In
computer science, a Boolean variable is a
variable that takes values in some Boolean domain. Some
programming languages feature
reserved words or symbols for the elements of the Boolean domain, for example false and true. However, many programming languages do not have a
Boolean datatype in the strict sense. In
C or
BASIC, for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1, and all variables that can take these values can also take any other numerical values.
Generalizations
The Boolean domain {0, 1} can be replaced by the
unit interval[0,1], in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed. Algebraically, negation (NOT) is replaced with conjunction (AND) is replaced with multiplication (), and disjunction (OR) is defined via
De Morgan's law to be .
Interpreting these values as logical
truth values yields a
multi-valued logic, which forms the basis for
fuzzy logic and
probabilistic logic. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or the probability that the proposition is true.
Drechsler, Rolf; Soeken, Mathias, eds. (2020) [March 2019]. Written at Bremen, Germany. Advanced Boolean Techniques - Selected Papers from the 13th International Workshop on Boolean Problems (1 ed.). Cham, Switzerland:
Springer Nature Switzerland AG.
doi:
10.1007/978-3-030-20323-8.
ISBN978-3-030-20322-1.
S2CID240782759. (vii+265+7 pages)
[6] (NB. Contains extended versions of the best manuscripts from the 13th International Workshop on Boolean Problems (IWSBP 2018) held in Bremen, Germany on 2018-09-19/21.)
Drechsler, Rolf; Große, Daniel, eds. (2021-04-30). Recent Findings in Boolean Techniques - Selected Papers from the 14th International Workshop on Boolean Problems (1 ed.).
Springer Nature Switzerland AG.
ISBN978-3-030-68070-1. (204 pages)
[7] (NB. Contains extended versions of the best manuscripts from the 14th International Workshop on Boolean Problems (IWSBP 2020) held
virtually on 2020-09-24/25.)