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If also the premises of a valid argument are proven true, this is said to be sound. [3] The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid".
Every argument's conclusion is a premise of other arguments. The word constituent may be used for either a premise or conclusion. In the context of this article and in most classical contexts, all candidates for consideration as argument constituents fall under the category of truth-bearer : propositions, statements, sentences, judgments, etc.
Validity is defined in classical logic as follows: An argument (consisting of premises and a conclusion) is valid if and only if there is no possible situation in which all the premises are true and the conclusion is false. For example a valid argument might run: If it is raining, water exists (1st premise) It is raining (2nd premise)
A form of argument is valid if and only if the conclusion is true under all interpretations of that argument in which the premises are true. Since the validity of an argument depends on its form, an argument can be shown invalid by showing that its form is invalid. This can be done by a counter example of the same form of argument with premises ...
The premise that contains the middle term and major term is called the major premise while the premise that contains the middle term and minor term is called the minor premise. [ 5 ] A premise can also be an indicator word if statements have been combined into a logical argument and such word functions to mark the role of one or more of the ...
An argument is valid if, and only if, it is necessary that, if all its premises are true, its conclusion is true. [38] [41] [42] Alternatively, an argument is valid if, and only if, it is impossible for all the premises to be true while the conclusion is false. [42] [38] Validity is contrasted with soundness. [42]
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In a Hilbert system, the premises and conclusion of the inference rules are simply formulae of some language, usually employing metavariables.For graphical compactness of the presentation and to emphasize the distinction between axioms and rules of inference, this section uses the sequent notation instead of a vertical presentation of rules.