Polysyllogism
A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on. Each constituent syllogism is called a prosyllogism except the last, because the conclusion of the last syllogism is not a premise for another syllogism.