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式(15.16)的推导 #142

@SoftSir

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@SoftSir

南瓜书P282处15.2.8关于式子(15.16)的推导中提到 $\theta_1$ 为笔误,但貌似这个式子可以通过下面的方式推导:

$$ \begin{aligned} (C_2 - \lbrace L_2 \rbrace )\theta_2 &= C - (C_1 - \lbrace L_1 \rbrace)\theta_1 \\ C_2\theta_2 &= \left(C - (C_1 - \lbrace L_1 \rbrace)\theta_1 \right) \lor (\lbrace L_2\rbrace \theta_2) \\ C_2 &= \left[ \left(C - (C_1 - \lbrace L_1 \rbrace)\theta_1 \right) \lor (\lbrace L_2\rbrace \theta_2) \right]\theta_2^{-1} \end{aligned} $$

注意到 $L_2 = (\neg L_1\theta_1)\theta_2^{-1}$,代入得:

$$ C_2 = \left[ \left(C - (C_1 - \lbrace L_1 \rbrace)\theta_1 \right) \lor (\neg L_1\theta_1) \right]\theta_2^{-1} $$

即为西瓜书中的式子(15.16)即是没有笔误

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