polyadic algebra with equality
for any and any
for every , and
, where , and denotes the function that maps to , and constant everywhere else.
Heuristically, we can interpret the conditions above as follows:
if and if we replace by, say , and by , then .
for every variable
The second condition is also known as the reflexive property of the equality predicate , and the third is known as the substitutive property of
A polyadic algebra with equality is a pair where is a polyadic algebra and is an equality predicate on . Paul Halmos introduced this concept and called this simply an equality algebra.
Below are some basic properties of the equality predicate in an equality algebra :
The degree and local finiteness of a polyadic algebra are defined as the degree and the local finiteness and degree of its underlying polyadic algebra .
|Title||polyadic algebra with equality|
|Date of creation||2013-03-22 17:51:37|
|Last modified on||2013-03-22 17:51:37|
|Last modified by||CWoo (3771)|