# Class 7: POP; Uncertainty; Creativity

Selmer Bringsjord

• Logistics:
• Midterms back soon
• Project 2 due for studio audience next class
• Student web pagebrowser

• Today:
• POP
• Uncertainty and OSCAR
• Creativity and BRUTUS

? (substitute '(a b c) (match '(?x ?y ?z) '(a b c)))
(A B C)
? (match '(?x ?y ?z) '(a b c))
((?Z C) (?Y B) (?X A) (T T))
? (substitute '(?x b c) '((?x a)))
(A B C)
? (substitute '(?x b ?y) '((?x a) (?y f)))
(A B F)
? (substitute '(?x (a b) ?y) '((?x a) (?y f)))
(A (A B) F)
? (substitute '(?x (a ?z) ?y) '((?x a) (?y f) (?z e)))
(A (A E) F)
? (rhs '((a b c) (d e f)))
(D E F)
? (lhs '((a b c) (d e f)))
(A B C)
? (apply-rule '(I am depressed)
'((I am ?x) (Why are you ?x ?)))
(WHY ARE YOU DEPRESSED ?)
? (apply-rule '(Man Socrates)
'((Man ?x) (Mortal ?x)))
(MORTAL SOCRATES)
? *grammar-rules*
(((JOHN ?V ?N) ((N JOHN)...
? (apply-rules '(John loves Mary) *grammar-rules*)
(S (N JOHN) (VP (V LOVES) (N MARY)))
? (match '(a b c) '(a b c))
((T T))

POP

A plan is a quadruple where

What are we looking for?

solution() iff complete() consistent(), where

complete() iff
))).

consistent() iff
there are no contradictions in and .

• Checking this out on the shopping example
• How challenging is it to check for inconsistency?

Uncertainty and OSCAR

• Defeasible logic (or revisable, or nonmonotonic, logic) arises from monotonicity in FOL:
• if is provable from KB, then adding new information to KB, no matter what that information is, never sees to the retraction of KB

• Our everyday reasoning isn't monotonic:

Nearly all of you will at one time or another have affirmed the proposition that birds can fly. Expressed in FOL, this fact could be captured by

(1)
.

You will also have confronted the fact that ostriches can't fly. Clearly, there is a need to revise what had earlier been believed. But just as clearly, it's very implausible that humans, in everyday reasoning, employ modifications of (1) like

because, for starters, there are an infinite number of exceptions to (1). The solution, in general, must (might?) be that we use a system that allows us to make defeasible or revisable inferences. Defeasible logics mark attempts to capture such systems.

• OSCAR is designed to handle tough problems involving uncertainty, e.g.,

Suppose you hold one ticket (tk, for some ) in a fair lottery consisting of 1 million tickets, and suppose it is known that one and only one ticket will win. Since the probability is only .000001 of tk's being drawn, it seems reasonable to believe that tk will not win. By the same reasoning it seems reasonable to believe that t1 will not win, that t2 will not win, , that t1000000 will not win. Therefore it is reasonable to believe

But we know that

So we have an outright contradiction.

• And the Paradox of the Preface
• How would you solve these problems using machinery gradually coming under your control in this course?
• Tackling this a good way to learn
• The guts" of OSCAR: only if you're interested
• But let's look at some pictures
• Comparing belief networks etc. on the hard cases

• Creativity, Chess & S3G
• defining creativity
• n-queens problemRalph
• Selmer's Challenge to Ralph: S3G
• JoyceBot2
• Brutus v. Selmer in S3G
• BRUTUS.1Browser
• BRUTUS.1 & Betrayal

DefB 1
Agent sr betrays agent sd iff there exists some state of affairs p such that
1
sd wants p to occur;
2
sr believes that sd wants p to occur;
4
sr intends that p not occur;
5
sr believes that sd believes that sr intends that p occur.

Problem: no need to do anything

DefB 2
Agent sr betrays agent sd iff there exists some state of affairs p such that
1
sd wants p to occur;
2
sr believes that sd wants p to occur;
3
sr agrees with sd that p ought to occur;
4
sr intends that p not occur;
5
sr believes that sd believes that sr intends that p occur.

Problem: Suppose that Horace wants President Clinton to make a trip to Moscow; and suppose as well that Joe believes that Horace wants Clinton to make this trip, and that Joe agrees with Horace that Clinton ought to go. However, assume in addition that Joe intends that Clinton not go -- but takes no action toward that end. In this case it seems that since Joe does nothing (relevant), even if Clinton fails to go, there is no betrayal in the picture.

DefB 5
Agent sr betrays agent sd iff there exists some state of affairs p such that
1
sd wants p to occur;
2
sr believes that sd wants p to occur;
3
sr agrees with sd that p ought to occur;
4'
there is some action a which sr performs in the belief that thereby p will not occur;
5'
sr believes that sd believes that there is some action a which sr performs in the belief that thereby p will occur;
6'
sd wants that there is some action a which sr performs in the belief that thereby p will occur.

DefC 1
Agent s is P-creative with respect to at t if and only if there is a time t' prior to t and knowledge-bases and such that
1
at t';
3
at t, where s changes to at some time t'' later than t' but not later than t.