Powerful Features of the Modern Syllogistic Method of Propositional Logic
Ali Muhammad Rushdi and Omar Mohammed Ba-Rukab
DOI : 10.3844/jmssp.2008.186.193
Journal of Mathematics and Statistics
Volume 4, Issue 3
In traditional propositional logic, many replacement and inference rules were involved to ascertain if the truth of several antecedents implied the truth of a particular consequent. This research described a powerful technique called the Modern Syllogistic Method (MSM), which ferreted out from a set of premises all that can be concluded from it and casted the resulting conclusions in the simplest and most compact form. We observed that all replacement rules were explicitly and inherently integrated within the MSM and proved that all inference rules were simply limited special cases of it. This meant that the MSM constituted a complete method of logic deduction. We also showed how to use the MSM in determining whether inconsistencies existed within a given set of premises and also in detecting formal logical fallacies. We demonstrated the applicability of the method in diverse fields via four examples that illustrated its mathematical details and exhibited the nature of conclusions it can come up with. In fact, these examples demonstrated the possibility of extracting deductions that were not so obvious and even surprising. The examples also showed how logic can be misused and how logic misuse can be avoided or detected.
© 2008 Ali Muhammad Rushdi and Omar Mohammed Ba-Rukab. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.