Logical Implication

Consider

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

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

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

See LogicNotes

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LogicalImplication

Logical Implication