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 X |= y [[latex2($$X \models y$$)]]
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To show X |= y, show that X => y is a tautology. To show [[latex2($$X \models y$$)]], show that [[latex2($$X \Rightarrow y$$)]] is a tautology.
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Therefore a tautology of the form A |= B is called a Logical Implication. Therefore a tautology of the form [[latex2($$A \models B$$)]] is called a Logical Implication.
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See In predicate calculus, we often times use [[latex2($$\vdash$$)]] to denote logical implication. In this case we must prove that the predicate calculus expression is valid.

See LogicNotes

Logical Implication

Consider

latex2($$X \models y$$)

where X is some set of premises and y is the conclusion. This simply means that the conjuction of all the premises logically implies the conclusion.

To show latex2($$X \models y$$), show that latex2($$X \Rightarrow y$$) is a tautology.

Therefore a tautology of the form latex2($$A \models B$$) is called a Logical Implication.

In predicate calculus, we often times use latex2($$\vdash$$) to denote logical implication. In this case we must prove that the predicate calculus expression is valid.

See LogicNotes

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LogicalImplication (last edited 2020-02-02 17:44:06 by scot)