Практические занятия Методические указания

ȼɫɹɤɨɣ ɡɚɦɤɧɭɬɨɣ ɮɨɪɦɭɥɟ A ɦɨɠɧɨ ɩɨɫɬɚɜɢɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɮɨɪɦɭɥɭ SA, ɧɟ ɫɨɞɟɪɠɚɳɭɸ ɤɜɚɧɬɨɪɨɜ ɫɭɳɟɫɬɜɨɜɚɧɢɹ, ɬɚɤɭɸ, ɱɬɨ ɮɨɪɦɭɥɵ A ɢ SA ɥɢɛɨ ɨɛɟ ɜɵɩɨɥɧɢɦɵ, ɥɢɛɨ ɨɛɟ ɧɟɜɵɩɨɥɧɢɦɵ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɨɜɟɪɤɚ ɧɟɜɵɩɨɥɧɢɦɨɫɬɢ ɮɨɪɦɭɥɵ A ɦɨɠɟɬ ɛɵɬɶ ɫɜɟɞɟɧɚ ɤ ɩɪɨɜɟɪɤɟ ɧɟɜɵɩɨɥɧɢɦɨɫɬɢ ɮɨɪɦɭɥɵ SA. Ɏɨɪɦɚ SA ɧɚɡɵɜɚɟɬɫɹ ɫɤɨɥɟɦɨɜɫɤɨɣ ɮɨɪɦɨɣ. Ⱥɥɝɨɪɢɬɦ ɩɨɥɭɱɟɧɢɹ ɫɤɨɥɟɦɨɜɫɤɨɣ ɮɨɪɦɵ (ɫɤɨɥɟɦɢɡɚɰɢɹ) ɢɡ ɡɚɦɤɧɭɬɨɣ ɩɪɟɞɜɚɪɟɧɧɨɣ ɮɨɪɦɵ ɜɤɥɸɱɚɟɬ ɫɥɟɞɭɸɳɢɟ ɲɚɝɢ:

1.ɋɨɩɨɫɬɚɜɢɬɶ ɤɚɠɞɨɣ -ɤɜɚɧɬɢɮɢɰɢɪɨɜɚɧɧɨɣ ɩɟɪɟɦɟɧɧɨɣ ɫɩɢɫɨɤ ɩɪɟɞɲɟɫɬɜɭɸɳɢɯ ɟɣ ɜ ɩɪɟɮɢɤɫɟ -ɤɜɚɧɬɢɮɢɰɢɪɨɜɚɧɧɵɯ ɩɟɪɟɦɟɧɧɵɯ ɢ ɧɟɤɨɬɨɪɵɣ ɮɭɧɤɰɢɨɧɚɥɶɧɵɣ ɫɢɦɜɨɥ, ɦɟɫɬɧɨɫɬɶ ɤɨɬɨɪɨɝɨ ɪɚɜɧɚ ɦɨɳɧɨɫɬɢ ɩɨɥɭɱɟɧɧɨɝɨ ɫɩɢɫɤɚ.

2.ȼ ɦɚɬɪɢɰɟ ɮɨɪɦɭɥɵ ɡɚɦɟɧɢɬɶ ɤɚɠɞɨɟ ɜɯɨɠɞɟɧɢɟ ɤɚɠɞɨɣ - ɤɜɚɧɬɢɮɢɰɢɪɨɜɚɧɧɨɣ ɩɟɪɟɦɟɧɧɨɣ ɧɚ ɬɟɪɦ, ɩɨɥɭɱɟɧɧɵɣ ɩɭɬɟɦ ɞɨɛɚɜɥɟɧɢɹ ɤ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦɭ ɮɭɧɤɰɢɨɧɚɥɶɧɨɦɭ ɫɢɦɜɨɥɭ ɫɩɢɫɤɚ ɚɪɝɭɦɟɧɬɨɜ, ɫɨɩɨɫɬɚɜɥɟɧɧɵɯ ɷɬɨɣ ɩɟɪɟɦɟɧɧɨɣ.

3.ɍɞɚɥɢɬɶ ɢɡ ɮɨɪɦɭɥɵ ɜɫɟ -ɤɜɚɧɬɢɮɢɤɚɰɢɢ.

ɋɤɨɥɟɦɢɡɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜ ɩɪɟɞɜɚɪɟɧɧɨɣ ɮɨɪɦɟ, ɩɨɥɭɱɟɧɧɭɸ ɜ ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɜɵɲɟ ɩɪɢɦɟɪɟ:

y x u z[Q(x, y) & P(y) R(v) & S(u, z)]

1.ɉɨɫɬɚɜɢɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɤɚɠɞɨɣ -ɤɜɚɧɬɢɮɢɰɢɪɨɜɚɧɧɨɣ ɩɟɪɟɦɟɧɧɨɣ ɮɭɧɤɰɢɨɧɚɥɶɧɭɸ ɮɨɪɦɭ ɨɬ ɩɪɟɞɲɟɫɬɜɭɸɳɢɯ ɟɣ ɜ ɩɪɟɮɢɤɫɟ - ɤɜɚɧɬɢɮɢɰɢɪɨɜɚɧɧɵɯ ɩɟɪɟɦɟɧɧɵɯ:

x - f(y); z - g(y, u).

2.ɉɨɞɫɬɚɜɢɦ ɜ ɮɨɪɦɭɥɭ ɮɭɧɤɰɢɨɧɚɥɶɧɵɟ ɮɨɪɦɵ:

y x u z[Q(f(y), y)&P(y) R(v)&S(u, g(y, u))].

3.ɍɞɚɥɢɦ -ɤɜɚɧɬɢɮɢɤɚɰɢɢ:

y u[Q(f(y), y)&P(y) R(v)&S(u, g(y, u))].

ɉɨɥɭɱɢɥɢ ɫɤɨɥɟɦɨɜɫɤɭɸ ɮɨɪɦɭ.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɤɨɥɟɦɨɜɫɤɚɹ ɮɨɪɦɚ - ɷɬɨ ɡɚɦɤɧɭɬɚɹ ɩɪɟɞɜɚɪɟɧɧɚɹ ɮɨɪɦɚ, ɩɪɟɮɢɤɫ ɤɨɬɨɪɨɣ ɫɨɞɟɪɠɢɬ ɬɨɥɶɤɨ -ɤɜɚɧɬɢɮɢɤɚɰɢɢ. Ʉɥɚɭɡɚɥɶɧɚɹ ɮɨɪɦɚ - ɷɬɨ ɫɤɨɥɟɦɨɜɫɤɚɹ ɮɨɪɦɚ, ɦɚɬɪɢɰɚ ɤɨɬɨɪɨɣ ɹɜɥɹɟɬɫɹ ɄɇɎ. ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ ɦɚɬɪɢɰɵ ɜ ɄɇɎ ɜɵɩɨɥɧɹɟɬɫɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɥɨɝɢɤɟ ɩɪɟɞɢɤɚɬɨɜ. Ⱦɥɹ ɧɚɲɟɝɨ ɩɪɢɦɟɪɚ ɩɨɫɥɟ ɩɪɢɦɟɧɟɧɢɹ ɩɪɚɜɢɥ ɞɢɫɬɪɢɛɭɬɢɜɧɨɫɬɢ ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɭɸ ɤɥɚɭɡɚɥɶɧɭɸ ɮɨɪɦɭ:

y u[(Q(f(y), y) R(v)) & (Q(f(y), y) S(u, g(y, u))) & (P(y) R(v)) & (P(y) S(u, g(y, u)))].

ɉɨɫɤɨɥɶɤɭ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ ɜ ɤлаузальной ɮɨɪɦɟ ɫɜɹɡɚɧɵ ɬолько - ɤɜɚɧɬɢɮɢɤɚɰɢɹɦɢ, ɬɨ ɩɪɟɮɢɤɫ ɦɨɠɟɬ ɛɵɬɶ ɨɩɭɳɟɧ. Ɉɤɨɧɱɚɬɟɥɶɧɨ ɢɦɟɟɦ ɦɧɨɠɟɫɬɜɨ ɞɢɡɴɸɧɤɬɨɜ:

{(Q(f(y),y) R(v)), (Q(f(y),y) S(u,g(y,u))), (P(y) R(v)), (P(y) S(u,g(y,u))}.

Ⱦɥɹ ɞɨɤɚɡɚɬɟɥɶɫɬɜɚ ɧɟɜɵɩɨɥɧɢɦɨɫɬɶɢ ɷɬɨɝɨ ɦɧɨɠɟɫɬɜɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɟɬɨɞ ɪɟɡɨɥɸɰɢɣ.

ɍɩɪɚɠɧɟɧɢɹ 1. ȼɵɩɨɥɧɢɬɶ ɫɤɨɥɟɦɢɡɚɰɢɸ ɫɥɟɞɭɸɳɢɯ ɮɨɪɦɭɥ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜ

ɩɪɟɞɜɚɪɟɧɧɨɣ ɮɨɪɦɟ:

ɚ) x y z u[(P(x, y) & Q(u)) o R(z, x, y)];

ɛ) v w t z[(R(w, t) S(r)) l (P(v) & S(w))];

ɜ) y z u x[Q(u, z) & R(u) & P(y, u) o S(x, u, z)]; ɝ) t x w y[(P(t, w) & Q(x, y) o S(y)) o R(x)];

ɞ) v u y z[(S(u, y) l P(z, y)) o (T(y) Q(z))]; ɟ) x y v z[(Q(z, v) & P(v, y) S(x)) o R(x, v)];

ɠ) z t x u[( R(u, z) T(x, u) P(t)) l Q(x, t, z)]; ɡ) y z x w[(T(x, w) (P(x, y) & S(x, z)) o R(x, w)]; ɢ) y z u x[( S(y, x) Q(u)) o R(z, x, y)];

ɤ) v w t z[(P(w, t) o Q(r)) & (R(v) Q(w))];

2.ɉɪɟɨɛɪɚɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɮɨɪɦɭɥɵ ɜ ɤɥɚɭɡɚɥɶɧɭɸ ɮɨɪɦɭ:

ɚ) x( (R(y) & Q(x)) o zP(z, x, y)];

ɛ) Q(w, z) & z[S(z) l x y(R(y) & T(x))]; ɜ) y[P(y) & y(S(x, y) & P(y) o zR(u, z))]; ɝ) R(t, w) x w[ (P(w) S(x)) o Q(w)]; ɞ) [P(y) & y zT(z, y)] o (R(z) & zQ(z));

ɟ) v zS(z, v) & R(v, y) x y(P(x) o R(x, y)); ɠ) x u( S(u, x) R(x, u) Q(t)) o z( tP(x, t, z)); ɡ) Q(x, w) x w(P(x, w) & Q(x, z)) S(z, w).

3.Ɂɚɩɢɫɚɬɶ ɫɥɟɞɭɸɳɢɟ ɩɪɟɞɥɨɠɟɧɢɹ ɜ ɜɢɞɟ ɮɨɪɦɭɥ ɥɨɝɢɤɢ ɩɪɟɞɢɤɚɬɨɜ

ɢɩɪɟɨɛɪɚɡɨɜɚɬɶ ɢɯ ɜ ɤɥɚɭɡɚɥɶɧɭɸ ɮɨɪɦɭ:

ɚ) ɉɨɝɨɞɚ ɩɥɨɯɚɹ ɬɨɝɞɚ ɢ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɧɟɜɟɪɧɨ, ɱɬɨ ɫɜɟɬɢɬ ɫɨɥɧɰɟ ɢ ɠɚɪɤɨ.

ɛ) ȿɫɥɢ ɫɭɳɟɫɬɜɭɸɬ ɦɚɪɫɢɚɧɟ ɢ ɨɧɢ ɪɚɡɭɦɧɵ, ɬɨɝɞɚ ɫɭɳɟɫɬɜɭɸɬ ɦɚɪɫɢɚɧɫɤɢɟ ɪɚɫɬɟɧɢɹ, ɤɨɬɨɪɵɟ ɫɴɟɞɨɛɧɵ ɢ ɩɢɬɚɬɟɥɶɧɵ.

ɜ) ȿɫɥɢ ɞɥɹ ɥɸɛɵɯ ɬɪɟɯ ɱɢɫɟɥ ɨɞɧɨ ɢɡ ɧɢɯ ɪɚɜɧɨ ɫɭɦɦɟ ɞɜɭɯ ɞɪɭɝɢɯ, ɬɨ ɫɭɳɟɫɬɜɭɸɬ ɞɜɚ ɱɢɫɥɚ, ɨɞɧɨ ɢɡ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɤɜɚɞɪɚɬɨɦ ɞɪɭɝɨɝɨ.

ɝ) Ʌɸɛɨɣ ɫɬɭɞɟɧɬ ɥɸɛɢɬ ɥɨɝɢɤɭ ɢɥɢ ɮɢɥɨɫɨɮɢɸ ɬɨɝɞɚ ɢ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɫɭɳɟɫɬɜɭɟɬ ɩɪɟɩɨɞɚɜɚɬɟɥɶ, ɤɨɬɨɪɵɣ ɥɸɛɢɬ ɢ ɥɨɝɢɤɭ ɢ ɮɢɥɨɫɨɮɢɸ.

ɞ) ȿɫɥɢ ɧɟɤɨɬɨɪɵɟ ɩɪɢɤɥɚɞɧɵɟ ɩɪɨɝɪɚɦɦɵ ɧɟɫɨɜɦɟɫɬɢɦɵ ɫ ɧɟɤɨɬɨɪɵɦɢ ɨɩɟɪɚɰɢɨɧɧɵɦɢ ɫɢɫɬɟɦɚɦɢ, ɬɨ ɜɫɟ ɫɬɭɞɟɧɬɵ, ɡɚɧɢɦɚɸɳɢɟɫɹ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟɦ, ɢɡɭɱɚɸɬ ɨɩɟɪɚɰɢɨɧɧɵɟ ɫɢɫɬɟɦɵ.

ɟ) ȿɫɥɢ ɞɥɹ ɥɸɛɵɯ ɞɜɭɯ ɱɟɥɨɜɟɤ, ɧɟ ɹɜɥɹɸɳɢɯɫɹ ɝɪɚɠɞɚɧɚɦɢ ɨɞɧɨɣ ɫɬɪɚɧɵ, ɫɭɳɟɫɬɜɭɟɬ ɬɪɟɬɢɣ ɱɟɥɨɜɟɤ, ɧɟ ɹɜɥɹɸɳɢɣɫɹ ɫɨɨɬɟɱɟɫɬɜɟɧɧɢɤɨɦ

ɩɟɪɜɵɯ ɞɜɭɯ, ɬɨ ɷɬɢ ɬɪɢ ɱɟɥɨɜɟɤɚ ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɱɥɟɧɚɦɢ ɨɞɧɨɣ ɧɚɰɢɨɧɚɥɶɧɨɣ ɫɛɨɪɧɨɣ ɩɨ ɮɭɬɛɨɥɭ.

ɠ) Ⱦɥɹ ɥɸɛɵɯ ɬɪɟɯ ɱɟɥɨɜɟɤ, ɢɝɪɚɸɳɢɯ ɜ ɨɞɧɨɣ ɛɚɫɤɟɬɛɨɥɶɧɨɣ ɤɨɦɚɧɞɟ, ɥɢɛɨ ɪɨɫɬ ɤɚɠɞɨɝɨ ɢɡ ɧɢɯ ɛɨɥɟɟ ɞɜɭɯ ɦɟɬɪɨɜ, ɥɢɛɨ ɨɞɢɧ ɢɡ ɧɢɯ ɹɜɥɹɟɬɫɹ ɪɚɡɵɝɪɵɜɚɸɳɢɦ.

ɡ) ȿɫɥɢ ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɵɯ ɦɚɲɢɧ ɢ ɟɫɥɢ ɤɚɠɞɚɹ ɢɞɟɚɥɶɧɚɹ ɦɚɲɢɧɚ ɹɜɥɹɟɬɫɹ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɣ ɦɚɲɢɧɨɣ, ɬɨ ɢɞɟɚɥɶɧɚɹ ɦɚɲɢɧɚ ɧɟ ɫɭɳɟɫɬɜɭɟɬ.

ɢ) ȿɫɥɢ ɤɚɠɞɵɣ ɨɛɦɚɧɳɢɤ ɹɜɥɹɟɬɫɹ ɩɪɟɫɬɭɩɧɢɤɨɦ ɢ ɜɫɹɤɢɣ, ɤɬɨ ɩɨɞɫɬɪɟɤɚɟɬ ɩɪɟɫɬɭɩɧɢɤɚ ɹɜɥɹɟɬɫɹ ɩɪɟɫɬɭɩɧɢɤɨɦ, ɬɨ ɫɭɳɟɫɬɜɭɟɬ ɬɪɭɫ, ɤɨɬɨɪɵɣ ɩɨɞɫɬɪɟɤɚɟɬ ɨɛɦɚɧɳɢɤɚ.

ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ 6 Ɇɟɬɨɞ ɪɟɡɨɥɸɰɢɣ ɜ ɥɨɝɢɤɟ ɩɪɟɞɢɤɚɬɨɜ. ɍɧɢɮɢɤɚɰɢɹ.

ɐɟɥɶ ɡɚɧɹɬɢɹ: ɉɪɚɤɬɢɱɟɫɤɨɟ ɨɫɜɨɟɧɢɟ ɦɟɬɨɞɚ ɪɟɡɨɥɸɰɢɣ ɜ ɥɨɝɢɤɟ ɩɪɟɞɢɤɚɬɨɜ.

Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ

ɉɨɞɫɬɚɧɨɜɤɚ V ɟɫɬɶ ɨɬɨɛɪɚɠɟɧɢɟ ɦɧɨɠɟɫɬɜɚ V ɩɟɪɟɦɟɧɧɵɯ ɜ ɦɧɨɠɟɫɬɜɨ T ɬɟɪɦɨɜ. ɉɨɞɫɬɚɧɨɜɤɚ V ɡɚɞɚɟɬɫɹ ɦɧɨɠɟɫɬɜɨɦ ɭɩɨɪɹɞɨɱɟɧɧɵɯ ɩɚɪ:

V = {(x1, t1), . . . ,(xn, tn)} ,

ɝɞɟ xi z tj. ɉɭɫɬɶ t - ɬɟɪɦ, ɚ V - ɩɨɞɫɬɚɧɨɜɤɚ, ɬɨɝɞɚ ɬɟɪɦ V[t] ɩɨɥɭɱɚɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨɣ ɡɚɦɟɧɨɣ ɜɫɟɯ ɜɯɨɠɞɟɧɢɣ ɩɟɪɟɦɟɧɧɵɯ x ɜ t ɧɚ ɢɯ ɨɛɪɚɡɵ

Ɍɟɪɦ t2 ɧɚɡɵɜɚɟɬɫɹ ɤɨɧɤɪɟɬɢɡɚɰɢɟɣ (ɱɚɫɬɧɵɦ ɫɥɭɱɚɟɦ, ɩɪɢɦɟɪɨɦ) ɬɟɪɦɚ t1, ɟɫɥɢ ɫɭɳɟɫɬɜɭɟɬ ɩɨɞɫɬɚɧɨɜɤɚ V, ɬɚɤɚɹ, ɱɬɨ t2 = V[t1]. Ɍɟɪɦ t ɜɩɨɥɧɟ ɤɨɧɤɪɟɬɢɡɢɪɨɜɚɧ, ɟɫɥɢ ɨɧ ɧɟ ɫɨɞɟɪɠɢɬ ɧɢ ɨɞɧɨɣ ɩɟɪɟɦɟɧɧɨɣ.

ɉɪɢɦɟɧɟɧɢɟ ɩɨɞɫɬɚɧɨɜɤɢ ɤ ɥɢɬɟɪɚɥɭ ɨɡɧɚɱɚɟɬ ɩɪɢɦɟɧɟɧɢɟ ɟɟ ɤɨ ɜɫɟɦ ɬɟɪɦɚɦ - ɚɪɝɭɦɟɧɬɚɦ ɷɬɨɝɨ ɥɢɬɟɪɚɥɚ. Ɋɟɡɭɥɶɬɚɬ ɩɪɢɦɟɧɟɧɢɹ ɩɨɞɫɬɚɧɨɜɤɢ V ɤ ɥɢɬɟɪɚɥɭ L ɨɛɨɡɧɚɱɢɦ V[L].

ɉɨɞɫɬɚɧɨɜɤɚ V ɧɚɡɵɜɚɟɬɫɹ ɭɧɢɮɢɤɚɬɨɪɨɦ ɞɥɹ ɦɧɨɠɟɫɬɜɚ ɥɢɬɟɪɚɥɨɜ

{L1, L2, ... , Lk}, ɟɫɥɢ ɢɦɟɟɬ ɦɟɫɬɨ ɪɚɜɟɧɫɬɜɨ: V[L1]=V[L2]= ... =V[Lk].

Ɇɧɨɠɟɫɬɜɨ {Li} ɥɢɬɟɪɚɥɨɜ ɧɚɡɵɜɚɟɬɫɹ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɭɧɢɮɢɰɢɪɭɟɦɵɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɧɢɮɢɤɚɬɨɪ ɩɨɪɨɠɞɚɟɬ ɨɛɳɢɣ ɩɪɢɦɟɪ ɞɥɹ ɦɧɨɠɟɫɬɜɚ ɥɢɬɟɪɚɥɨɜ.

ɇɚɢɛɨɥɟɟ ɨɛɳɢɦ (ɢɥɢ ɩɪɨɫɬɟɣɲɢɦ) ɭɧɢɮɢɤɚɬɨɪɨɦ (ɇɈɍ) ɞɥɹ {Li} ɧɚɡɵɜɚɟɬɫɹ ɬɚɤɨɣ ɭɧɢɮɢɤɚɬɨɪ V1, ɱɬɨ, ɟɫɥɢ V2 - ɤɚɤɨɣ-ɧɢɛɭɞɶ ɭɧɢɮɢɤɚɬɨɪ ɞɥɹ {Li}, ɞɚɸɳɢɣ V2{Li}, ɬɨ ɧɚɣɞɟɬɫɹ ɩɨɞɫɬɚɧɨɜɤɚ V3, ɬɚɤɚɹ, ɱɬɨ V2{Li} = (V3 q V1){Li}. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɇɈɍ ɫɜɨɞɢɦ ɤ ɥɸɛɨɦɭ ɞɪɭɝɨɦɭ ɭɧɢɮɢɤɚɬɨɪɭ

1.ɉɨɥɨɠɢɬɶ k:=0, Vk:=H (ɩɭɫɬɚɹ ɩɨɞɫɬɚɧɨɜɤɚ). ɉɟɪɟɣɬɢ ɤ ɩ.2.

2.ȿɫɥɢ Vk{Li} ɧɟ ɹɜɥɹɟɬɫɹ ɨɞɧɨɷɥɟɦɟɧɬɧɵɦ ɦɧɨɠɟɫɬɜɨɦ, ɬɨ ɩɟɪɟɣɬɢ ɤ ɩ. 3. ɂɧɚɱɟ ɩɨɥɨɠɢɬɶ ɇɈɍ:= Vk ɢ ɡɚɤɨɧɱɢɬɶ ɪɚɛɨɬɭ.

3.Ʉɚɠɞɚɹ ɢɡ ɥɢɬɟɪ ɜ Vk{Li} ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɰɟɩɨɱɤɚ ɫɢɦɜɨɥɨɜ ɢ ɜɵɞɟɥɹɸɬɫɹ ɩɟɪɜɵɟ ɬɟɪɦɵ - ɚɪɝɭɦɟɧɬɵ, ɧɟ ɹɜɥɹɸɳɢɯɫɹ ɨɞɢɧɚɤɨɜɵɦɢ ɭ ɜɫɟɯ

ɷɥɟɦɟɧɬɨɜ Vk{Li}. ɗɬɢ ɩɨɞɜɵɪɚɠɟɧɢɹ ɨɛɪɚɡɭɸɬ ɦɧɨɠɟɫɬɜɨ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ Bk. ɗɬɨ ɦɧɨɠɟɫɬɜɨ ɭɩɨɪɹɞɨɱɢɜɚɸɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɜ ɧɚɱɚɥɟ ɪɚɫɩɨɥɚɝɚɥɢɫɶ ɩɟɪɟɦɟɧɧɵɟ, ɚ ɡɚɬɟɦ - ɨɫɬɚɥɶɧɵɟ ɬɟɪɦɵ. ɉɭɫɬɶ Vk - ɩɟɪɜɵɣ ɷɥɟɦɟɧɬ Bk, ɚ Uk - ɫɥɟɞɭɸɳɢɣ ɡɚ ɧɢɦ ɷɥɟɦɟɧɬ. Ɍɨɝɞɚ, ɟɫɥɢ Vk - ɩɟɪɟɦɟɧɧɚɹ,

ɧɟ ɜɯɨɞɹɳɚɹ ɜ Uk, ɬɨ ɩɪɢɧɹɬɶ Vk+1 := {(Uk ,Vk)} q Vk, k:=k+1, ɩɟɪɟɣɬɢ ɤ ɩ. 2. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɨɤɨɧɱɢɬɶ ɪɚɛɨɬɭ ɫ ɨɬɪɢɰɚɬɟɥɶɧɵɦ ɪɟɡɭɥɶɬɚɬɨɦ.

Ɂɚɞɚɱɚ. ɇɚɣɬɢ ɧɚɢɛɨɥɟɟ ɨɛɳɢɣ ɭɧɢɮɢɤɚɬɨɪ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɨɛɳɢɣ ɩɪɢɦɟɪ ɞɥɹ ɫɥɟɞɭɸɳɟɝɨ ɦɧɨɠɟɫɬɜɚ ɥɢɬɟɪɚɥɨɜ ɢɥɢ ɭɫɬɚɧɨɜɢɬɶ, ɱɬɨ ɦɧɨɠɟɫɬɜɨ ɧɟɭɧɢɮɢɰɢɪɭɟɦɨ:

{Li}={P(x, z, v,), P(x, f(y),y), P(x, z, b)}.

Ɋɟɲɟɧɢɟ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɟɧɧɵɦ ɚɥɝɨɪɢɬɦɨɦ ɜɵɩɨɥɧɢɦ ɫɥɟɞɭɸɳɢɟ ɲɚɝɢ:

1. ɉɨɥɨɠɢɬɶ k:=0, V0:=H.

ɂɦɟɟɦ V0q{Li} = {P(x, z, v,), P(x, f(y),y), P(x, z, b)}. ɗɥɟɦɟɧɬɵ ɦɧɨɠɟɫɬɜɚ ɪɚɡɥɢɱɧɵ, ɩɨɷɬɨɦɭ ɩɟɪɟɯɨɞɢɦ ɤ ɫɨɫɬɚɜɥɟɧɢɸ ɦɧɨɠɟɫɬɜɚ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ.

2. B0 = {z, f(y), z} = {z, f(y)}, ɨɬɫɸɞɚ V1 := {(z, f(y))} q H = {(z, f(y))}.

V1q {Li} = {P(x, f(y), v,), P(x, f(y),y), P(x, f(y), b)} - ɷɥɟɦɟɧɬɵ ɦɧɨɠɟɫɬɜɚ ɪɚɡɥɢɱɧɵ.

3. B1={v, y, b}, V2 = {(v, y)} q V1={(v, y)}q{(z, f(y))}={(z, f(y)), (v, y)}. V2q{Li}={P(x, f(y), y,), P(x, f(y),y), P(x, f(y), b)} = {P(x, f(y),y), P(x, f(y), b)} -

ɷɥɟɦɟɧɬɵ ɦɧɨɠɟɫɬɜɚ ɪɚɡɥɢɱɧɵ.

4. B2 ={y, b}, V3 = {(y, b)} q V2 = {(z, f(b)), (v, b), (y, b)}. V3q{Li} = {P(x, f(b), b,), P(x, f(b),b), P(x, f(b), b)} = {P(x, f(b),b)}.

ɉɨɥɭɱɢɥɢ ɨɞɧɨɷɥɟɦɟɧɬɧɨɟ ɦɧɨɠɟɫɬɜɨ, ɫɨɞɟɪɠɚɳɟɟ ɨɛɳɢɣ ɩɪɢɦɟɪ ɞɥɹ ɢɫɯɨɞɧɨɝɨ ɦɧɨɠɟɫɬɜɚ ɥɢɬɟɪɚɥɨɜ, ɚ V3 - ɟɫɬɶ ɇɈɍ.

Ⱦɜɚ ɥɢɬɟɪɚɥɚ ɭɧɢɮɢɰɢɪɭɟɦɵ, ɟɫɥɢ ɨɧɢ ɩɨɫɬɪɨɟɧɵ ɢɡ ɨɞɧɨɝɨ ɩɪɟɞɢɤɚɬɧɨɝɨ ɫɢɦɜɨɥɚ, ɩɪɢɦɟɧɟɧɧɨɝɨ ɤ ɩɨɩɚɪɧɨ ɭɧɢɮɢɰɢɪɭɟɦɵɦ ɬɟɪɦɚɦ. ɉɨɷɬɨɦɭ ɡɚɞɚɱɚ ɭɧɢɮɢɤɚɰɢɢ ɫɜɨɞɢɬɫɹ ɤ ɭɧɢɮɢɤɚɰɢɢ ɦɧɨɠɟɫɬɜɚ ɬɟɪɦɨɜ.

Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɞɨɤɚɡɚɬɟɥɶɫɬɜɚ ɥɨɝɢɱɟɫɤɨɝɨ ɫɥɟɞɨɜɚɧɢɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɚ ɪɟɡɨɥɸɰɢɣ ɜ ɥɨɝɢɤɟ ɩɪɟɞɢɤɚɬɨɜ.

Ɂɚɞɚɱɚ. Ɂɚɩɢɫɚɬɶ ɫɥɟɞɭɸɳɟɟ ɪɚɫɫɭɠɞɟɧɢɟ ɧɚ ɹɡɵɤɟ ɥɨɝɢɤɢ ɩɪɟɞɢɤɚɬɨɜ ɢ ɞɨɤɚɡɚɬɶ ɟɝɨ ɫɩɪɚɜɟɞɥɢɜɨɫɬɶ, ɢɫɩɨɥɶɡɭɹ ɦɟɬɨɞ ɪɟɡɨɥɸɰɢɣ:

ɉɨɫɵɥɤɢ: ɇɟɤɨɬɨɪɵɦ ɧɪɚɜɢɬɫɹ ɗɥɜɢɫ. ɇɟɤɨɬɨɪɵɟ ɧɟ ɥɸɛɹɬ ɧɢɤɨɝɨ, ɤɨɦɭ ɧɪɚɜɢɬɫɹ ɗɥɜɢɫ.

Ɂɚɤɥɸɱɟɧɢɟ: ɇɟɤɨɬɨɪɵɯ ɥɸɛɹɬ ɧɟ ɜɫɟ.

Ɋɟɲɟɧɢɟ. ȼɜɟɞɟɦ ɧɟɨɛɯɨɞɢɦɵɟ ɮɨɪɦɚɥɶɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ:

P(x, y) - «x ɧɪɚɜɢɬɫɹ y»; a - «ɗɥɜɢɫ». Ɍɨɝɞɚ ɞɚɧɧɨɟ ɪɚɫɫɭɠɞɟɧɢɟ ɮɨɪɦɚɥɶɧɨ ɡɚɩɢɲɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:

{xP(x, a), x y(P(y, a) o P(x, y)) } »= z( vP(v, z)).

ɉɟɪɟɧɨɫɢɦ ɡɚɤɥɸɱɟɧɢɟ ɜ ɥɟɜɭɸ ɱɚɫɬɶ ɫ ɨɬɪɢɰɚɧɢɟɦ:

{xP(x, a), x y(P(y, a) o P(x, y)), z( vP(v, z)) }.

ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ ɮɨɪɦɭɥ ɜ ɤɥɚɭɡɚɥɶɧɭɸ ɮɨɪɦɭ:

1.xP(x, a). Ɏɨɪɦɭɥɚ ɭɠɟ ɜ ɩɪɟɞɜɚɪɟɧɧɨɣ ɮɨɪɦɟ. ɋɤɨɥɟɦɢɡɢɪɭɹ, ɡɚɦɟɧɹɟɦ x ɧɚ b ɢ ɩɨɥɭɱɢɦ: P(b, a);

2.x y(P(y, a) o P(x, y)). Ɏɨɪɦɭɥɚ ɜ ɩɪɟɞɜɚɪɟɧɧɨɣ ɮɨɪɦɟ. ɉɪɟɨɛɪɚɡɭɹ ɦɚɬɪɢɰɭ ɜ ɄɇɎ ɢ ɡɚɦɟɧɹɹ ɩɪɢ ɫɤɨɥɟɦɢɡɚɰɢɢ x ɧɚ c ɩɨɥɭɱɢɦ:

P(y, a) P(c, y);

3. z( vP(v, z)) = z( vP(v, z)) = z vP(v, z). Ɍогда клаузальная ɮорма ɟɫɬɶ: P(v, z).

ɉɨɥɭɱɢɥɢ ɦɧɨɠɟɫɬɜɨ ɞɢɡɴɸɧɤɬɨɜ:

1.P(b, a);

2.P(y, a) P(c, y);

3.P(v, z).

ɉɪɢɦɟɧɹɹ ɩɪɚɜɢɥɨ ɪɟɡɨɥɸɰɢɣ ɢ ɭɧɢɮɢɤɚɰɢɸ ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɢɣ ɜɵɜɨɞ (â

ɍɩɪɚɠɧɟɧɢɹ 1. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɟɟ ɨɛɳɢɣ ɭɧɢɮɢɤɚɬɨɪ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɟɦɭ

ɨɛɳɢɣ ɩɪɢɦɟɪ ɞɥɹ ɫɥɟɞɭɸɳɟɝɨ ɦɧɨɠɟɫɬɜɚ ɬɟɪɦɨɜ ɢɥɢ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɦɧɨɠɟɫɬɜɨ ɧɟɭɧɢɮɢɰɢɪɭɟɦɨ.

ɚ) { f(z, g(y, a), h(b)), f(w, g(c, x), h(u)), f(c, g(v, w), h(x))};

ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ2. Ɇетод ɪезолюций в ɥогике ɜысɤɚɡɵɜɚɧɢɣ ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ3. Ɉɰɟɧɤɚ ɫɥɨɠɧɨɫɬɢ ɚɥɝɨɪɢɬɦɨɜ ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ4. əɡɵɤ ɥɨɝɢɤɢ ɩɪɟɞɢɤɚɬɨɜ ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ5. ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ ɮɨɪɦɭɥ ɥɨɝɢɤɢ ɩɪɟɞɢɤɚɬɨɜ ɜ ɤɥɚɭɡɚɥɶɧɭɸ ɮɨɪɦɭ.

ȼȺɊɂȺɇɌɕ ɄɈɇɌɊɈɅɖɇɕɏ ɊȺȻɈɌ ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ