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  1. A Matricial Vue of Classical Syllogistic and an Extension of the Rules of Valid Syllogism to Rules of Conclusive Syllogisms with Indefinite Terms.Dan Constantin Radulescu - 2022 - Journal of Logic, Language and Information 31 (3):465-491.
    One lists the distinct pairs of categorical premises formulable via only the positive terms, S,P,M, by constructing a six by six matrix obtained by pairing the six categorical P-premises, A, O, A, O, where P* ∈ {P,P′}, with the six, similar, categorical S-premises. One shows how five rules of valid syllogism, select only 15 distinct PCPs that entail logical consequences belonging to the set L+: = {A, O, A, E, O, I}. The choice of admissible LCs can be regarded as (...)
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  • Aristotelian Logic Axioms in Propositional Logic: The Pouch Method.Enrique Alvarez-Fontecilla & Tomas Lungenstrass - 2018 - History and Philosophy of Logic 40 (1):12-21.
    A new theoretical approach to Aristotelian Logic based on three axioms has been recently introduced. This formalization of the theory allowed for the unification of its uncommunicated traditional branches, thus restoring the theoretical unity of AL. In this brief paper, the applicability of the three AL axioms to Propositional Logic is explored. First, it is shown how the AL axioms can be applied to some simple PL arguments in a straightforward manner. Second, the development of a proof method for PL (...)
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