The Full Wiki

More info on Conditional syllogism

Conditional syllogism: Wikis


Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.


(Redirected to Hypothetical syllogism article)

From Wikipedia, the free encyclopedia

In logic, a hypothetical syllogism has two uses. In propositional logic it expresses one of the rules of inference, while in the history of logic, it is a short-hand for the theory of consequence.

Propositional logic

Hypothetical syllogism is one of the proof rules in classical logic that may or may not be available in a non-classical logic. The hypothetical syllogism (abbr. H.S.) is a valid argument of the following form:

P → Q.
Q → R.
Therefore, P → R.

Symbolically, this is expressed:

 P \rightarrow Q, Q \rightarrow R \vdash P \rightarrow R


If I do not wake up, then I cannot go to work.
If I cannot go to work, then I will not get paid.
Therefore, if I do not wake up, then I will not get paid.

See also


  1. ^ Ym


Got something to say? Make a comment.
Your name
Your email address