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    Hypothetical syllogism - Wikipedia

    • In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms. See more

    Types

    Hypothetical syllogisms come in two types: mixed and pure. A mixed hypothetical syllogism has two premises: one … See more

    Propositional logic

    In propositional logic, hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). The rule may b… See more

    Applicability

    The rule of hypothetical syllogism holds in classical logic, intuitionistic logic, most systems of relevance logic, and many other systems of logic. However, it does not hold in all logics, including, for example, non-monotonic l… See more

    Alternative forms

    An alternative form of hypothetical syllogism, more useful for classical propositional calculus systems with implication and negation (i.e. without the conjunction symbol), is the following:
    (HS1) … See more

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    Table of Contents
    Types
    Propositional logic
    Applicability
    Alternative forms
    See also
    External links
     
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