Differences between revisions 5 and 6

Logical Implication or Entailment

Consider

where X is some set of premises and y is the conclusion. This simply means that the conjuction of all the premises entail the conclusion. We say that latex2($X \models y$) if and only if all the models of latex2($X$) are models of latex2($y$).

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

We call a tautology of the form latex2( $A ⊨ B$ ) 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. (Update this!!!)

See LogicNotes

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-  ⇤ ← Revision 5 as of 2005-06-28 02:57:49 → 
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+   ← Revision 6 as of 2006-07-18 23:41:16 → ⇥
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-= Logical Implication =
+= Logical Implication or Entailment =
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-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.
+where X is some set of premises and y is the conclusion. This simply means that the conjuction of all the premises entail the conclusion. We say that [[latex2($X \models y$)]] if and only if all the models of [[latex2($X$)]] are models of [[latex2($y$)]].
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-Therefore a tautology of the form [[latex2( $A ⊨ B$ )]] is called a Logical Implication.
+We call a tautology of the form [[latex2( $A ⊨ B$ )]] a Logical Implication.
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-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.
+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. (Update this!!!)

Diff for "LogicalImplication"

Logical Implication or Entailment