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(2) If
and
are actions, then
;
,
G
, and
* are all actions;
(3) If
ϕ
is an assertion formula, then
ϕ
? is action.
2.12.3
Semantics of dynamic description logic
The semantics of DDL can be illustrated by a structure composed of the
following components:
(1) Non-empty set
, which is the set of all individuals discussed in a specified
domain;
(2) The set of state W, which is the set of all state of the world in specified
domain;
(3) An interpretation I which explains each individual, concept and role in DDL
as follows:
①
Each individual constant is interpreted as an element of
;
②
Each concept is interpreted as a subset of
;
③
Each role is interpreted as a binary relation on
.
(4) Each action is mapped into a binary relation on W.
Next we will explain the semantics of DDL in detail. First, for a state u in DDL,
an explanation I(u) = (
, •
I(u)
) in u is composed of two components, written
I(u)
I(u)
as I(u) = (
,•
maps each concept into a
subset of
and maps each role into a binary relations on
×
.
), where explanation function •
·
ն
I
(
u
)
=
;
·
շ
I
(
u
)
= ∅;
I
(
u
)
·
C
;
