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Some Reflections on the Set-based and the Conditional-based Interpretations of Statements in Syllogistic Reasoning

Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other one, the so-called conditional interpretation, assumes that quantified propositions talk about conditional propositions and how strong are the links between the antecedent and the consequent. Both interpretations are compared attending to three different questions (existential import, singular statements and non-proportional quantifiers) from the point of view of their impact on the further development of this type of reasoning.