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Creating Tableaux By Hand

Creating Tableaux By Hand. To show: TD, TD=>BP, BP=>~BD |= ~BD. 1. Start a tree with wfps labeled T: or F:. T:TD, T:TD=>BP, T:BP=>~BD, F:~BD. T:BD. 2. Add nodes by reducing non-atomic wfps acc. to Wang rules. T:BP. F:TD. X. T:~BD. F:BP. 3. Close any branch that contains T:p and F:p. X.

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Creating Tableaux By Hand

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  1. Creating Tableaux By Hand To show: TD, TD=>BP, BP=>~BD |= ~BD 1. Start a tree with wfps labeled T: or F: T:TD, T:TD=>BP, T:BP=>~BD, F:~BD T:BD 2. Add nodes by reducing non-atomic wfps acc. to Wang rules. T:BP F:TD X T:~BD F:BP 3. Close any branch that contains T:p and F:p. X X 4. If all branches close, root is unsatisfiable.

  2. Tableau For a Contingent Wfp To show: TD=>BP, BP=>~BD |= ~BD T:TD=>BP, T:BP=>~BD, F:~BD T:BD T:BP F:TD T:~BD F:BP T:~BD F:BP X X X A complete, but unclosed branch is a satisfying model of the root.

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