Polysyllogism

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A polysyllogism (also called multi-premise syllogism, climax, or gradatio) is a string of any number of syllogisms such that the conclusion of one is a premise for the next, and so on. Each constituent syllogism is called a prosyllogism except the very last, because the conclusion of the last syllogism is not a premise for another syllogism.

A sorites argument is a specific kind of polysyllogism. Sorites comes from the Greek word for "heap" or "pile." In other words, a sorites is a heap of propositions chained together. Example:

All A are B

All B are C

All C are D

All D are E

Therefore all A are E