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sav08:herbrand_s_expansion_theorem [2008/03/24 11:24] vkuncak |
sav08:herbrand_s_expansion_theorem [2008/03/24 11:38] vkuncak |
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===== Constructing a Propositional Model ===== | ===== Constructing a Propositional Model ===== | ||
- | We can view the set $expand(S)$ as a set of propositional variables with "long names". | + | We can view the set $expand(S)$ as a set of propositional formulas whose propositional variables have "long names". |
For an expansion of clause $C_G$ we can construct the corresponding propositional formula $p(C_G)$. | For an expansion of clause $C_G$ we can construct the corresponding propositional formula $p(C_G)$. | ||
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===== Constructing Herbrand Model ===== | ===== Constructing Herbrand Model ===== | ||
- | For $I = (HU,\alpha_H)$ we define $\alpha_H(R)$ so that $I_H$ evaluates ground formulas $expand(S)$ same as in $I_P$ (and thus same as in $I$). | + | For $I = (GT,\alpha_H)$ we define $\alpha_H(R)$ so that $I_H$ evaluates ground formulas $expand(S)$ same as in $I_P$ (and thus same as in $I$). |
We ensure that atomic formulas evaluate the same: | We ensure that atomic formulas evaluate the same: |