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In-Depth Information
∀
t
' (
t
<
t
'
ŗ
¬Holds-on(
s
,(
t,t
'))));
2
ŗ
∃
t
(A6) Holds-on(
s
,(
t
2
,t
3
))
∧
¬Holds-at(
s,t
1
)
∧
t
1
<
t
Holds-on(
s
,(
t
1
,
t
2
))
∧
∀
t
' (
t
<
'
ŗ
¬Holds-on(
2
)))).
Axioms (A1) and (A2) indicate that if there is a relation
t
s
,(
t',t
R
on the interval
i
,
there must be a perturbation relation of
R
, which exists at the beginning moment
or the ending moment of this interval.
Axioms (A3) and (A4) indicate that if there is a relation
R
at the moment
t
,
there must be moment
t
'
1
and moment
t
'
2
, which makes the perturbation relation
of R respectively exists on (
2
).
Axioms (A5) and (A6) indicate that if there is a state
t'
,t
) and (
t,t'
1
s
on the interval (
t
1
,
t
2
)
and it no longer exists at moment
t
3
, there must be a moment
t
in (
t
2
,
t
3
)(
t
3
>
t
2
) or
(
t
3
,
t
1
)(
t
3
<
t
1
) at which the state of
s
transits.
4.7.3.
Applications of temporal and spatial logic
The above axioms system can be used in the reasoning about the relations of
spatial objects. For example, if it is known that DC(
a,b
) exists at moment
t
1
,
PO(
a,b
) exists at moment
t
2
and
t
1
<
t
2
, it must be a moment
t
in (
t
1
,
t
2
), at which
EC(
) exists. That is:
Holds-at(DC(
a,b
a,b
),
t
1
)
∧
Holds-at(PO(
a,b
),
t
2
)
∧
t
1
<
t
2
ŗ
))
These theories can also be used to description and reasoning about events.
Predicates are introduced:
Occurs-at (
t(div(
t,(t
1
,t
2
))
∧
Holds-at(EC(
a,b),t
T,t
) indicates event
T
occurred at tieme
t
.
Occurs-on (
T,i
) indicates event
T
occurred on interval
i
.
2
.
The two predicates connect event with time. Function Trans builds mapping
relations between state and event. Galton has classified event into seven kinds:
Function Trans(
R
,R
2
) indicates the event that state
R
1
transits to state
R
1
(1)
R
1
is position state,
R
2
is motion state,
R
2
is the perturbation of
R
1
.
(2)
R
1
is motion state,
R
2
is position state,
R
2
is the perturbation of
R
1
.
(3)
R
1
and
R
2
which have same perturbation
R
3
are motion states.
(4)
R
1
and
R
2
which have no same perturbation are motion states.
(5)
R
1
and
R
2
are all position states.
(6)
R
1
is position state,
R
2
is motion state, but they are not the perturbation of
each other.
