Encyclopedia > Logical equivalence

  Article Content

Logical equivalence

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
Charles V, Holy Roman Emperor

... force along the Mediterranean coast posed a threat to Hapsburg lands and the peace of Western Europe. In 1535 Charles won an important victory at Tunis, but in 1536 Francis ...

 
 
 
This page was created in 32.9 ms