Logic Programming
The attempts to use logic programming such as prolog to represent knowledge and build artificial intelligent systems has not provided the anticipated thrust to solving interesting problems. The lack of generalization and learning capability of these systems and exponential growth of the IF-THEN ELSE rules has made this approach unpopular. An example to illustrate the failure of the rule-based system is the following flawed proof:
| Start with 81/4 = 81/4 |
| Adding -20 to LHS and RHS gives: -20 + 81/4 = -20 + 81/4 |
| Splitting –20 as ( -36 + 16 ) on the LHS and ( -45 + 25 ) on the RHS: 16 + 81/4 -36 = -45 + 81/4 +25 |
| Now expressing the terms 16, 25 and 81/4 as squares of 4, 5 and 9/2 respectively: 4² + (9/2)² - 2 * (9/2) * 4 = 5² + (9/2)² – 2 * (9/2) * 5 |
| Expressing this as a² + b² – 2*a*b = (a-b)² gives: (4 - 9/2)² = (5 - 9/2)² |
| Taking the square roots, 4 - 9/2 = 5 – 9/2 |
This would imply that 4 = 5, which a wrong result. While taking the square roots, the step of considering the signs has been missed. This has resulted in an absurd outcome. A rule based system, even if it missed a simple rule in its database may yield such an unacceptable output.
Another interesting mathematical proof gone wrong is as follows:
- Let a = b
- Multiply both sides by b
- ab = b²
- Subtract a² from both sides
- ab - a² = b² - a²
- Factor each side
- a(b - a) = (b+a)( b - a )
- cancelling (b-a) from both sides
- a = b+a
If a = 1, then we get an absurd result of 1 = 2
Read more about this topic: Lateral Computing, Logical Thinking and Artificial Intelligence
Famous quotes containing the words logic and/or programming:
“Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic.”
—Sir Peter Frederick Strawson (b. 1919)
“If there is a price to pay for the privilege of spending the early years of child rearing in the driver’s seat, it is our reluctance, our inability, to tolerate being demoted to the backseat. Spurred by our success in programming our children during the preschool years, we may find it difficult to forgo in later states the level of control that once afforded us so much satisfaction.”
—Melinda M. Marshall (20th century)