Implication
From Encyclopedia of Mathematics
The logical operation corresponding to the formation of the expression "if A, then B" from two expressions 
and 
. In formal languages, implication is most often denoted by one of the symbols 
, 
or 
. The expression 
is called the premise of 
, while the expression 
is called the consequence. The precise meaning of the expression 
differs in the classical, constructive and other approaches to the semantics of the language. In languages with classical semantics, the use of implication is in accordance with the following truth table:'
and . In formal languages, implication is most often denoted by one of the symbols , or . The expression is called the premise of , while the expression is called the consequence. The precise meaning of the expression differs in the classical, constructive and other approaches to the semantics of the language. In languages with classical semantics, the use of implication is in accordance with the following truth table:'
|
Implication as understood in the above sense is called material implication.
Comments
References
| [a1] | J.L. Bell, M. Machover, "A course in mathematical logic" , North-Holland (1977) |
How to Cite This Entry:
Implication. V.E. Plisko (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Implication&oldid=12929
Implication. V.E. Plisko (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Implication&oldid=12929
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098