Information Technology Reference
In-Depth Information
2. Default Assumptions
Let {
F
1
, …,
F
n
} be the set of alternative default nodes, let G be a node which
represents the reason for making an assumption to choose the default. To make
Fi the default, justify it with the following SL justification:
n
) ) (2.23)
If no additional information about the value exists, none of the alternative nodes
except
( SL (G) (
F
1
, …,
F
i-1
,
F
i+1
, …,
F
F
i
will have a valid justification, so
F
i
will be an IN-node and each
F
j
with
j
will be OUT-node. However, if a valid justification is added to some other
alternative node and cause that alternative to become an IN-node, then the
aboving SL justification will be invalid and make
i
F
i
an OUT-node. Consider the
case that
F
i
has been selected as default assumption and a contradiction is derived
from
F
i
as an assumption because it depends on the other alternative nodes being OUT.
The backtracker may then justify one of the other alternative nodes, say
F
i
, then the dependency-directed backtracking mechanism will recognize
F
j
, and
make
F
i
an OUT-node. Where, the backtracker-produced justification for
F
j
will
have the following form:
( SL <various nodes> <remainder nodes> )
(2.24)
where <remainder nodes> represent the set of nodes except
F
j
.
The aboving approach will not work in the case that the complete set of
alternatives cannot be known in advance but must be discovered piecemeal. To
solve this problem, we can use a slightly different set of justifications with which
the set of alternatives can be gradually extended.
Retaining the above notation and let ¬
F
i
be a node which represents the
negation of
F
i
and
F
i
. Then, arrange
F
i
to be believed if ¬
F
i
is an OUT-node, and set up
justifications so that if
F
j
is distinct from
F
i
then
F
j
supports ¬
F
i
. I.e.,
F
i
is
justified with
( SL (G) (¬
F
i
))
(2.25)
and ¬
F
i
is justified with
( SL (
F
j
) (
j
i
) )
(2.26)
where
F
j
is an alternative distinct from
F
i
.
F
i
will be assumed if no reasons exist for
using any other alternative. However, if some contradiction is derived from
According to these justifications,
F
i
,
then ¬
F
i
will become an IN-node and correspondingly
F
i
become an OUT-node.
