# Hypothetical syllogism

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Hypothetical syllogism

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:

If P → Q.
If Q → R.

____________________

Then P → R.

Symbolically, this is expressed:

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

Example of use:

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.

## References

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### Look at other dictionaries:

• hypothetical syllogism — noun Etymology: translation of Late Latin hypotheticus syllogismus 1. : a syllogism consisting wholly of hypothetical propositions called also pure hypothetical syllogism 2. : a syllogism consisting partly of hypothetical propositions called also …   Useful english dictionary

• mixed hypothetical syllogism — noun see hypothetical syllogism …   Useful english dictionary

• pure hypothetical syllogism — noun see hypothetical syllogism …   Useful english dictionary

• Syllogism — A syllogism (Greek: συλλογισμός – syllogismos – conclusion, inference ) is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a certain form. In antiquity, there were… …   Wikipedia

• syllogism — /ˈsɪlədʒɪzəm / (say siluhjizuhm) noun 1. Logic an argument with two premises and a conclusion. Both the premises of a categorical syllogism are categorical propositions, containing just three distinct terms between them, e.g. all men are mortal… …   Australian English dictionary

• syllogism — /sil euh jiz euhm/, n. 1. Logic. an argument the conclusion of which is supported by two premises, of which one (major premise) contains the term (major term) that is the predicate of the conclusion, and the other (minor premise) contains the… …   Universalium

• hypothetical — /haɪpəˈθɛtɪkəl / (say huypuh thetikuhl) adjective Also, hypothetic. 1. assumed by hypothesis; supposed: a hypothetical case. 2. relating to, involving, or of the nature of hypothesis: hypothetical reasoning. 3. given to making hypotheses: a… …   Australian English dictionary

• hypothetical — hypothetically, adv. /huy peuh thet i keuhl/, adj. 1. assumed by hypothesis; supposed: a hypothetical case. 2. of, pertaining to, involving, or characterized by hypothesis: hypothetical reasoning. 3. given to making hypotheses. 4. Logic. a. (of a …   Universalium

• Disjunctive syllogism — Rules of inference Propositional calculus Modus ponens (A→B, A ⊢ B) Modus tollens (A→B, ¬B ⊢ ¬A) …   Wikipedia

• logic — logicless, adj. /loj ik/, n. 1. the science that investigates the principles governing correct or reliable inference. 2. a particular method of reasoning or argumentation: We were unable to follow his logic. 3. the system or principles of… …   Universalium