɦɚɥɶɧɨɣ ɥɨɝɢɤɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɬɨɥɶɤɨ ɫɢɧɬɚɤɫɢɫ ɭɬɜɟɪɠɞɟɧɢɣ, ɧɨ ɧɟ ɢɯ ɫɟɦɚɧɬɢɤɚ /1/ . Ɏɨɪɦɚɥɢɡɦ ɩɨɡɜɨɥɹɟɬ ɨɬɞɟɥɢɬɶ ɡɧɚɧɢɹ
ɨɬ ɪɚɫɫɭɠɞɟɧɢɣ. ɗɬɨ ɫɜɨɣɫɬɜɨ ɮɨɪɦɚɥɢɡɦɚ ɜɚɠɧɨ ɩɪɢ ɜɵɪɚɛɨɬɤɟ ɩɪɢɧɹɬɢɹ ɪɟɲɟɧɢɹ, ɢ
ɬɟɦ ɫɚɦɵɦ, ɫɨɡɞɚɧɢɢ ɨɩɬɢɦɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ.
Ʉɨɝɧɢɬɢɜɧɚɹ ɝɪɚɦɦɚɬɢɤɚ ɜɜɟɥɚ ɩɨɧɹɬɢɟ ɮɪɟɣɦɨɜ ɞɥɹ ɩɨɧɢɦɚɧɢɹ ɩɪɟɞɥɨɠɟɧɢɹ,
ɧɨ ɧɟɬ ɟɞɢɧɫɬɜɚ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɩɨɧɹɬɢɹ ɮɪɟɣɦɚ. ɇɟɤɨɬɨɪɵɟ ɚɜɬɨɪɵ ɫɪɚɜɧɢɜɚɸɬ ɮɪɟɣɦɵ ɫɨ ɡɪɢɬɟɥɶɧɵɦɢ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦɢ, ɞɪɭɝɢɟ - ɫɨ ɫɯɟɦɚɦɢ, ɫɰɟɧɚɦɢ ɢ ɦɨɞɟɥɹɦɢ, ɤɨɬɨɪɵɟ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɩɚɤɟɬɵ ɢɧɮɨɪɦɚɰɢɢ, ɯɪɚɧɢɦɵɟ ɜ ɩɚɦɹɬɢ ɢɥɢ ɫɨɡɞɚɜɚɟɦɵɟ ɜ
ɧɟɣ ɩɨ ɦɟɪɟ ɧɚɞɨɛɧɨɫɬɢ. Ɍɚɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɨɡɜɨɥɹɸɬ ɭɫɬɚɧɚɜɥɢɜɚɬɶ ɫɜɹɡɚɧɧɨɫɬɶ
ɬɟɤɫɬɚ ɧɚ ɦɢɤɪɨ- ɢ ɦɚɤɪɨɭɪɨɜɧɟ ɢ ɮɨɪɦɢɪɨɜɚɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ɭɦɨɡɚɤɥɸɱɟɧɢɹ. ȼ ɷɬɨɦ
ɫɥɭɱɚɟ ɷɮɮɟɤɬɢɜɧɨ ɪɚɛɨɬɚɟɬ ɮɨɪɦɚɥɶɧɚɹ ɥɨɝɢɤɚ.
ȼ ɮɨɪɦɚɥɶɧɨɣ ɥɨɝɢɤɟ ɫɦɵɫɥ ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ ɢ ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɬɨɥɶɤɨ ɮɨɪɦɚ ɢɥɢ
ɜɧɟɲɧɟɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ. Ʌɨɝɢɤɚ ɫɬɚɧɨɜɢɬɫɹ ɬɚɤɢɦ ɦɨɳɧɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɢɦɟɧɧɨ ɛɥɚɝɨɞɚɪɹ ɢɫɩɨɥɶɡɭɟɦɨɣ ɜ ɧɟɣ ɤɨɧɰɟɩɰɢɢ (ɨɫɧɨɜɨɩɨɥɚɝɚɸɳɚɹ ɢɞɟɹ; ɟɞɢɧɵɣ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɡɚɦɵɫɟɥ) ɨɬɞɟɥɟɧɢɹ ɮɨɪɦɵ ɨɬ ɫɦɵɫɥɚ, ɢɥɢ ɫɟɦɚɧɬɢɤɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɬɞɟɥɟɧɢɹ
ɮɨɪɦɵ ɨɬ ɫɟɦɚɧɬɢɤɢ ɩɨɹɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɟɤɬɢɜɧɨ ɨɰɟɧɢɬɶ, ɹɜɥɹɟɬɫɹ ɥɢ ɞɨɤɚɡɚɬɟɥɶɫɬɜɨ ɞɟɣɫɬɜɢɬɟɥɶɧɵɦ, ɧɟ ɢɫɩɵɬɵɜɚɹ ɜɨɡɞɟɣɫɬɜɢɹ ɩɪɟɞɭɛɟɠɞɟɧɢɣ, ɜɵɡɜɚɧɧɵɯ
ɫɟɦɚɧɬɢɤɨɣ. ȿɳɟ ɨɞɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɮɨɪɦɚɥɶɧɨɣ ɥɨɝɢɤɢ ɹɜɥɹɟɬɫɹ ɜɜɟɞɟɧɢɟ ɩɭɫɬɨɝɨ
ɤɥɚɫɫɚ ɨɛɴɟɤɬɨɜ, ɱɬɨ ɜ ɩɪɢɧɰɢɩɟ ɩɪɨɬɢɜɨɪɟɱɢɥɨ ɷɤɡɢɫɬɟɧɰɢɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ ɜ ɥɨɝɢ-
332
1/2011
ВЕСТНИК
МГСУ
ɤɟ Ⱥɪɢɫɬɨɬɟɥɹ ɢ ɮɨɪɦɭɥɢɪɨɜɤɚ ɚɤɫɢɨɦ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɫɢɦɜɨɥɨɜ. Ⱥɤɫɢɨɦɵ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɨɩɪɟɞɟɥɟɧɢɹ, ɧɚ ɨɫɧɨɜɚɧɢɢ ɤɨɬɨɪɵɯ ɫɨɡɞɚɸɬɫɹ ɥɨɝɢɱɟɫɤɢɟ
ɫɯɟɦɵ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɚɤɫɢɨɦ ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɬɟɨɪɟɦɵ - ɷɬɨ ɭɬɜɟɪɠɞɟɧɢɹ, ɤɨɬɨɪɵɟ
ɫɥɟɞɭɸɬ ɢɡ ɚɤɫɢɨɦ, ɬ.ɟ. ɢɫɩɨɥɶɡɭɟɬɫɹ ɹɡɵɤ ɦɚɬɟɦɚɬɢɤɢ. Ⱥɪɢɮɦɟɬɢɱɟɫɤɢɟ ɨɩɟɪɚɰɢɢ
ɨɛɪɚɡɭɸɬ ɧɚ ɦɧɨɠɟɫɬɜɟ ɱɢɫɟɥ ɩɨɥɟ, ɤɨɬɨɪɨɟ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɨ, ɩɨɷɬɨɦɭ ɪɚɫɫɦɚɬɪɢɜɚɬɶ
ɟɝɨ ɧɟ ɛɭɞɟɦ. ȿɫɥɢ ɩɪɨɫɥɟɞɢɬɶ ɞɢɧɚɦɢɤɭ ɪɚɡɜɢɬɢɹ (ɢɫɬɨɪɢɸ) ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɩɨɧɢɦɚɧɢɹ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ (ɚɧɚɥɢɡ, ɫɢɧɬɟɡ), ɬɨ ɦɨɠɧɨ ɭɜɢɞɟɬɶ, ɜ ɫɯɟɦɚɬɢɱɧɨɦ ɩɪɟɞɫɬɚɜɥɟɧɢɢ, ɧɟ ɜɧɢɤɚɹ ɜ ɞɟɬɚɥɢ, ɚ ɭɤɪɭɩɧɟɧɨ, ɱɬɨ ɨɧɚ ɩɪɨɲɥɚ ɩɭɬɶ ɨɬ ɥɨɝɢɤɢ Ⱥɪɢɫɬɨɬɟɥɹ (ɫɢɥɥɨɝɢɡɦɵ) ɤ ɫɢɦɜɨɥɢɱɟɫɤɨɣ ɥɨɝɢɤɟ Ȼɭɥɹ (ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɥɨɝɢɤɟ), ɡɚɬɟɦ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɚɹ ɥɨɝɢɤɚ, ɥɨɝɢɤɚ ɩɪɟɞɢɤɚɬɨɜ, ɧɟɱɟɬɤɚɹ ɥɨɝɢɤɚ, ɦɟɬɨɞɵ ɩɨɫɬɪɨɟɧɢɹ ɥɨɝɢɤɨɥɢɧɝɜɢɫɬɢɱɟɫɤɢɯ ɦɨɞɟɥɢ ɜ ɭɩɪɚɜɥɟɧɢɢ. Ʉɚɠɞɵɣ ɢɡ ɷɬɢɯ ɦɟɬɨɞɨɜ ɛɚɡɢɪɭɟɬɫɹ ɧɚ ɫɜɨɟɣ
ɫɢɦɜɨɥɢɤɟ (ɚɥɮɚɜɢɬɟ), ɚɤɫɢɨɦɚɯ, ɝɢɩɨɬɟɡɚɯ ɢ ɬɟɨɪɟɦɚɯ. Ɋɚɫɫɦɨɬɪɢɦ ɛɨɥɟɟ ɩɨɞɪɨɛɧɨ
ɥɨɝɢɱɟɫɤɢɟ ɨɩɟɪɚɰɢɢ ɢ ɩɟɪɟɣɞɟɦ ɤ ɩɨɫɬɪɨɟɧɢɸ ɧɟɞɨɫɬɚɸɳɢɯ ɫɜɹɡɨɤ ɫɥɟɞɭɹ ɥɨɝɢɤɨɥɢɧɝɜɢɫɬɢɱɟɫɤɨɝɨ ɯɚɪɚɤɬɟɪɚ ɫɥɟɞɭɹ ɪɟɤɨɦɟɧɞɚɰɢɹɦ Ⱦ.Ⱥ. ɉɨɫɩɟɥɨɜɚ /5/.
Ɂɚ ɨɫɧɨɜɭ ɜɡɹɬɚ ɦɟɬɨɞɨɥɨɝɢɹ ɚɥɝɟɛɪɵ. Ⱥɥɝɟɛɪɚ - ɷɬɨ ɮɨɪɦɚɥɶɧɚɹ ɥɨɝɢɤɚ ɱɢɫɟɥ.
Ʉɚɤ ɚɥɝɟɛɪɚ ɩɨɡɜɨɥɹɟɬ ɫɨɫɪɟɞɨɬɨɱɢɬɶ ɜɫɟ ɜɧɢɦɚɧɢɟ ɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɚɧɢɩɭɥɹɰɢɢ
ɛɟɡ ɭɱɟɬɚ ɬɨɝɨ, ɱɬɨ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɨɛɴɟɤɬɵ, ɬɚɤ ɢ ɮɨɪɦɚɥɶɧɚɹ ɥɨɝɢɤɚ ɩɨɡɜɨɥɹɟɬ
ɜɫɟ ɭɫɢɥɢɹ ɧɚɩɪɚɜɢɬɶ ɧɚ ɪɚɫɫɭɠɞɟɧɢɹ, ɧɟ ɜɧɢɤɚɹ ɜ ɨɩɪɟɞɟɥɟɧɢɹ ɫɚɦɢɯ ɨɛɴɟɤɬɨɜ. Ⱥɥɝɟɛɪɚ A ɷɬɨ ɫɨɜɨɤɭɩɧɨɫɬɶ ɧɨɫɢɬɟɥɹ A ɢ ɫɢɝɧɚɬɭɪɵ Ȉ
A = < A, Ȉ>
Ɍɟɩɟɪɶ ɧɭɠɧɨ ɤɨɧɤɪɟɬɢɡɢɪɨɜɚɬɶ, ɱɬɨ ɬɚɤɨɟ ɧɨɫɢɬɟɥɹ A ɢ ɱɬɨ ɬɚɤɨɟ ɫɢɝɧɚɬɭɪɚ Ȉ. ɇɨɫɢɬɟɥɟɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɹɜɥɹɸɬɫɹ ɩɨɜɟɫɬɜɨɜɚɬɟɥɶɧɵɟ ɡɚɤɪɵɬɵɟ ɩɪɟɞɥɨɠɟɧɢɹ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɹɡɵɤɚ - ɜɵɫɤɚɡɵɜɚɧɢɹ, ɬ. ɟ. ɷɬɨ ɦɧɨɠɟɫɬɜɨ ɹɜɥɹɸɳɟɟɫɹ ɩɨɞɦɧɨɠɟɫɬɜɨɦ ɩɪɟɞɥɨɠɟɧɢɣ, ɚ ɫɢɝɧɚɬɭɪɚ ɷɬɨ ɦɧɨɠɟɫɬɜɨ ɜɫɟɯ ɚɪɢɮɦɟɬɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ, ɚ ɬɚɤɠɟ ɫɜɹɡɤɢ ɢ
ɤɜɚɧɬɨɪɵ ɥɨɝɢɤɢ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɧɢɯ ɩɨɞɪɨɛɧɟɟ, ɱɬɨɛɵ ɪɚɫɤɪɵɬɶ ɫɦɵɫɥ ɢ ɢɯ ɪɨɥ ɜ
ɧɚɲɟɦ ɩɨɫɬɪɨɟɧɢɢ. ɂɧɨɝɞɚ ɜɵɫɤɚɡɵɜɚɧɢɹ ɜɧɟɲɧɟ ɜɵɝɥɹɞɹɬ ɤɚɤ ɪɚɫɫɭɠɞɟɧɢɹ, ɯɨɬɹ
ɨɧɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɡɧɚɧɢɹ.
ȼ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɨɣ ɥɨɝɢɤɟ (proposition ɥɚɬ. ɩɪɟɞɥɨɠɟɧɢɟ) ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɣ ɬɢɩ ɩɪɟɞɥɨɠɟɧɢɣ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɹɡɵɤɚ, ɚ ɫɚɦɢ ɩɪɟɞɥɨɠɟɧɢɹ ɩɨɞɪɚɡɞɟɥɹɸɬɫɹ ɧɚ ɱɟɬɵɪɟ ɨɫɧɨɜɧɵɯ ɬɢɩɚ: ɩɨɜɟɥɢɬɟɥɶɧɨɟ, ɜɨɩɪɨɫɢɬɟɥɶɧɨɟ, ɜɨɫɤɥɢɰɚɬɟɥɶɧɨɟ ɢ
ɩɨɜɟɫɬɜɨɜɚɬɟɥɶɧɨɟ. ȼ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɨɣ ɥɨɝɢɤɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɩɨɞɦɧɨɠɟɫɬɜɚ
ɩɪɟɞɥɨɠɟɧɢɣ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɫɨɛɨɣ ɩɨɜɟɫɬɜɨɜɚɬɟɥɶɧɵɟ ɩɪɟɞɥɨɠɟɧɢɹ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ
ɩɨɞɪɚɡɞɟɥɹɬɶɫɹ ɧɚ ɢɫɬɢɧɧɵɟ ɢɥɢ ɥɨɠɧɵɟ. ȼɜɟɞɟɦ ɤɨɧɤɪɟɬɢɡɚɰɢɸ, ɢ ɛɭɞɟɦ ɩɪɢɞɟɪɠɢɜɚɬɶɫɹ ɫɥɟɞɭɸɳɟɣ ɬɟɪɦɢɧɨɥɨɝɢɢ. ɉɪɟɞɥɨɠɟɧɢɟ, ɢɫɬɢɧɧɨɫɬɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɨ, ɬ.ɟ. ɢɡɜɟɫɬɧɨ a priori ɢɫɬɢɧɧɨ ɨɧɨ ɢɥɢ ɥɨɠɧɨ, ɧɚɡɵɜɚɟɬɫɹ ɭɬɜɟɪɠɞɟɧɢɟɦ, ɢɥɢ ɜɵɫɤɚɡɵɜɚɧɢɟɦ. ȼɵɫɤɚɡɵɜɚɧɢɟ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɬɚɤɠɟ ɡɚɤɪɵɬɵɦ
ɩɪɟɞɥɨɠɟɧɢɟɦ, ɩɨɫɤɨɥɶɤɭ ɟɝɨ ɢɫɬɢɧɧɨɫɬɧɨɟ ɡɧɚɱɟɧɢɟ ɧɟ ɜɵɡɵɜɚɟɬ ɫɨɦɧɟɧɢɣ ɢ, ɩɨɷɬɨɦɭ ɧɟ ɩɨɞɥɟɠɢɬ ɨɛɫɭɠɞɟɧɢɸ. Ɍɟɩɟɪɶ ɢɡ ɩɨɞɦɧɨɠɟɫɬɜɚ ɩɨɜɟɫɬɜɨɜɚɬɟɥɶɧɵɯ ɩɪɟɞɥɨɠɟɧɢɣ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɬɨɥɶɤɨ ɩɨɞɦɧɨɠɟɫɬɜɨ ɡɚɤɪɵɬɵɯ ɩɪɟɞɥɨɠɟɧɢɣ, ɬɚɤ ɤɚɤ ɟɫɬɶ
ɩɪɟɞɥɨɠɟɧɢɟ, ɧɚ ɤɨɬɨɪɨɟ ɧɟɜɨɡɦɨɠɧɨ ɞɚɬɶ ɨɞɧɨɡɧɚɱɧɵɣ ɨɬɜɟɬ, ɢ ɧɚɡɵɜɚɸɬɫɹ ɨɧɢ ɨɬɤɪɵɬɵɦ ɩɪɟɞɥɨɠɟɧɢɟɦ.
ɉɪɢɱɢɧɵ ɨɬɤɪɵɬɨɫɬɢ ɩɪɟɞɥɨɠɟɧɢɹ, ɪɚɫɫɦɨɬɪɢɦ ɧɚ ɤɨɧɤɪɟɬɧɵɯ ɩɪɢɦɟɪɚɯ, ɤɨɬɨɪɵɟ ɜɵɞɟɥɹɸɬ ɤɥɚɫɫɵ ɨɬɤɪɵɬɵɯ ɩɪɟɞɥɨɠɟɧɢɣ ɢ ɩɨɤɚɡɵɜɚɸɬ ɩɪɢɡɧɚɤɢ ɢɡ-ɡɚ ɤɨɬɨɪɵɯ
ɩɪɨɢɫɯɨɞɢɬ ɢɫɤɥɸɱɟɧɢɟ ɷɬɢɯ ɩɪɟɞɥɨɠɟɧɢɣ ɢɡ ɦɧɨɠɟɫɬɜɚ ɧɨɫɢɬɟɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ
ɚɥɝɟɛɪɚɢɱɟɫɤɨɣ ɫɬɪɭɤɬɭɪɵ.
1. Ɍɚɤɢɦ ɨɬɤɪɵɬɵɦ ɩɪɟɞɥɨɠɟɧɢɟɦ ɹɜɥɹɟɬɫɹ, ɧɚɩɪɢɦɟɪ, ɩɪɟɞɥɨɠɟɧɢɟ «Ʉɢɪɩɢɱ
ɨɬɥɢɱɧɵɣ ɫɬɪɨɢɬɟɥɶɧɵɣ ɦɚɬɟɪɢɚɥ». ȿɫɬɶ ɡɚɤɚɡɱɢɤɢ, ɤɨɬɨɪɵɟ ɩɪɟɞɩɨɱɢɬɚɸɬ ɞɟɪɟɜɨ, ɚ
333
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ɟɫɬɶ ɡɚɤɚɡɱɢɤɢ, ɩɪɟɞɩɨɱɢɬɚɸɳɢɟ ɛɟɬɨɧ ɢɥɢ ɞɪɭɝɢɟ ɫɬɪɨɢɬɟɥɶɧɵɟ ɦɚɬɟɪɢɚɥɵ, ɬ. ɟ. ɭɫɬɚɧɨɜɢɬɶ ɡɞɟɫɶ ɢɫɬɢɧɧɨɫɬɶ ɧɟɜɨɡɦɨɠɧɨ.
2. ȼ ɩɪɟɞɥɨɠɟɧɢɢ ɧɟɬ ɤɨɧɤɪɟɬɧɨɫɬɢ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɟɫɬɨɢɦɟɧɢɟ. ɉɪɢɦɟɪ, «Ɉɧ
ɨɬɥɢɱɧɨɝɨ ɤɚɱɟɫɬɜɚ» - ɱɬɨ ɢɦɟɧɧɨ, ɤɢɪɩɢɱ ɢɥɢ ɞɪɭɝɨɣ ɫɬɪɨɢɬɟɥɶɧɵɣ ɦɚɬɟɪɢɚɥ. ȼ ɷɬɨɦ
ɩɪɟɞɥɨɠɟɧɢɢ ɧɟɥɶɡɹ ɭɫɬɚɧɨɜɢɬɶ ɢɫɬɢɧɧɨɫɬɶ. ɗɬɨ ɨɬɤɪɵɬɨɟ ɩɪɟɞɥɨɠɟɧɢɟ ɞɨ ɬɟɯ ɩɨɪ,
ɩɨɤɚ ɧɟ ɛɭɞɟɬ ɩɪɨɢɡɜɟɞɟɧɚ ɤɨɧɤɪɟɬɢɡɚɰɢɹ.
3. ɋɥɟɞɭɸɳɢɦ ɩɪɢɦɟɪɨɦ ɨɬɤɪɵɬɨɝɨ ɩɪɟɞɥɨɠɟɧɢɹ ɛɭɞɟɬ ɩɪɟɞɥɨɠɟɧɢɟ «ɇɚ
ɫɬɪɨɣɤɟ ɪɚɛɨɬɚɟɬ ɦɧɨɝɨ ɪɚɛɨɱɢɯ». ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨ ɫɥɨɜɨ «ɦɧɨɝɨ» ɢɦɟɟɦ
ɤɨɥɢɱɟɫɬɜɟɧɧɭɸ ɧɟɨɞɧɨɡɧɚɱɧɨɫɬɶ. Ɍɨɱɧɨ ɬɚɤɠɟ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɨɜɚ «ɦɚɥɨ» ɢɥɢ
ɧɚɩɪɢɦɟɪ, «ɉɨɫɬɚɜɳɢɤ ɧɚɯɨɞɢɬɫɹ ɞɚɥɟɤɨ (ɛɥɢɡɤɨ)» - ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. Ⱥɧɚɥɨɝɢɱɧɨ ɜɜɨɞɢɬɫɹ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ ɜɨ ɜɪɟɦɟɧɢ ɫɥɨɜɚɦɢ «ɩɨɡɞɧɨ», «ɪɚɧɨ» ɢ
ɬ.ɞ. ȼɫɟ ɷɬɨ ɭɤɚɡɵɜɚɟɬ ɧɚ ɬɨ, ɱɬɨ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɚɹ ɥɨɝɢɤɚ ɧɟ ɫɩɪɚɜɥɹɟɬɫɹ ɫ ɞɚɧɧɵɦɢ
ɡɚɞɚɱɚɦɢ, ɧɨ ɟɟ ɜɨɡɦɨɠɧɨɫɬɢ ɦɨɠɧɨ ɪɚɫɲɢɪɢɬɶ, ɟɫɥɢ ɜɜɟɫɬɢ ɧɟɱɟɬɤɭɸ ɥɨɝɢɤɭ, ɬ.ɟ. ɟɫɥɢ
ɧɟɬ ɨɞɧɨɡɧɚɱɧɨɫɬɢ ɩɨɧɹɬɢɹ (ɬɹɠɟɥɵɣ, ɜɵɫɨɤɢɣ, ɞɨɪɨɝɨɣ, ɞɚɥɟɤɨ ɢ ɬ.ɩ.) – ɪɟɲɟɧɢɟ
ɩɪɨɛɥɟɦɵ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɡɚ ɫɱɟɬ ɩɪɢɦɟɧɟɧɢɹ ɧɟɱɟɬɤɨɣ ɥɨɝɢɤɢ.
ȼɨɡɦɨɠɧɨɫɬɢ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɨɣ ɥɨɝɢɤɢ ɦɨɠɧɨ ɪɚɫɲɢɪɢɬɶ ɩɭɬɟɦ ɩɪɢɦɟɧɟɧɢɹ
ɥɨɝɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ (ɫɜɹɡɨɤ) ɤ ɨɬɞɟɥɶɧɵɦ ɜɵɫɤɚɡɵɜɚɧɢɹɦ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɛɭɞɭɬ
ɫɮɨɪɦɢɪɨɜɚɧɵ ɫɨɫɬɚɜɧɵɟ ɜɵɫɤɚɡɵɜɚɧɢɹ. ɇɟ ɫɬɚɜɹ ɰɟɥɶɸ ɪɚɡɛɨɪɚ ɷɬɢɯ ɥɨɝɢɱɟɫɤɢɯ
ɮɭɧɤɰɢɢ, ɬɚɤ ɜɫɟ ɢɯ ɫɜɨɣɫɬɜɚ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɜ ɛɭɥɟɜɨɣ ɚɥɝɟɛɪɟ, ɨɬɦɟɬɢɦ
ɬɨɥɶɤɨ, ɱɬɨ ɨɞɧɚ ɢɡ ɧɢɯ ɭɧɚɪɧɚɹ – ɨɬɪɢɰɚɧɢɟ (NOT, ™ ), ɨɫɬɚɥɶɧɵɟ ɛɢɧɚɪɧɵɟ. Ʉ ɛɢɧɚɪɧɵɦ ɫɜɹɡɤɚɦ ɨɬɧɨɫɹɬɫɹ ɤɨɧɴɸɧɤɰɢɹ (ɂ, AND, š ), ɞɢɡɴɸɧɤɰɢɹ (ɂɅɂ, OR, › ),
ɦɚɬɟɪɢɚɥɶɧɚɹ ɢɦɩɥɢɤɚɰɢɹ (IF-THEN, ɟɫɥɢ…, ɬɨ…, o ), ɷɤɜɢɜɚɥɟɧɬɧɨɫɬɶ (ɟɫɥɢ ɢ
ɬɨɥɶɤɨ ɟɫɥɢ, l ), ɲɬɪɢɯ ɒɟɮɮɟɪɚ (ɚɧɬɢɤɨɧɴɸɧɤɰɢɹ) (NAND, ɧɟ-ɂ,
), ɫɬɪɟɥɤɚ
ɉɢɪɫɚ (ɚɧɬɢɞɢɡɴɸɧɤɰɢɹ) (NOR, ɧɟ-ɂɅɂ, p ), ɫɥɨɠɟɧɢɟ ɩɨ ɦɨɞɭɥɸ ɞɜɚ (ɚɧɬɢɷɤɜɢɜɚɥɟɧɬɧɨɫɬɶ) ( † ).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɫɨɫɬɚɜ ɫɢɝɧɚɬɭɪɵ Ȉ, ɤɚɤ ɦɧɨɠɟɫɬɜɚ ɨɩɟɪɚɰɢɣ, ɜɯɨɞɢɬ ɩɨɞɦɧɨ-
^
`
ɠɟɫɬɜɨ ɜ ɜɢɞɟ ™,š,›, o, l, , p,† .
^™,š,›, o, l,
, p,†`  6 .
Ɉɬɦɟɬɢɦ, ɱɬɨ ^™,š,›` ɨɛɪɚɡɭɸɬ ɛɚɡɢɫ, ɬ.ɟ. ɥɸɛɭɸ ɥɨɝɢɱɟɫɤɭɸ ɮɭɧɤɰɢɸ ɦɨɠɧɨ
ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɷɬɢ ɞɜɟ ɛɢɧɚɪɧɵɟ ɮɭɧɤɰɢɢ ɢ ɨɞɧɭ ɭɧɚɪɧɭɸ. ɋɨɝɥɚɫɧɨ ɬɟɨɪɟɦɵ ɉɨɫɬɚ
ɬɚɤɢɟ ɮɭɧɤɰɢɢ ɤɚɤ ɲɬɪɢɯ ɒɟɮɮɟɪɚ (
), ɫɬɪɟɥɤɚ ɉɢɪɫɚ ( p ), ɨɛɪɚɡɭɸɬ ɬɚɤ ɠɟ ɛɚɡɢɫ,
ɧɨ ɫɨɫɬɨɹɳɢɣ ɬɨɥɶɤɨ ɢɡ ɨɞɧɨɣ ɮɭɧɤɰɢɢ.
Ɉɬɦɟɬɢɦ ɟɳɟ, ɱɬɨ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɚɹ ɥɨɝɢɤɚ ɢɦɟɟɬ ɨɫɧɨɜɧɨɣ ɧɟɞɨɫɬɚɬɨɤ ɜ ɬɨɦ,
ɱɬɨ ɨɧɚ ɧɟ ɩɨɡɜɨɥɹɟɬ ɢɫɫɥɟɞɨɜɚɬɶ ɜɧɭɬɪɟɧɧɸɸ ɫɬɪɭɤɬɭɪɭ ɜɵɫɤɚɡɵɜɚɧɢɹ, ɨɧɚ ɪɚɛɨɬɚɟɬ
ɬɨɥɶɤɨ ɫ ɩɨɥɧɵɦɢ ɜɵɫɤɚɡɵɜɚɧɢɹɦɢ. ɂɫɱɢɫɥɟɧɢɟ ɜɵɫɤɚɡɵɜɚɧɢɣ ɧɟɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɡɚɞɚɧɢɹ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɥɨɝɢɱɟɫɤɢɯ ɪɚɫɫɭɠɞɟɧɢɣ, ɨɧɚ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɧɚɥɢɱɢɟ
ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɫɜɨɣɫɬɜɚ ɧɚ ɤɨɧɟɱɧɨɦ ɦɧɨɠɟɫɬɜɟ ɷɥɟɦɟɧɬɨɜ ɫɥɭɱɚɟ ɛɟɫɤɨɧɟɱɧɨɝɨ ɦɧɨɠɟɫɬɜɚ ɞɥɹ ɭɫɬɚɧɨɜɥɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɫɜɨɣɫɬɜɚ ɭ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɚɛɫɬɪɚɤɬɧɨɝɨ
ɩɨɧɹɬɢɹ ɧɟɨɛɯɨɞɢɦɨ ɜɜɟɞɟɧɢɟ ɮɭɧɤɰɢɣ, ɚɪɝɭɦɟɧɬɵ ɤɨɬɨɪɵɯ ɩɪɨɛɟɝɚɸɬ ɛɟɫɤɨɧɟɱɧɨɟ
ɱɢɫɥɨ ɡɧɚɱɟɧɢɣ ɜ ɦɧɨɠɟɫɬɜɟ M.
Ɏɭɧɤɰɢɹ P, ɩɪɢɧɢɦɚɸɳɚɹ ɨɞɧɨ ɢɡ ɡɧɚɱɟɧɢɣ, 0 ɢɥɢ 1, ɚɪɝɭɦɟɧɬɵ ɤɨɬɨɪɨɣ ɩɪɨɛɟɝɚɸɬ ɡɧɚɱɟɧɢɹ ɢɡ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɦɧɨɠɟɫɬɜɚ M , ɧɚɡɵɜɚɟɬɫɹ ɩɪɟɞɢɤɚɬɨɦ P ɜ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ M. ɑɢɫɥɨ ɚɪɝɭɦɟɧɬɨɜ ɩɪɟɞɢɤɚɬɚ P(x1, x2,…, xn) ɧɚɡɵɜɚɟɬɫɹ ɟɝɨ ɩɨɪɹɞɤɨɦ.
ɉɨɷɬɨɦɭ ɞɥɹ ɚɧɚɥɢɡɚ ɨɛɳɢɯ ɫɥɭɱɚɟɜ ɛɵɥɚ ɪɚɡɪɚɛɨɬɚɧɚ ɥɨɝɢɤɚ ɩɪɟɞɢɤɚɬɨɜ /1/.
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МГСУ
ɉɪɨɫɬɟɣɲɚɹ ɮɨɪɦɚ ɟɺ - ɥɨɝɢɤɚ ɩɪɟɞɢɤɚɬɨɜ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ, ɧɚ ɛɚɡɟ, ɤɨɬɨɪɨɣ
ɪɚɡɪɚɛɨɬɚɧɵ ɹɡɵɤɢ ɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɚɩɪɢɦɟɪ, PROLOG. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɚɹ ɥɨɝɢɤɚ ɹɜɥɹɟɬɫɹ ɩɨɞɦɧɨɠɟɫɬɜɨɦ ɥɨɝɢɤɢ ɩɪɟɞɢɤɚɬɨɜ.
Ʌɨɝɢɤɚ ɩɪɟɞɢɤɚɬɨɜ ɩɨɡɜɨɥɹɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɜɧɭɬɪɟɧɧɸɸ ɫɬɪɭɤɬɭɪɭ ɩɪɟɞɥɨɠɟɧɢɣ; ɜ ɧɟɣ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɬɚɤɢɯ ɫɩɟɰɢɚɥɶɧɵɯ ɫɥɨɜ ɤɚɤ «ɜɫɟ», «ɧɟɤɨɬɨɪɵɟ»
ɢ «ɧɢ ɨɞɢɧ», ɤɨɬɨɪɵɟ ɧɚɡɵɜɚɸɬɫɹ ɤɜɚɧɬɨɪɚɦɢ /1/. Ʉɜɚɧɬɨɪ (ɥɚɬ. quantum ɫɤɨɥɶɤɨ) –
ɷɬɨ ɫɢɦɜɨɥ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɥɨɝɢɤɢ ɢ ɤɚɤ ɥɨɝɢɱɟɫɤɚɹ ɨɩɟɪɚɰɢɹ ɞɚɟɬ ɤɨɥɢɱɟɫɬɜɟɧɧɭɸ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɨɛɥɚɫɬɢ ɩɪɟɞɦɟɬɨɜ, ɤ ɤɨɬɨɪɵɦ ɨɬɧɨɫɢɬɫɹ ɜɵɪɚɠɟɧɢɟ, ɩɨɥɭɱɚɟɦɨɟ ɜ
ɪɟɡɭɥɶɬɚɬɟ ɟɟ ɩɪɢɦɟɧɟɧɢɹ. Ʉɜɚɧɬɨɪɵ ɨɬɜɟɱɚɸɬ ɧɚ ɜɨɩɪɨɫ «ɫɤɨɥɶɤɨ» ɢ ɩɨɡɜɨɥɹɸɬ ɩɪɢɫɜɚɢɜɚɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɵɟ ɨɰɟɧɤɢ ɞɪɭɝɢɦ ɫɥɨɜɚɦ ɢ ɬɟɦ ɫɚɦɵɦ ɪɚɫɲɢɪɹɸɬ ɤɪɭɝ ɜɵɪɚɠɟɧɢɣ. ȼ ɥɨɝɢɤɟ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɜɚ ɫɬɚɧɞɚɪɬɧɵɯ ɤɜɚɧɬɨɪɚ, ɤɨɬɨɪɵɟ
ɧɚɡɵɜɚɸɬ ɤɜɚɧɬɨɪɚɦɢ ɜɫɟɨɛɳɧɨɫɬɢ ( - ɩɟɪɟɜɟɪɧɭɬɚɹ ɛɭɤɜɚ Ⱥ ɨɛɨɡɧɚɱɚɟɬ «all» - ɜɫɟ
ɢ ɱɢɬɚɟɬɫɹ - «ɞɥɹ ɜɫɟɯ …») ɢ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ( ).ɋɭɳɟɫɬɜɭɟɬ ɬɚɤɠɟ ɤɜɚɧɬɨɪ ɩɥɸɪɚɥɶɧɨɫɬɢ (ɤɜɚɧɬɨɪ Ɋɟɲɟɪɚ) W (ɩɟɪɟɜɺɪɧɭɬɚɹ M). Wx ɨɡɧɚɱɚɟɬ «ɞɥɹ ɛɨɥɶɲɢɧɫɬɜɚ x».
ɉɪɢɦɟɧɟɧɢɟ ɤɜɚɧɬɨɪɚ ɜɫɟɨɛɳɧɨɫɬɢ ( ). Ʉɜɚɧɬɨɪ ɜɫɟɨɛɳɧɨɫɬɢ ɩɨɡɜɨɥɹɟɬ ɮɨɪɦɢɪɨɜɚɬɶ ɭɬɜɟɪɠɞɟɧɢɹ ɨ ɤɚɠɞɨɦ ɨɛɴɟɤɬɟ. ɉɪɢ ɜɵɪɚɠɟɧɢɢ ɨɛɳɢɯ ɩɪɚɜɢɥ ɜ ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɨɣ ɥɨɝɢɤɟ ɜɨɡɧɢɤɚɸɬ ɬɪɭɞɧɨɫɬɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɮɨɪɦɚɥɢɡɚɰɢɟɣ ɡɚɩɢɫɢ ɨɛɳɟɝɨ
ɫɜɨɣɫɬɜɚ (ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ) ɢ ɡɚɩɢɫɚɬɶ
xPx Ÿ Q x ɑɬɨ ɩɨɧɢɦɚɟɬɫɹ ɤɚɤ «ɞɥɹ ɜɫɟɯ x, ɟɫɥɢ x ɥɨɝɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ P , ɬɨ x ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨ Q », ɝɞɟ x ɟɫɬɶ ɩɟɪɟɦɟɧɧɚɹ, ɩɪɢɧɚɞɥɟɠɚɳɚɹ ɧɟɤɨɬɨɪɨɦɭ ɦɧɨɠɟɫɬɜɭ X, ɬɟɦ ɫɚɦɵɦ
ɞɚɧɨ ɨɩɢɫɚɧɢɟ ɦɧɨɠɟɫɬɜɚ, ɚ ɧɟ ɬɨɥɶɤɨ ɟɞɢɧɢɱɧɨɝɨ ɷɥɟɦɟɧɬɚ. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ,
ɱɬɨ ɫɚɦɚ ɩɟɪɟɦɟɧɧɚɹ x ɦɨɠɟɬ ɹɜɥɹɬɶɫɹ ɬɟɪɦɨɦ, ɤɨɬɨɪɵɣ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɫɥɭɠɢɬɶ ɩɚɪɚɦɟɬɪɨɦ ɮɭɧɤɰɢɢ. ȼɵɫɤɚɡɵɜɚɧɢɟ xP x ɨɡɧɚɱɚɟɬ, ɱɬɨ ɨɛɥɚɫɬɶ ɢɫɬɢɧɧɨɫɬɢ ɩɪɟɞɢɤɚɬɚ P(x) ɫɨɜɩɚɞɚɟɬ ɫ ɨɛɥɚɫɬɶɸ ɡɧɚɱɟɧɢɣ ɩɟɪɟɦɟɧɧɨɣ x, ɬ. ɟ. «ɩɪɢ ɜɫɟɯ ɡɧɚɱɟɧɢɹɯ (x)
ɭɬɜɟɪɠɞɟɧɢɟ ɜɟɪɧɨ». ȼɵɫɤɚɡɵɜɚɧɢɟ xP x , ɝɞɟ P - ɥɸɛɨɟ ɥɨɝɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ,
ɨɡɧɚɱɚɟɬ, ɱɬɨ P ɹɜɥɹɟɬɫɹ ɢɫɬɢɧɧɵɦ ɞɥɹ ɤɚɠɞɨɝɨ ɨɛɴɟɤɬɚ x, ɬ.ɟ. ɷɬɨ ɮɨɪɦɚɥɶɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɢɧɬɭɢɬɢɜɧɨɝɨ ɫɦɵɫɥɚ ɩɪɢɦɟɧɟɧɢɟ ɤɜɚɧɬɨɪɚ ɜɫɟɨɛɳɧɨɫɬɢ. ȼ ɜɵɪɚɠɟɧɢɢ
x  M Ax ɮɨɪɦɭɥɚ A(x) ɧɚɡɵɜɚɟɬɫɹ ɨɛɥɚɫɬɶɸ ɞɟɣɫɬɜɢɹ ɤɜɚɧɬɨɪɚ x . Ʉɜɚɧɬɨɪ ɜɫɟɨɛɳɧɨɫɬɢ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɨɛɨɛɳɟɧɢɟ ɤɨɧɴɸɧɤɰɢɢ. ȿɫɥɢ ɩɪɟɞɦɟɬɧɚɹ
ɨɛɥɚɫɬɶ ɤɨɧɟɱɧɚ ɢ ɫɨɫɬɨɢɬ ɢɡ ɷɥɟɦɟɧɬɨɜ m1, m2, …, mn , ɬɨ ɮɨɪɦɭɥɚ xP x ɦɨɠɟɬ
ɛɵɬɶ ɜɵɪɚɠɟɧ ɫ ɩɨɦɨɳɶɸ ɤɨɧɴɸɧɤɰɢɢ
ɷɥɟɦɟɧɬɨɜ mi ɦɧɨɠɟɫɬɜɚ A:
Pm1 š Pm2 š ... š Pmn , ɝɞɟ ɩɨɞ P ɦɨɠɧɨ, ɧɚɩɪɢɦɟɪ, ɩɨɧɢɦɚɬɶ «ɷɤɫɤɚɜɚɬɨɪɵ»,
ɚ mi – i-ɵɣ ɩɚɪɚɦɟɬɪ ɷɤɫɤɚɜɚɬɨɪɚ.
ɉɪɢɦɟɧɟɧɢɟ ɤɜɚɧɬɨɪɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ( ). Ʉɜɚɧɬɨɪ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɩɨɡɜɨɥɹɟɬ
ɮɨɪɦɢɪɨɜɚɬɶ ɭɬɜɟɪɠɞɟɧɢɹ ɨ ɧɟɤɨɬɨɪɨɦ ɨɛɴɟɤɬɟ ɛɟɡ ɟɝɨ ɢɦɟɧɨɜɚɧɢɹ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ,
ɤ ɨɞɧɨɦɭ ɷɥɟɦɟɧɬɭ ɨɛɥɚɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ, ɬ.ɟ. ɨɧ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɨɝɪɚɧɢɱɟɧɧɭɸ
ɮɨɪɦɭ ɤɜɚɧɬɨɪɚ ɜɫɟɨɛɳɧɨɫɬɢ. ɉɪɢ ɡɚɩɢɫɢ ɡɚ ɤɜɚɧɬɨɪɨɦ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɦɨɝɭɬ ɫɥɟɞɨɜɚɬɶ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɩɟɪɟɦɟɧɧɵɯ, ɧɚɩɪɢɦɟɪ, ( x) (ɤɪɚɧ(x) š ɦɚɪɤɚ (401Ⱥ)), ɬ.ɟ. ɧɚ
ɫɬɪɨɣɤɟ ɢɦɟɟɬɫɹ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɨɞɢɧ ɤɪɚɧ ɦɚɪɤɢ 401Ⱥ. Ʉɜɚɧɬɨɪ ɫɭɳɟɫɬɜɨɜɚɧɢɹ
ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧ ɫ ɩɨɦɨɳɶɸ ɞɢɡɴɸɧɤɰɢɢ
ɷɥɟɦɟɧɬɨɜ mi ɦɧɨɠɟɫɬɜɚ A:
Pm1 › Pm2 › ... › Pmn , ɝɞɟ ɩɨɞ P ɦɨɠɧɨ, ɧɚɩɪɢɦɟɪ, ɩɨɧɢɦɚɬɶ «ɝɪɭɡɨɩɨɞɴɟɦɧɵɟ ɦɚɲɢɧɵ», ɚ
mi – i-ɵɣ ɩɚɪɚɦɟɬɪ ɝɪɭɡɨɩɨɞɴɟɦɧɨɣ ɦɚɲɢɧɵ.
ȼɵɫɤɚɡɵɜɚɧɢɟ
335
ВЕСТНИК
МГСУ
1/2011
xP x ɨɡɧɚɱɚɟɬ, ɱɬɨ ɨɛɥɚɫɬɶ ɢɫɬɢɧɧɨɫɬɢ ɩɪɟɞɢɤɚɬɚ P(x) ɧɟɩɭɫɬɚɹ ɢ ɨɡɧɚɱɚɟɬ «ɫɭɳɟɫɬɜɭɟɬ (x) ɩɪɢ ɤɨɬɨɪɨɦ ɭɬɜɟɪɠɞɟɧɢɟ ɜɟɪɧɨ».
ɇɚɞ ɤɜɚɧɬɨɪɚɦɢ ɦɨɠɧɨ ɩɨɜɨɞɢɬɶ ɨɩɟɪɚɰɢɢ. ɉɪɚɜɢɥɨ ɨɬɪɢɰɚɧɢɹ ɤɜɚɧɬɨɪɨɜ —
ɩɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɨɬɪɢɰɚɧɢɣ ɜɵɫɤɚɡɵɜɚɧɢɣ, ɫɨɞɟɪɠɚɳɢɯ ɤɜɚɧɬɨɪɵ, ɢ ɢɦɟɟɬ
ɜɢɞ:
™x P x x ™Px ; ™x P x x ™P x ɋɜɹɡɶ ɦɟɠɞɭ ɤɜɚɧɬɨɪɚɦɢ ɢ . Ʉɜɚɧɬɨɪ ɢ ɬɟɫɧɨ ɫɜɹɡɚɧɵ ɞɪɭɝ ɫ ɞɪɭɝɨɦ
ɱɟɪɟɡ ɨɬɪɢɰɚɧɢɟ. ȼ ɨɩɪɟɞɟɥɟɧɢɢ ɮɨɪɦɭɥɵ ɜ ɱɢɫɥɟ ɨɫɧɨɜɧɵɯ ɫɢɦɜɨɥɨɜ ɨɬɫɭɬɫɬɜɭɟɬ
ɡɧɚɤ ɞɥɹ ɤɜɚɧɬɨɪɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ, ɬɚɤ ɤɚɤ ɟɝɨ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ ɫɨɤɪɚɳɟɧɧɭɸ
ɡɚɩɢɫɶ ɞɥɹ x A x .
ɉɪɟɞɦɟɬɧɚɹ ɩɟɪɟɦɟɧɧɚɹ, ɜɯɨɞɹɳɚɹ ɜ ɮɨɪɦɭɥɭ ɧɚɡɵɜɚɟɬɫɹ ɫɜɨɛɨɞɧɨɣ ɟɫɥɢ ɨɧɚ
ɧɟ ɫɥɟɞɭɟɬ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɡɚ ɤɜɚɧɬɨɪɚɦɢ ɧɟ ɜɯɨɞɢɬ ɜ ɨɛɥɚɫɬɶ ɞɟɣɫɬɜɢɹ ɤɜɚɧɬɨɪɚ ɩɨ
ɷɬɨɣ ɩɟɪɟɦɟɧɧɨɣ, ɜɫɟ ɞɪɭɝɢɟ ɩɟɪɟɦɟɧɧɵɟ, ɜɯɨɞɹɳɢɟ ɜ ɮɨɪɦɭɥɭ, ɧɚɡɵɜɚɸɬɫɹ ɫɜɹɡɚɧɧɵɦɢ.
ɂɡ ɛɚɡɨɜɵɯ ɷɥɟɦɟɧɬɨɜ ɨɛɪɚɡɭɸɬɫɹ ɩɪɨɢɡɜɨɞɧɵɟ ɷɥɟɦɟɧɬɵ, ɤɨɬɨɪɵɟ ɜ ɢɫɱɢɫɥɟɧɢɢ ɩɪɟɞɢɤɚɬɨɜ ɛɵɜɚɸɬ ɬɪɟɯ ɬɢɩɨɜ: ɬɟɪɦɵ, ɚɬɨɦɵ ɢ ɮɨɪɦɭɥɵ.
Ɍɟɪɦ ɨɛɪɚɡɭɸɬɫɹ ɩɨ ɫɥɟɞɭɸɳɟɦɭ ɩɪɚɜɢɥɭ.
1. ȼɫɹɤɚɹ ɩɪɟɞɦɟɬɧɚɹ ɩɟɪɟɦɟɧɧɚɹ ɢɥɢ ɩɪɟɞɦɟɬɧɚɹ ɤɨɧɫɬɚɧɬɚ ɟɫɬɶ ɬɟɪɦ
3. ȿɫɥɢ ij - n-ɦɟɫɬɧɵɣ ɮɭɧɤɰɢɨɧɚɥɶɧɵɣ ɫɢɦɜɨɥ, ɚ t1, t2,…, tn - ɬɟɪɦɵ, ɬɨ ij(t1,
t2,…, tn ) ɬɚɤɠɟ ɬɟɪɦ.
4. Ⱦɪɭɝɢɯ ɬɟɪɦɨɜ ɧɟɬ.
Ⱥɬɨɦ. ȿɫɥɢ P ɟɫɬɶ ɧɟɤɨɬɨɪɵɣ n-ɦɟɫɬɧɵɣ ɩɪɟɞɢɤɚɬɧɵɣ ɫɢɦɜɨɥ, ɚ ɚ t1, t2,…, tn ɬɟɪɦɵ, ɬɨ P(t1, t2,…, tn ) ɟɫɬɶ ɚɬɨɦ.
Ɏɨɪɦɭɥɚ.
1. Ⱥɬɨɦ ɟɫɬɶ ɮɨɪɦɭɥɚ (ɚɬɨɦɚɪɧɚɹ ɮɨɪɦɭɥɚ)
2. ȿɫɥɢ ȍ ɢ Ȅ ɮɨɪɦɭɥɵ, ɬɨ ™: , : & ; , : › ; , : Š ; , : ~ ; ɬɚɤɠɟ ɮɨɪɦɭɥɵ.
3. ȿɫɥɢ ȍ ɟɫɬɶ ɮɨɪɦɭɥɚ, ɚ x ɩɟɪɟɦɟɧɧɚɹ, ɜɯɨɞɹɳɚɹ ɜ ɧɟɟ, ɬɨ x: ɢ x: ɬɚɤɠɟ ɮɨɪɦɭɥɵ.
4. Ⱦɪɭɝɢɯ ɮɨɪɦɭɥ ɧɟɬ.
Ʌɨɝɢɤɚ ɩɪɟɞɢɤɚɬɨɜ ɢɦɟɟɬ ɛɨɥɟɟ ɲɢɪɨɤɭɸ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ
ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɨɣ ɥɨɝɢɤɨɣ, ɧɨ ɧɟɤɨɬɨɪɵɟ ɬɢɩɵ ɭɬɜɟɪɠɞɟɧɢɣ ɧɟɜɨɡɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɧɚ ɨɫɧɨɜɟ ɥɨɝɢɤɢ ɩɪɟɞɢɤɚɬɨɜ, ɬɨ ɟɫɬɶ ɨɧɚ ɬɪɟɛɭɟɬ ɪɚɫɲɢɪɟɧɢɹ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ
ɪɟɲɚɬɶ ɤɨɧɤɪɟɬɧɵɟ ɡɚɞɚɱɢ, ɜɵɞɜɢɝɚɟɦɵɟ ɩɪɚɤɬɢɤɨɣ. Ʉɜɚɧɬɨɪɵ ɜɫɟɨɛɳɧɨɫɬɢ ɢ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɧɟ ɨɬɜɟɱɚɸɬ ɧɚ ɧɟɤɨɬɨɪɵɟ ɩɨɫɬɚɜɥɟɧɧɵɟ ɜɨɩɪɨɫɵ, ɩɨɷɬɨɦɭ ɞɨɥɠɧɵ ɛɵɬɶ
ɩɪɟɞɭɫɦɨɬɪɟɧɵ ɧɟɤɨɬɨɪɵɟ ɫɩɟɰɢɚɥɶɧɵɟ ɩɪɟɞɢɤɚɬɵ ɞɥɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɡɚɞɚɱ. Ɍɚɤ
ɤɜɚɧɬɨɪ «ɛɨɥɶɲɢɧɫɬɜɨ» ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧ ɜ ɬɟɪɦɢɧɚɯ ɤɜɚɧɬɨɪɨɜ ɜɫɟɨɛɳɧɨɫɬɢ ɢ
ɫɭɳɟɫɬɜɨɜɚɧɢɹ. Ɍɚɤɠɟ ɧɭɠɧɨ ɭɱɟɫɬɶ, ɱɬɨ ɧɟɤɨɬɨɪɵɟ ɭɬɜɟɪɠɞɟɧɢɹ ɢɧɨɝɞɚ ɢɫɬɢɧɵ, ɚ ɧɟ
ɜɫɟɝɞɚ (ɜ ɞɪɭɝɢɯ ɨɛɫɬɨɹɬɟɥɶɫɬɜɚɯ ɷɬɢ ɠɟ ɩɪɟɞɢɤɚɬɵ ɥɨɠɧɵ). ȼɵɯɨɞ ɢɡ ɷɬɨɝɨ ɩɨɥɨɠɟɧɢɹ ɞɚɟɬ ɧɟɱɟɬɤɚɹ ɥɨɝɢɤɚ, ɤɨɬɨɪɚɹ ɞɨɫɬɚɬɨɱɧɨ ɩɨɥɧɨ ɪɚɡɪɚɛɨɬɚɧɚ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɪɟɚɥɶɧɵɯ ɡɚɞɚɱ ɫɜɨɞɢɬɫɹ ɜ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ ɤ ɤɨɦɩɶɸɬɟɪɧɨɦɭ ɦɨɞɟɥɢɪɨɜɚɧɢɸ, ɤɨɬɨɪɨɟ ɬɟɫɧɨ ɫɜɹɡɚɧɨ ɫ ɩɪɨɝɪɚɦɦɧɨɬɟɯɧɢɱɟɫɤɢɦɢ ɫɪɟɞɫɬɜɚɦɢ. Ⱦɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɢɧɹɬɢɹ ɪɟɲɟɧɢɹ ɩɨ ɭɩɪɚɜɥɟɧɢɸ ɧɟɨɛɯɨɞɢɦɨ ɫɨɡɞɚɜɚɬɶ ɱɟɥɨɜɟɤɨ-ɦɚɲɢɧɧɨɝɨ ɹɡɵɤɚ ɫ ɩɚɪɚɥɥɟɥɶɧɨɣ ɨɛɪɚɛɨɬɤɨɣ ɢɧɮɨɪɦɚɰɢɢ ɫ ɜɜɟɞɟɧɢɟɦ ɪɚɞɢɤɚɥɨɜ.
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ВЕСТНИК
МГСУ
Ʌɢɬɟɪɚɬɭɪɚ
1. Ⱦɠɚɪɪɚɬɚɧɨ Ⱦɠɨɡɟɮ, Ɋɚɣɥɢ Ƚɚɪɢ. ɗɤɫɩɟɪɬɧɵɟ ɫɢɫɬɟɦɵ: ɩɪɢɧɰɢɩɵ ɪɚɡɪɚɛɨɬɤɢ ɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ, 4-ɟ ɢɡɞɚɧɢɟ. : ɉɟɪ. ɫ ɚɧɝɥ. – Ɇ. : ɈɈɈ «ɂ.Ⱦ. ȼɢɥɶɹɦɫ» , 2007. – 1152 ɫ.
2. Ʉɢɦ Ⱦ.ɉ. Ɍɟɨɪɢɹ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ. Ɍ.1. Ʌɢɧɟɣɧɵɟ ɫɢɫɬɟɦɵ – 2-ɟ ɢɡɞɚɧɢɟ. – Ɇ.:
ɎɂɁɆȺɌɅɂɌ, 2007. -312 ɫ.
3.ɘɪɟɜɢɱ ȿ.ɂ. Ɍɟɨɪɢɹ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ. – 3-ɟ ɢɡɞ. – ɋɩɛ.: Ȼɏȼ-ɉɟɬɟɪɛɭɪɝ, 2007. –
560 ɫ.
4. Ɋɚɫɫɟɥ ɋɬɸɚɪɬ. ɇɨɪɜɢɝ ɉɢɬɟɪ. ɂɫɤɭɫɫɬɜɟɧɧɵɣ ɢɧɬɟɥɥɟɤɬ : ɫɨɜɪɟɦɟɧɧɵɣ ɩɨɞɯɨɞ. 2-ɟ ɢɡɞ, -Ɇ.:
ɂɡɞɚɬɟɥɶɫɤɢɣ ɞɨɦ «ȼɢɥɶɹɦɫ», 2007 - 1408 ɫ.
5. ɉɨɫɩɟɥɨɜ Ⱦ. Ⱥ. Ʌɨɝɢɤɨ-ɥɢɧɝɜɢɫɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɜ ɫɢɫɬɟɦɚɯ ɭɩɪɚɜɥɟɧɢɹ. – Ɇ.: ɗɧɟɪɝɨɢɡɞɚɬ,
1981. -232 ɫ.
6. Ʉɭɪɚɧɬ Ɋ.Ȼ., Ɋɨɛɛɢɧɫ Ƚ. ɑɬɨ ɬɚɤɨɟ ɦɚɬɟɦɚɬɢɤɚ? – 4-ɟ ɢɡɞ., ɫɬɟɪɟɨɬɢɩɧɨɟ. – Ɇ.: ɆɐɇɆɈ, 2007.
– 568 ɫ.
The literature
1. Joseph C. Giarratano, Gary D. Riley Expert Systems: principles and programming, fourth edition;
Thomson, Course Technology.
2. Kim D.P. The Theory of the autocontrol. Vol.1. Linear systems - 2-end edition. - M.: FIZMATLIT,
2007. - 312 p.
3. Yurevich E.I. Theory automatic management. - 3-d publishing - SPb.: BHV-Petersburg, 2007. – 560
p.
4. Stuart J. Russell and Peter Norvig. Artificial Intelligence A modern approach. Second edition, New Jersey 07458.
5. Pospelov D. A. Logician-linguistical models in system of management. - M.: Energoizdat, 1981. 232 p.
6. What is Mathematics? An elementary approach to ideas methods by Richard Courant and Herbert
Robbins. Oxford University Press/ London – New York – Toronto.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɫɬɪɨɢɬɟɥɶɫɬɜɨ, ɩɪɢɧɹɬɢɟ ɪɟɲɟɧɢɹ, ɩɪɨɩɨɡɢɰɢɨɧɚɥɶɧɚɹ ɥɨɝɢɤɚ, ɤɜɚɧɬɨɪɵ,
ɩɪɟɞɢɤɚɬɵ, ɮɨɪɦɚɥɢɡɦ, ɥɨɝɢɤɨ-ɥɢɧɝɜɢɫɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ.
The Keywords: construction, decision making, sentential logic, quantifiers, predicates, formalism, logician-linguistically methods.
Ɋɟɰɟɧɡɟɧɬ: ɗ.ɉ. Ƚɪɢɝɨɪɶɟɜ ɩɪɨɮɟɫɫɨɪ ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ȼɇɂɂɌɗ
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