  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.
