Information Technology Reference
In-Depth Information
made along the inference process. Such a formalization will facilitate the semantic
analysis of the system carried out in Section 22.5. Section 22.6 summarizes results.
22.2
Preliminary Definitions
In this section we define a pair of concepts that we will need to describe the inference
process in CADIAG2.
First we define a partial ordering relation.
Definition 27.
Let
be the partial ordering relation on
[
0
,
1
]
defined as follows: for
a
,
b
∈
[
0
,
1
]
,a
b if and only if
0
<
a
≤
bor
0
≤
a
<
1
and b
=
0
.
We define the strict partial ordering
in the conventional way.
As we will see later, the definition of the ordering
≺
from
responds to the use of both
0 and 1 as maximal values in CADIAG2 for the interval
. The value 0 denotes
certainty in the non-occurrence of an event or falsity of a statement and the value 1
denotes certainty in its occurrence or its truth.
For the next definition let
[
0
,
1
]
D =[
,
]
×
[
,
]
−{
(
,
)
,
(
,
)
}.
0
1
0
1
0
1
1
0
Definition 28.
The function
max
∗
:
D
−→
R
is defined as follows, for all
(
a
,
b
)
∈
D
:
a fb
a
botherwise
≺
max
∗
(
,
)=
a
b
In words, max
∗
(
a
,
b
)
returns the biggest value among
a
and
b
with respect to the
ordering
just defined.
22.3
The Medical Expert System CADIAG2
In this section we briefly introduce the medical expert system CADIAG2 -for more
details on its design one can look at [1], [2] or [3]-.
As already mentioned in the introduction, CADIAG2 consists of two fundamen-
tal pieces: the knowledge base and the inference engine. We first describe the dif-
ferent types of rules in the system, mostly in relation to the role they play along
the inference process, and later describe the essentials of the inference mechanism.
Before getting started some notation is needed.
Let
p
1
,...,
p
l
denote the
basic
medical entities that occur in CADIAG2 (i.e., the
symptoms and diagnoses in the system), for some
l
. CADIAG2 deals also with
compound
entities, build from basic ones by means of conjunction (
∈
N
∧
), disjunction
(
) (i.e., built as Boolean combinations of basic ones).
Strictly speaking, the system regards two additional types of connectives called
at least n out of m
and
at most n out of m
, with
n
∨
) and negation (
∼
m
.However,these
can be expressed in terms of conjunction and disjunction and thus are not taken into
account in this paper. As an example,
,
m
∈
N
and
n
≤
