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Knowledge, Rationality, & Action. Courtesy of Prof. Wiebe van der Hoek Computer Science The University of Liverpool United Kingdom.

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Knowledge, Rationality, & Action

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Knowledge, Rationality, & Action

Courtesy of Prof. Wiebe van der Hoek

Computer Science

The University of Liverpool

United Kingdom


``..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

Agents’ Paradigm


sense

sense

act

act

goal

info

sense

act

sense-plan-act cycle (Agents)

plan


sense

sense

act

act

goal

info

sense

act

sense-plan-act cycle (MAS)

plan


Rationality

A

B

B

A

A

A

1

4

$4

$3

$1

$5

$2

$4

$7

$3

$6

$5

$1 for A

$6 for B


Rationality

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


K(f y)  (Kf  Ky)

agents reason logically

Kf  f

veridicality

Kf  KKf

positive introspection

¬Kf  K¬Kf

negative introspection

Epistemic Logic Relies on 4 Axioms


Multiagent Knowledge

KAm: A knows m

A sends m to B

KAm ?

KBm ? Em ?

KAKB m?

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


Knowledge

: Monica and Chandler are ...

¬: they are just friends


Nested Knowledge

Post:

Kc, Km, Kj

E{cmj} , E{cmj}E{cmj} 

E{cmj} (¬Kr & ¬Kp &¬Kro)

Goal{m,c}(¬Kr & ¬Kp &¬Kro)

Goalj(Kr & Kp &Kro)


Rachel Finds Out …

  • Pre:

  • Kj, ¬Kr, Br

  • ¬KjKr, ¬Kj ¬Kr


Rachel Found Out 

  • Pre:

  • Kj, ¬Kr, Br

  • ¬KjKr, ¬Kj ¬Kr

  • Post:

  • Kj, Kr,

  • KjKr, KrKj,

  • E{j,r}, E{j,r} E{j,r} 


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


Phoebe Found Out 

  • Pre:

  • Kj, Km, Kp, Kr, Kc

  • EF,

  • ¬EFEF

  • Post:

  • EFEF

  • ¬KmEF, ¬KcEF

  • ¬ELEF, Goalp ¬ELEF, Goalj ELEF

    (Phoebe tries to seduce Chandler)


m and c Learn EF

  • Post:

  • EFEF

  • ¬KmEF, ¬KcEF

  • ¬ELEF

    (Chandler tells Monica about the attempted seduction)


m and c Learn EF

  • Pre:

  • EFEF

  • ¬KmEF, ¬KcEF

  • ¬ELEF

  • Post:

  • KmEF, KcEF

  • EL EF

  • ¬EF EL EF


p and r Learn EL EF

  • Pre:

  • KmEF, KcEF

  • EL EF

  • ¬EF EL EF, BF EL EF


p and r learn EL EF

  • Pre:

  • KmEF, KcEF

  • EL EF

  • ¬EF EL EF, BF EL EF

  • Post:

  • EF EL EF

  • ¬E LEFELEF


E (Friends) Happy?


Common Knowledge

  • Ej: Everybody knows j

  • Ej  EEj

  • Cj: it is Common Knowledge that j

  • idea: Cj = Ej & EEj & EEEj & EEEEj & …..

  • so: ¬Cj if somebody

    • considers it possible that

      • somebody considers it possible thatsomebody considers it possible that…………. j does not hold


Enemies

“The message is, that

There 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


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.”


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


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