Polysyllogism

A polysyllogism, sometimes called multi-premise syllogism, is a string of any number of syllogisms such that the conclusion of one is a premise for the next, and so on.

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