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Logical equivalence - Definition and Overview |
| Related Words: Affinity, Agreement, Balance, Chorus, Coherence, Coincidence, Communion, Community, Compatibility, Concert, Concord, Concordance, Conformation, Conformity, Congruence, Congruency |
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In logic, statements p and q are logically equivalent if they have the same logical content.
Syntactically, p and q are equivalent if each can be proved from the other.
Semantically, p and q are equivalent if they have the same truth value in every model.
Logical equivalence is often confused with material equivalence.
The former is a statement in the metalanguage, claiming something about statements p and q in the object language.
But the material equivalence of p and q (often written "p ↔ q") is itself another statement in the object language.
There is a relationship, however; p and q are syntactically equivalent if and only if p ↔ q is a theorem, while p and q are semantically equivalent if and only if p ↔ q is a tautology.
Logical equivalence is sometimes denoted p ≡ q or p ⇔ q.
However, the latter notation is also used for material equivalence.
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Example Usage of equivalence |
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tonykatz: @greeninoc ...ok...but now you are dealing in moral equivalence, and not focusing on the bill at hand. You need to focus on the issue #tcot |
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Radiology_help: Radiology publications: Testing efficiency transfer codes for equivalence.
http://bit.ly/2g6AuO |
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s_dog: If I hear one more Lefty draw moral equivalence between US workers "going postal" and acts of deliberate Islamic terrorism, I may scream. |
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