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Unformatted text preview: Applied Logic Lecture Notes 31-01-08 1 Assertion and Refutation Labellings The key concept of the lecture is that of the assertion and refutation labellings of the for- mation tree of a proposition . This is a signed labelling much like the evaluation labelling that we saw earlier. However, contrary to evaluation labellings, these labellings are defined from the root down to the leaves instead of from the leaves up to the root. The idea behind these two labellings is that they assigns to each node the truth value that would ensure the correct evaluation of the root ( T for assertion and F for refutation). Definition. The assertion labelling (resp. refutation labelling ) of the formation tree of is defined as follows: The root is labelled T (resp. F ). If a node is labelled ( ) T then its unique child is labelled F . If a node is labelled ( ) F then its unique child is labelled T . If a node is labelled ( ) T then its two children are labelled T and T , respec- tively. If a node is labelled ( ) F then its two children are labelled F and F , respectively....
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This note was uploaded on 02/23/2008 for the course MATH 4860 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).
- Spring '08