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sav08:ground_terms [2008/03/28 17:35] giuliano |
sav08:ground_terms [2013/05/10 09:53] vkuncak |
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| **Example**\\ | **Example**\\ | ||
| - | ${\cal L}=\{a, f_1\}$ \\ | + | ${\cal L}=\{a, f\}$ \\ |
| $GT=\{a, f(a), f(f(a)), f(f(f(a))), ...\}$ | $GT=\{a, f(a), f(f(a)), f(f(f(a))), ...\}$ | ||
| Line 23: | Line 23: | ||
| Let $ar(f)=n$. Then $f : GT^n \to GT$ | Let $ar(f)=n$. Then $f : GT^n \to GT$ | ||
| - | $\alpha_H(f)(t_1,\ldots,t_n) =$ ++| $f(t_1,\ldots,t_n)$++ | + | $\alpha_H(f)(t_1,\ldots,t_n) = f(t_1,\ldots,t_n)$ |
| - | This defines $\alpha_H(f)$. How to define $\alpha_H(R)$ to ensure that elements of a set are true, i.e. that $e_S(S)(I_H) = {\it true}$? | + | This defines $\alpha_H(f)$. How to define $\alpha_H(R)$ to ensure that elements of a set are true, i.e. that $e_S(S)(I_H) = {\it true}$?\\ |
| - | * is this possible for arbitrary set? | + | Partition $GT^n$ in two sets, one over which $\alpha_H(R)(t_1,...,t_n)$ is true and the other over which it is false. |
| + | * is this possible for arbitrary set? no | ||
| **Example** | **Example** | ||
| + | Consider a set that is not satisfiable : $\{P(a),\ \neg P(a)\}$ | ||
| ===== Ground Atoms ===== | ===== Ground Atoms ===== | ||
| Line 44: | Line 46: | ||
| **Example**\\ | **Example**\\ | ||
| + | ${\cal L}=\{a, f_1, P_1, R_2\}$ \\ | ||
| + | $GT=\{a, f(a), f(f(a)), f(f(f(a))), ...\}$\\ | ||
| $HA=\{P(a), R(a,a), P(f(a)), R(a, f(a)), ...\}$\\ | $HA=\{P(a), R(a,a), P(f(a)), R(a, f(a)), ...\}$\\ | ||
| $V=\{p_1, p_2, p_3, p_4, ...\}$\\ | $V=\{p_1, p_2, p_3, p_4, ...\}$\\ | ||
| We define p such that :\\ | We define p such that :\\ | ||
| - | $p(P(a))=v_1,\ p(R(a,a))=v_2,\ p(P(f(a)))=p_3,\ p(R(a, f(a)))=p_4,...$ | + | $p(P(a))=p_1,\ p(R(a,a))=p_2,\ p(P(f(a)))=p_3,\ p(R(a, f(a)))=p_4,...$ |