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logic1
http://www.openmath.org/cd
http://www.openmath.org/cd/logic1.ocd
2006-03-30
2004-03-30
4
0
Author: OpenMath Consortium SourceURL: https://github.com/OpenMath/CDs
official
This CD holds the basic logic functions.
equivalent
application
This symbol is used to show that two boolean expressions are logically equivalent, that is have the same boolean value for any inputs.
The condition (A is equivalent to B) is equivalent to the condition that (A implies B and B implies A)
not
application
This symbol represents the logical not function which takes one boolean argument, and returns the opposite boolean value.
for all x | not(not(x))=x
and
application
This symbol represents the logical and function which is an n-ary function taking boolean arguments and returning a boolean value. It is true if all arguments are true or false otherwise.
for all x | x and not(x) = false
nand
application
This symbol represents the logical nand function which is an n-ary function taking boolean arguments and returning a boolean value. It is false if all arguments are true or true otherwise.
for all x | x nand not(x) = true
xor
application
This symbol represents the logical xor function which is an n-ary function taking boolean arguments and returning a boolean value. It is true if there are an odd number of true arguments or false otherwise.
for all x | x xor x = false
for all x | x xor not(x) = true
xnor
application
This symbol represents the logical xnor function which is an n-ary function taking boolean arguments and returning a boolean value. It is false if there are an odd number of true arguments or true otherwise.
for all x | x xnor x = true
for all x | x xnor not(x) = false
or
application
This symbol represents the logical or function which is an n-ary function taking boolean arguments and returning a boolean value. It is true if any of the arguments are true or false otherwise.
for all x | x or not(x) = true
for all a,b | not(a and b)= (not(a) or not(b))
nor
application
This symbol represents the logical nor function which is an n-ary function taking boolean arguments and returning a boolean value. It is false if any of the arguments are true or true otherwise.
for all x | x nor not(x) = false
for all a,b | a and b = (not(a) nor not(b))
implies
application
This symbol represents the logical implies function which takes two boolean expressions as arguments. It evaluates to false if the first argument is true and the second argument is false, otherwise it evaluates to true.
for all x | false implies x
true
constant
This symbol represents the boolean value true.
not true = false
false
constant
This symbol represents the boolean value false.
not false = true