Knowledge, Rationality, & Action

Courtesy of Prof. Wiebe van der Hoek

Computer ScienceThe University of Liverpool

United Kingdom

2

Agents’ Paradigm

``..eventually, when you put enough feelingless calculations together in a huge coordinated organization, you’ll get something that has properties on another level. You can see it .... as a system of tendencies and desires and beliefs and so on’’

Hofstadter, 1981, Scientific American

3

sensesense

planplanactact

sense-plan-act cycle (Agents)

infoinfogoalgoal

sensesensesensesense

actact actact

4

sensesense

planplanactact

sense-plan-act cycle (MAS)

infoinfogoalgoal

sensesensesensesense

actact actact

5

Rationality

B

A

A AA

B

$1 for A$6 for B

$2$4

$7$3

$6$5

$4$3

$1$5

14

6

Rationality

B

A

A AA

B

24

73

65

43

15

14

$1 for A$6 for B

7

Rationality

B

A

A AA

B

24

73

65

43

15

14

$1 for A$6 for B

8

Rationality

B

A

A AA

B

24

73

65

43

15

14

$1 for A$6 for B

9

Rationality

B

A

A AA

B

$1 for A$6 for B

24

73

65

43

15

14

10

Rationality

B

A

A AA

B

24

73

65

43

15

14

$1 for A$6 for B

11

Rationality

B

A

A AA

B

24

73

65

43

15

14

$1 for A$6 for B

12

Epistemic Logic Relies on 4 Axioms

agents reason logically

veridicality

positive introspection

¬K¬K negative introspection

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Multiagent Knowledge

KAm: A knows m

A sends m to B

KAm ?KBm ? Em ?

KAKB m?

KBKAKB m? KAKBKAKB m, ..., Cm?

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Knowledge

: Monica and Chandler are ...

¬: they are just friends

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Nested Knowledge

Post:Kc, Km, KjE{cmj} , E{cmj}E{cmj} E{cmj} (¬Kr & ¬Kp &¬Kro)

Goal{m,c} (¬Kr & ¬Kp &¬Kro)

Goalj (Kr & Kp & Kro)

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Rachel Finds Out …

Pre: Kj, ¬Kr, Br ¬KjKr, ¬Kj

¬Kr

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Rachel Found Out

Post: Kj, Kr, KjKr, KrKj, E{j,r}, E{j,r} E{j,r}

Pre: Kj, ¬Kr, Br ¬KjKr, ¬Kj ¬Kr

22

Phoebe Found Out

Pre: Kj, Km, Kp, Kr E{j,r,p}, ¬E{j,r,p}E{j,r,p}

Let us call this team the Friends team (r, p, and j) and let {c, m, and j } be the Lovers team: ¬EFEF

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Phoebe Found Out

Post: EFEF ¬KmEF, ¬KcEF ¬ELEF, Goalp ¬ELEF, Goalj ELEF

(Phoebe tries to seduce Chandler)

Pre: Kj, Km, Kp, Kr, Kc EF,

¬EFEF

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m and c Learn EF

Post: EFEF ¬KmEF, ¬KcEF ¬ELEF

(Chandler tells Monica about the attempted seduction)

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28

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m and c Learn EF

Post: KmEF, KcEF EL EF ¬EF EL EF

Pre: EFEF ¬KmEF, ¬KcEF ¬ELEF

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p and r Learn EL EF

Pre: KmEF, KcEF EL EF ¬EF EL EF, BF EL EF

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p and r learn EL EF

Pre: KmEF, KcEF EL EF ¬EF EL EF, BF EL EF

Post: EF EL EF ¬E LEFELEF

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E (Friends) Happy?

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Common Knowledge

EEverybody knows EEE Cit is Common Knowledge that idea: CEEE &

EEEEEEE ….. so: ¬C if somebody

considers it possible that somebody considers it possible that

somebody considers it possible that …………. does not

hold

Enemies“The message is, thatThere are known knowns, there are things we

know that we know. There are known unknowns, that is to say,

there are things that we now know, we don’t know.

But there are also unknown unknowns—there are things we do not know we don’t know.

And each year, we discover a few more of those unknown unknowns.’’ Play

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Foot in Mouth Award “Despite Mr. Rumsfeld’s

rather outlandish mode of speaking, fans of the though-talking US defence secretary argue he is misunderstood.”

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Knowledge, Rationality, Action

Knowledge about world, other’s knowledge, & rationality uncertainty, beliefs, suspicion dynamic aspects: updating, learning

Rationality optimize utilities, do what is best/most

economic Action

emphasis on choice abilities: physical (robots), computational epistemic actions