Editing Deductive reasoning (section)

==== Hypothetical syllogism ====
{{main|hypothetical syllogism}}
A ''hypothetical [[syllogism]]'' is an inference that takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form:
# <math>P \rightarrow Q</math>
# <math>Q \rightarrow R</math>
# Therefore, <math>P \rightarrow R</math>.

In there being a subformula in common between the two premises that does not occur in the consequence, this resembles syllogisms in [[term logic]], although it differs in that this subformula is a proposition whereas in Aristotelian logic, this common element is a term and not a proposition.

The following is an example of an argument using a hypothetical syllogism:

# If there had been a thunderstorm, it would have rained.
# If it had rained, things would have gotten wet.
# Thus, if there had been a thunderstorm, things would have gotten wet.<ref>{{Cite journal |last=Morreau |first=Michael |year=2009 |title=The Hypothetical Syllogism |journal=Journal of Philosophical Logic |volume=38 |issue=4 |pages=447–464 |doi=10.1007/s10992-008-9098-y |issn=0022-3611 |jstor=40344073 |s2cid=34804481}}</ref>