The Automation of Syllotistic Ii Optimization And Complexity Issues
The Automation of Syllotistic Ii Optimization And Complexity Issues
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Definition 2 Given p as above, for any x and y occurring in p we put X ^p y ff and only :/ p, — ♦ (i •-► y) is tautological, where p, is obtained from p as in Definition 1. Lemma 2 ^p is an equivalence relation. Proof. The lemma follows at once from the reflexivity, symmetry and trauisi- tivity of «-••■. ■ An important property of the equivalence relation ~p is stated in the fol- lowing lemma. Lemma 3 Let ~ be a p-compatible equivalence relation. Then (i) t/x ~p y then i ~ y, for x, y in X; (ii...) ~p IS p-compattble. (In other words, ~p is the finest p-compatible equivalence relation over the set X of variables occurring in p). Proof. Let x ~p y. Then p« — ► (x ♦-► y) is a tautology. If P is an acceptable place of p, ~, then XP satisfies p^, eind in particular p. . Hence (i *-♦ y)^'' = TRUE. This shows that x y T^. Vf, s (and hence y ~. Wo ' °ot implying y ~, v, z, y ~Af, i not implying y ~. V„ z ) whenever Mo belongs to the first class and M\ belongs to the second.
What to read after The Automation of Syllotistic Ii Optimization And Complexity Issues?
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To quickly assess the difficulty of the text, read a short excerpt:
Definition 2 Given p as above, for any x and y occurring in p we put X ^p y ff and only :/ p, — ♦ (i •-► y) is tautological, where p, is obtained from p as in Definition 1. Lemma 2 ^p is an equivalence relation. Proof. The lemma follows at once from the reflexivity, symmetry and trauisi- tivity of «-••■. ■ An important property of the equivalence relation ~p is stated in the fol- lowing lemma. Lemma 3 Let ~ be a p-compatible equivalence relation. Then (i) t/x ~p y then i ~ y, for x, y in X; (ii...) ~p IS p-compattble. (In other words, ~p is the finest p-compatible equivalence relation over the set X of variables occurring in p). Proof. Let x ~p y. Then p« — ► (x ♦-► y) is a tautology. If P is an acceptable place of p, ~, then XP satisfies p^, eind in particular p. . Hence (i *-♦ y)^'' = TRUE. This shows that x y T^. Vf, s (and hence y ~. Wo ' °ot implying y ~, v, z, y ~Af, i not implying y ~. V„ z ) whenever Mo belongs to the first class and M\ belongs to the second.
What to read after The Automation of Syllotistic Ii Optimization And Complexity Issues?
You can find similar books in the "Read Also" column, or choose other free books by D Cantone to read onlineMoreLess
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