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M = M
v
M
f
is
a set of attributes or elements, with simple valued or functional
valued.M
v
= {x
v1
, x
v2
, …, x
vk
} is the set of simple valued variables. M
f
= {x
f1
, x
f2
, … x
fm
} is
the set of functional valued elements.
R = R
vv
R
fv
R
vf
R
fvf
is the set of deduction rules, and R is the union of four subsets
of rules R
vv
, R
fv
, R
vf
, R
fvf
. Each rule r has the form r: u(r)v(r), with u(r) is the
hypotheses of r and v(r) is the conclusion of r. A rule is also one of the four cases below.
Case 1: r R
vv
. For this case, u(r) M
v
and v(r) M
v
.
Case 2: r R
fv
. For this case, u(r) M
f
and v(r) M
v
.
Case 3: r R
vf
. For this case, u(r) M
v
and v(r) M
f
.
Case 4: r R
fvf
. For this case, u(r) M, u(r) M
f
, u(r) M
v
, and v(r) M
f
.
Each rule in R has the corresponding computational relation in F = F
vv
F
fv
F
vf
F
fvf
.
Definition 3.10:
An
extensive computational Object
(ECom-Object) is an object O has structure
including:
A set of attributes Attr(O) = M
v
M
f
, with M
v
is a set of simple valued variables; M
f
is a
set of functional variables. Between the variables (or attributes) there are internal
relations, that are deduction rules or the computational relations.
The object O has behaviors of reasoning and computing on attributes of objects or facts
such as: find the closure of a set A Attr(O); find a solution of problems which has the
form A→B, with A Attr(O) and B Attr(O); perform computations; consider
determination of objects or facts.
Definition 3.11:
An
extensive computational objects network
is a model
(O, M, F, T)
that has the
components below.
O = {O
1
, O
2
, …, O
n
} is the set of extensive computational objects.
M is a set of object attributes. We will use the following notations: M
v
(O
i
) is the set of
simple valued attributes of the object O
i
, M
f
(O
i
) is the set of functional attributes of O
i
,
M(O
i
) = M
v
(O
i
) M
f
(O
i
), M(O) = M(O
1
) M(O
2
) … M(O
n
), and M M(O).
F = F(O) is the set of the computational relations on attributes in M and on objects in O.
T={t
1
, t
2
, …, t
k
} is set of operators on objects.
On the structure (O,T), there are expressions of objects. Each expression of objects has its
attributes as if it is an object.
4. Design of main components
The main components of an IPSE are considered here consists of the knowledge base, the
inference engine. Design of these components will be discussed and presented in this
section.
4.1 Design of knowledge base
The design process of the system presented in section 2 consists of seven stages. After stage
1 for collecting real knowledge, the knowledge base design includes stage 2 and stage 3. It
includes the following tasks.
