Namespaces
Variants
Actions

Implication

From Encyclopedia of Mathematics
Revision as of 19:01, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
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:'
<tbody> </tbody>
T T T
T F F
F T T
F F T

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. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Implication&oldid=12929
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article