Truth tree short-cut rules for biconditional and exclusive disjunction propositions
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https://doi.org/10.70736/ijoess.1754Keywords:
Biconditional, exclusive disjunction, truth tree, branching, stackingAbstract
In this article, it is tried to decide shortcut rules for checking biconditional and exclusive disjunction propositions using the truth tree method. In the first part of the study, it is put forward that since biconditional and exclusive disjunction propositions cannot be directly reduced to conjunction, disjunction, conditional and converse conditional propositions, the decompositions made by using the antecedent component and then the posterior component related to stacking and branching cannot be determined as a shortcut rule by using the truth tree method. In the second part of the study, the biconditional and exclusive disjunction propositions are decomposed by first taking the posterior component and then the antecedent component. Accordingly, it is shown that none of the four branching variations, and the stacking variations in which the posterior component is taken first and then the antecedent component, and the posterior component is taken first and then the negation of the antecedent component, give the same results as the analyses made with the standard truth tree rules; and therefore, these decompositions cannot be used as shortcut rules by the truth tree method. However, when it is stacked and first the negation of the posterior component and then the negation of the antecedent component are taken, it is put forward that the affirmation of the biconditional proposition and the negation of the exclusive disjunction proposition give the same results as the standard truth tree method; in addition, when it is stacked and first the negation of the posterior component and then the antecedent component are taken, it is seen that the negation of the biconditional proposition and the affirmation of the exclusive disjunction proposition give the same results as the standard truth tree method.
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