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(7) TPP
-1
(
x,y
): indicating
y
is a strict part of
x
and they are tangent.
(8) NTPP
-1
(
x,y
): indicating
y
is a strict part of
x
and they don't touch each other.
) and some
assistant description functions, which have used some transitional state
predicates such as P(
The definition of these eight relation can be constructed by C(
x,y
x,y
) (partly belong to), PP(
x,y
)(strictly partly belong to)
O(
x,y
)(cover), etc.
2. The connections between the basic relations
This spatial logic is similar to the Allen's logic, which also expresses the possible
connections between binary relations with the pre-calculated transitivity table.
With any relation R
3
(
a,c
) in the table, all the possible binary relations R
1
(
a,b
) and
R
2
(
) can be found out. This table is useful to qualitative simulation. While
recent research hasn't given the building algorithm of the transitivity table. But
Randell has mentioned that his simulation program has used this table to verify
the consistency of state description during envisionment process.
Besides, the relation between geometric object and geometric area is
expressed by function space(
b,c
x,t
). It denotes that the geometric area occupied by
geometric object
). t can be ignored regardless of
time. Usually, in order to simplify operation, variable
x
at the moment of t is space(
x,t
x
is directly used to express
the geometric area occupied by geometric object
x
if there is no different
meanings.
3. The transition between the basic relations
According to the shapes of the two regions, the eight basic relations mentioned
above can be divided into six subsets:
(1) DC EC PO =
(2) DC EC PO TPP
(3) DC EC PO TPP
-1
(4) DC EC PO TPP NTPP
(5) DC EC PO TPP
-1
NTPP
-1
(6) DC EC PO
The division of the six subsets can be understood as: If the shapes of two
geometric areas are totally the same, the way they exist in the space can only be
the four situations listed in subset (1). If there are a sphere and a hemisphere with
