Wikifunctions:Catalogue/Boolean operations
Appearance

These are the basic blocks from which to build logic states.
- not (Z10216): takes a truth value and returns its opposite
- and (Z10174): Performs a Boolean and operation
- or (Z10184): Performs a Boolean OR operation
- Boolean equality (Z844): returns true only if both inputs are equal
- Boolean inequality (Z10237): returns true only if both inputs are different
Boolean pairwise functions
Name | ZID | Value |
---|---|---|
nullary false | nullary false (Z10206) | F |
nullary true | nullary true (Z10210) | T |
Name | ZID | F | T |
---|---|---|---|
unary false | unary false (Z10214) | F | F |
identity | Boolean identity (Z10215) | F | T |
not | not (Z10216) | T | F |
unary true | unary true (Z10217) | T | T |
Name | ZID | F ∗ F | F ∗ T | T ∗ F | T ∗ T |
---|---|---|---|---|---|
binary false | binary false (Z10257) | F | F | F | F |
and | and (Z10174) | F | F | F | T |
not (A → B) | not boolean implication (Z10962) | F | F | T | F |
A | Boolean left (Z10265) | F | F | T | T |
not (B → A) | not backwards Boolean implication (Z10964) | F | T | F | F |
B | Boolean right (Z10298) | F | T | F | T |
xor | Boolean inequality (Z10237) | F | T | T | F |
or | or (Z10184) | F | T | T | T |
nor | nor (Z10231) | T | F | F | F |
xnor/eqv | Boolean equality (Z844) | T | F | F | T |
not B | Boolean not right (Z10306) | T | F | T | F |
B → A | backwards Boolean implication (Z10348) | T | F | T | T |
not A | Boolean not left (Z10272) | T | T | F | F |
A → B | Boolean implication (Z10329) | T | T | F | T |
nand | nand (Z10243) | T | T | T | F |
binary true | binary true (Z10287) | T | T | T | T |
- and (quaternary) (Z11828): takes four boolean inputs and returns true if and only if they are all true
- and (octanary) (Z11849): takes eight boolean inputs and returns true if and only if they are all true
- is truthy (Z15684): returns True if the argument is truthy
- are all true (Z12684): returns true if every list item is true
- is any true (Z12698): checks whether in a list of Boolean any is true
- are all false (Z13445): returns true if every list item is false
- is any false (Z16798): checks whether any members in a Boolean list is false
- Boolean to Sign (Z17053): Return positive if true, or negative if false
Kleenean functions
- Kleenean identity (Z22120): This checks whether the two values have the same identity. For the Kleenean notion of equality, a different function is available.
- and (Kleenean) (Z22143): prend deux triléens et renvoie leur valeur: "vrai", "peut-être" ou "faux"
- or (Kleenean) (Z22168): no description
- if (Kleenean) (Z22202): no description
- is Kleenean True? (Z22131): conservative conversion between Kleenean and Boolean, such that Maybe is called false
- Boolean as Kleenean (Z22126): no description
- not (Kleenean) (Z22207): negates a Kleenean value
- equality of Kleenean and Boolean (Z22257): only true if the Kleenean is True or False, and the Boolean is equal to it
- Z