A valid logical inference consisting of the concatenation of two or more conditional statements.
For example:
When it rains, the road gets wet.
When the road is wet, it is slippery.
Therefore, when it rains, the road gets slippery.
or as a formula:
A ⟶ B– if A, then B.
B ⟶ C– if B, then C.
∴A ⟶ C– therefore: if A, then C.
The name refers to the principle that conditionals can also be formulated as categorical statements and therefore these inferences could also be expressed as syllogisms.
The example above could also be formulated as a Modus Barbara, for example as follows:
For all situations where it is raining, it is true that the road will get wet.
For all situations in which the road is wet, it is true that road will get slippery.
Therefore, for all situations in which it is raining, it is true that the road will get slippery.
Obviously, the formulation as an “if … then”-statement is much easier to understand; logically, however, they are equivalent.
For more information, see: Syllogism.
A variant of the hypothetical syllogism that combines multiple conditionals (typically more than two) is also sometimes called a “chain argument”. This can be seen as a variation of the Sorites based on conditionals. Alternatively, the hypothetical syllogism can be seen as a special case of the chain argument with exactly two premisses, similar to how the Modus Barbara can be seen as a special form of the Sorites with exactly two universal quantifications.