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

On (A, Ta) ∧ On (B, Ta) ∧On (C, Ta) ∧ On (D, Ta) ∧ Box (A)
∧Box (B) ∧Cone (C) ∧ Sphere (D).
Suppose we have the following rules to define the height of an object from the
table.
1. If On (X, Y ) ∧ On (Y, Z) ∧On (Z, Ta) Then Height-of (X, 3).
2. If On (X, Y ) ∧On (Y, Ta) Then Height-of (X, 2).
3. If On (X, Ta) Then Height-of (X, 1).
We could define height by a generic approach. But to illustrate the
concept of the optimization, the present definition is adequate.
The optimization problem in the present context is: Maximize h, such
that On(c,_) ∧ Height-of (c, h) is true, where ‘_’ denotes something. The
solution of the problem can be evaluated easily by considering all the possible
stacking, such that C is on top. Note that D being spherical is excluded from
the stack.
The possible stackings are:
i) On (C, Ta) ∧ Height-of (C,1).
ii) On (C,A) ∧On (A, Ta ) ∧ Height-of (C, 2)
iii) On (C, B) ∧On(B, Ta) ∧ Height-of (C,2)
iv) On(C, B) ∧ On(B, A) ∧On(A, Ta) ∧ Height-of (C,3).
v) On(C, A) ∧On(A, B) ∧On (B, Ta) ∧ Height-of (C,3).
Out of these 5 possible stackings, the last two yield Height (=3) for C.
So, we may select any of them as the solution (see fig 19.6 (a) &(b)).
D
(a ) On (C,B) ∧ On (B,A) ∧ On (A, Ta) ∧ Height- of (C, 3).
B
A
C