Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

The resolution tree for linear selection is presented in fig. 6.3. It is clear
that two clauses from the set S1 = S ∪ { ¬ Goal} are first used for resolution
and the resolvent is next used for resolution with a third clause from the same
set S1. The process is continued until a null clause is generated. In the linear
selection process, one clause, however, can be used more than once for
resolution.
An alternative way to represent the resolution process in a tree with
linear selection is presented below. Such trees are generally referred to as SLD
trees. Let us now consider the following Logic program and draw the SLD
tree for the program.
Example 6.4: The Logic program built with definite clauses and the goal
are presented below.
1. P (X, Z) ← Q (X, Y) , P (Y, Z)
2. P (X, X) ←
3. Q (a, b) ←
Goal : ← P (X, b)
For the construction of the SLD tree, we would match the head of a
clause with the same consequent clause in another's body, during the process
of resolution of two clauses. This, however, in no way imposes restriction in
the general notion of resolution. Rather, it helps the beginners to mechanically
realize the resolution process. The SLD tree of a Logic Program becomes infinite,
if one uses the same rule many times. For instance using rule 1 many
times, we find an infinite SLD tree like fig. 6.4 for the current example.
6.6 Controlling Backtracking by CUT
Since a PROLOG compiler searches for the solution using a “depth first
search” strategy, the leftmost sub-tree in fig. 6.4 being infinite does not yield
any solution of the system. Such a problem, however, can be taken care of by
appropriately positioning “CUT” statements in the Logic Program. Since
depth first search in PROLOG programs are realized by stack, an infinitely
large SLD tree results in a stack overflow.