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Two possible strategies toward constructing semantics for syllogistic theories are known in literature: extensional and intensional. The former is more customary while the latter received a lot of attention only recently. In this work we present a kind of intensional semantics for Venn’s and Vasiliev’s syllogistics. The distinctive feature of our approach is to close the interpretation of categorical statements under the notion of logical consequence from the logic of first-degree entailment.