Information Technology Reference
In-Depth Information
This algebra system is defined upon real number R and symbol S' = {+,-,0,?},
allowing quantitative operations in R and qualitative operations in S', such as +, -,
× and / operations in R ;
⊕
,
½
, ⊗ and
⊘
operations in S' and qualitative operator
. Commutative law, associative law and distributive law are all tenable ,
except that
⊕
has no inverse element in S',
⊕
, ⊗. So:
s
⊕
u = t
⊕
u
⇏
s = t
s
⊕
t= u
⇏
s = u
½
t
This system can be used for designing. For example, there are an auto loaded
drinking bottle and a drinking storage container. A device is required to change
the liquid height of the bottle and the container. So when the liquid height H of
the bottle drops, the bottle can get drinking supply from the container. This
design process can be assumed directly as that:
The rise or drop of the liquid height H
b
is decided by the drinking flux Q
b
.
The pressure P of container bottom is in proportion to the drinking density,
namely, pressure is decided by height. It is required that when the pressure of the
bottle decreases in relation to the pressure of the container. Drinking flows to the
bottle from the container. Obviously, the required device can be implemented by
a pipe between the bottle and the container. The reasoning process of this design
involves not only the value and qualitative symbol but also the accurate
relationship in some place.
The mentioned mixed algebra can be used to describe and this problem.
MINIMA system can automatically deal with this problem.
d
H
−
H
=
[
H
]
Object
v
b
b
dt
H
b
× A
b
= V
b
//container model, the drinking volume is the product of
sectional area and height
H
b
=
V
b
/
A
b
d
V
H
−
H
=
[
(
b
)]
v
b
dt
A
b
d
H
−
H
=
[(
V
) /
A
]
v
b
b
b
dt
d
H
−
H
=
[(
V
)]
⊘
[
A
b
]
v
b
b
dt
