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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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love_unity: Our entire problem is that we lack equivalence of form with wider ranges of information that remain outside of us.http://bit.ly/3tty78 |
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executive_b: @CassCassandra richmond isn't 'THAT' bad its norfolk that's infested with the equivalence of swine flu of lame niggas |
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luqui: My Agda Hello World: two fib implementations and proof of equivalence: http://bit.ly/4tNKXY |
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