Logical statements may be joined via operations listed in the following table.
Operation |
Notation |
(read as) |
is true if and only if |
Negation |
![$ \lnot A$](/inhalt/aussage/aussage104/img1.png) |
(not ) |
is false |
Conjunction |
![$ A\land B$](/inhalt/aussage/aussage104/img3.png) |
( and ) |
both and are true |
Disjunction |
![$ A\lor B$](/inhalt/aussage/aussage104/img5.png) |
( or ) |
or is true (or both are true) |
Antivalence |
![$ A \not\equiv B$](/inhalt/aussage/aussage104/img6.png) |
(either or ) |
and are assigned different truth values |
Implication |
|
( implies ) |
|
( follows from ) |
|
|
is false or is true |
Equivalence |
![$ A\Leftrightarrow B$](/inhalt/aussage/aussage104/img9.png) |
( is equivalent to ) |
and are assigned identical truth values |
In order to reduce the usage of parentheses in logical formulas, we define that
is more closely linked to a symbol than
and
, which in turn are more closely linked than
,
and
.
Note that an implication
only requires the truth of
if
is true.
A false proposition implies anything, hence both true and false implications can be drawn.
Usually, the or-connective is symbolised by a v, derived from the word vel (Latin: or), yet it is also
common practice
to use the symbol ,,
``; then ,,
``symbolizes the and-connective. Using 0 to refer to the truth value ,,false``while interpreting any other value as ,,true``enables us to determine the truth value of logical formulas via calculation with natural numbers.
Particularly computer-linguists frequently use the English terms NOT (negation), AND (conjunction), OR (disjunction), EXOR or XOR (exclusive or, antivalence) as well as their negations NAND (negated conjunction), NOR (negated disjunction) and NXOR (equivalence).
(Authors: Höllig/Hörner/Kimmerle/Abele)
|
automatically generated
5/25/2009 |