2250 Lecture Notes - Mathematical Induction, Atomic Sentence, Glossary Of Video Game Terms
5 Feb 2013
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T"s and f"s do not appear on trees (unless, of course, they are there as sentence letters ra- ther than as truth value assignments). It is therefore a serious question whether the results ob- tained on the truth table will be reflected by trees in all cases. These two questions concern the soundness and the completeness of the tree method respec- tively. Soundness: if the tree method tells us that a set is t-f inconsistent, then that set really is t-f inconsistent. Completeness: if a set is t-f inconsistent, the tree method will tell us that it is. The tree test might not pick out all the t-f inconsis- tent sets, even though any sets that it does pick out are t-f inconsistent. In that case, it would be sound but not complete. Or it might not only pick out all the t-f inconsistent sets, but also some t-f consistent ones.
