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Logical Implication

Consider

latex2( $X ⊨ y$ )

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( $X ⊨ y$ ), 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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-  ⇤ ← Revision 3 as of 2003-10-08 23:43:32 → 
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+   ← Revision 4 as of 2005-06-28 02:57:24 → ⇥
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-Deletions are marked like this.
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- X |= y
+ [[latex2( $X ⊨ y$ )]]
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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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-In predicate calculus, we often times use |- to denote logical implication. In this case we must prove that the predicate calculus expression is valid.
+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.

Diff for "LogicalImplication"

Logical Implication