Backtracking

Control Knowledge:

You need to know how to use the facts you have.
 

Backtracking:

	If we knew what goes wrong in S2 didn't depend on S1, but on I.S., we could go back to the I.S.

{ Assumption }
{ Premises     }
{ Actions       }

If p then q   [ axioms ]
             p
-------------  [ rules of inference ]
             q   [ modus ponens ]
 

Examples of Backtracking :

- Driving car -> You realize you took wrong exit -> You don't go back to the previous street.
                   -> You know you have to go back to the highway and go take the previous exit.

Every decision we make, we keep track of why we're making this decision.

Each choice leads to a belief, and cancellation of other beliefs.

OJ Simpson case -> Let's say half the class believes he's guilty.

belief O.J.S. is guilty :

OJ has motive

No other suspect

Beliefs you cancelled must have justifications too
         -> Every new belief has a justification structure.

IN :  Justification for beliefs that I believe now, did not believe earlier.

OUT : Justification for beliefs that I don't believe anymore, but used to earlier.
 

Scientific discovery uses dependency-directed backtracking
  If your beliefs don't match your data, you gotta go back to your theorems
  and their justifications.

- Characteristic of intelligence is the ability to go both forward and backward.

- Reasoning is not monotonic or one dimensional.

Issue :  - How do we change the direction of reasoning ?
           - How do we backtrack ?
          (- How far to retract our reasoning ?)
 

Hypothesis :  - Beliefs
                  - Justifications    [ IN, OUT]
                                         [ + ,  -    ]

Implementations of this :
  Truth Maintenance System      - Doyle
  ATMS
  JTMS
 

Real Environment :  Doesn't have all the data to begin with.

Monotonic Reasonint :  As your data accumulates, so do your beliefs.
 -> As more proofs are presented, you believe stronger that OJ Simpson is guilty.

- You need links between beliefs

- You reason about your beliefs, you also reason about yourself. (Why do I believe in that stuff ?)
 

More examples of retracting beliefs:

Two ways of interpreting this sentence:
(-> He brought flowers to her.)
(-> He took her flowers away.)

B1-> John is a nice guy.

B1, B11 -> He brought her flowers.

(More data comes in) :

B1, B11 -> John loved flowers.

B1, B11 -> He stole them whenever he could.

Eventually our first belief (B1) gets retracted.
Now, when you retract B1, you retract B11 too.

Eg: Movie Memento is an excellent example of retraction.
 
 

Issue of Probability:

Contention since Plato in the last 2000 years:
 

Logic	Probability
- Given right information, come to right   conclusion. - Why do logic?  1. Consistency                        2. Completeness

Consistency :  If initial beliefs are correct, every belief youadd will be correct.

Completeness :  There is no fact in the world that cannot be proven.
 

microworld:

axioms                    b1 . . . . . . . . . bn   rule of inference          modus ponens                                    bn+1, bn+2, . . . . . . . . . bn+r                                      bz

This is assumed to be a closed world -> The assumption that limits logic.