The number system 
,
which uses 
to track 
,
will be used in the definitions that follow.
The value of for 
is specified by 
.
For 
,
and 
.
When an interval has several properties, a specific
property may be referenced by giving its label:
references the continuity property,
for example.
A model 
of the m-ary function g satisfies the inclusion property
if for all appropriate 
, 
, and 
:
must also satisfy the value inclusion
property.
The value inclusion property is defined as before.
The interval extension
of the m-ary function g is defined as:
and 
are:
of
g is both the interval value extension
and the interval extension.
| Jeff Tupper | March 1996 |