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| Deletions are marked like this. | Additions are marked like this. |
| Line 5: | Line 5: |
| X |= y | [[latex2($$X \models y$$)]] |
| Line 9: | Line 9: |
| 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($$\vdash$$)]] to denote logical implication. In this case we must prove that the predicate calculus expression is valid. |
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($$X \models y$$), 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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