Encyclopedia > Logically equivalent

  Article Content

Logical equivalence

Redirected from Logically equivalent

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 "pq") is itself another statement in the object language. There is a relationship, however; p and q are syntactically equivalent if and only if pq is a theorem, while p and q are semantically equivalent if and only if pq is a tautology.

Logical equivalence is sometimes denoted pq or pq. However, the latter notation is also used for material equivalence.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Dana International

...     Contents Dana International Dana International (born Yaron Cohen February 2, 1972) is an Israeli transsexual pop singer, who won ...

 
 
 
This page was created in 40.1 ms