3.3Single030409

3.3Single030409 - 1 3.3. Single Clauses (duplicates). In...

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3.3. Single Clauses (duplicates). In this section we handle the relatively easy case of ordered pairs α , β of clauses, where α = β . We these duplicate ordered pairs as single clauses, α . As we shall see, several single clauses have ¬ NON, and so any ordered pair of clauses, at least one of which is such a clause, also has ¬ NON, and does not have to be further considered. This will allow us to cut down significantly on the number of pairs of clauses that have to be considered in sections 3.4 - 3.13. By Lemma 3.1.5, we see that every clause is equivalent to a clause whose inner signature is AA or AB. Here are what we call the AA and AB tables, together with the outcomes of our five attributes, INF, AL, ALF, FIN, NON, introduced in section 3.1. These entries are justified by the Lemmas that follow. AA 1. A . fA A . gA. ¬ INF. ¬ AL. ¬ ALF. ¬ FIN. ¬ NON. 2. A . fA A . gB. ¬ INF. ¬ AL. ¬ ALF. ¬ FIN. ¬ NON. 3. A . fA A . gC. ¬ INF. ¬ AL. ¬ ALF. ¬ FIN. ¬ NON. 4. B . fA A . gA. ¬ INF. AL. ¬ ALF. ¬ FIN. NON. 5. B . fA A . gB. ¬ INF. AL. ¬ ALF. ¬ FIN. NON. 6. B . fA A . gC. ¬ INF. AL. ¬ ALF. ¬ FIN. NON. 7. C . fA A . gA. ¬ INF. AL. ¬ ALF. ¬ FIN. NON. 8. C . fA A . gB. ¬ INF. AL. ¬ ALF. ¬ FIN. NON. 9. C . fA A . gC. ¬ INF. AL. ¬ ALF. ¬ FIN. NON. AB 1. A . fA B . gA. INF. AL. ALF. FIN. NON. 2. A . fA B . gB. INF. AL. ALF. FIN. NON. 3. A . fA B . gC. INF. AL. ALF. FIN. NON. 4. B . fA B . gA. ¬ INF. ¬ AL. ¬ ALF. ¬ FIN. ¬ NON. 5. B . fA B . gB. ¬ INF. ¬ AL. ¬ ALF. ¬ FIN. ¬ NON. 6. B . fA B . gC. ¬ INF. ¬ AL. ¬ ALF. ¬ FIN. ¬ NON. 7. C . fA B . gA. INF. AL. ALF. FIN. NON. 8. C . fA B . gB. INF. AL. ALF. FIN. NON. 9. C . fA B . gC. INF. AL. ALF. FIN. NON. According to the procedure specified at the beginning of
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3.3Single030409 - 1 3.3. Single Clauses (duplicates). In...

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