Information Technology Reference
In-Depth Information
called concept instance assertion, i.e. concept assertion.
a
∈C is denoted as C(
a
);
a
∉C is denoted as ¬C(
).
Given two individuals
a
a, b
and a role
R
, if individual
a
and individual
b
satisfy role
).
In general, according to the constructor provided, description logic may
construct complex concept and role based on simple concept and role.
Description logic includes the following constructors at least: intersection (
<
),
union(
G
), negation(¬), existential quantification(
∃
), and value restriction(
∀
).
The description logic which possesses these constructors is called ALC. Base on
ALC, different constructors may be added to it, so that different description
logics may be formed. For example, if number restrictions “
” and “
” are added
to the description logic ALC, then a new kind of description logic ALCN is
formed. Table 2.3 shows the syntax and semantics of description logic ALC.
An interpretation I = (
I
, ·
I
) consists of a domain
I
and an interpretation
function ·I, where interpretation function ·I maps each primitive concept to subset
of domain
I
, and maps each primitive role to subset of domain
I
×
I
. With
respect to an interpretation, concept of ALC is interpreted as a domain subset,
and role is interpreted as binary relation.
R
, then
aRb
is role instance assertion, and it is denoted as
R
(
a, b
(1) An interpretation I is a model of subsumption assertion C
¥
D, if and only if
C
I
¥
D
I
;
(2) An interpretation I is a model of C(a), if and only if a
∈
C
I
; an interpretation I
is a model of P(a, b), if and only if (a, b)
∈
P
I
;
(3) An interpretation I is a model of knowledge base K, if and only if I is a model
of each subsumption assertion and instance assertion of knowledge base K;
(4) If knowledge base K has a mode l, then K is satisfiable;
(5) As to each model of knowledge base K, if assertion δ is satisfiable, then we
say that knowledge base K logically implicate δ, and it is denoted as K|=δ.
(6) As to concept C, if knowledge base K has a model I, and C
I
φ
, then concept
C is satisfiable. The concept C of knowledge base K is satisfiable if and only
if K
|
C
⊆
⊥
.
