The mathematics of knowledge rationality action
Download
1 / 38

The Mathematics of Knowledge, Rationality, & Action - PowerPoint PPT Presentation


  • 98 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' The Mathematics of Knowledge, Rationality, & Action' - tuwa


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
The mathematics of knowledge rationality action

The Mathematics of Knowledge, Rationality, & Action

Courtesy of Prof. Wiebe van der Hoek

Computer Science

University of Liverpool

United Kingdom


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

Agents’ Paradigm


Perceive reason act cycle each agent

sense 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’’

sense

act

act

goal

info

sense

act

Perceive-Reason-Act Cycle (Each Agent)

reason


Perceive reason act cycle multiple agents

sense 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’’

sense

act

act

goal

info

sense

act

Perceive-Reason-Act Cycle (Multiple Agents)

reason


Rationality
Rationality 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’’

A

B

B

A

A

A

$1

$4

$4

$3

$1

$5

$2

$4

$7

$3

$6

$5

$1 for A

$6 for B


Rationality1
Rationality 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’’

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality2
Rationality 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’’

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality3
Rationality 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’’

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality4
Rationality 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’’

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality5
Rationality 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’’

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


Rationality6
Rationality 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’’

A

B

B

A

A

A

1

4

4

3

1

5

2

4

7

3

6

5

$1 for A

$6 for B


E pistemic l ogic relies on 4 axioms f and y are facts

K(f 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’’y)  (Kf  Ky)

An agent reasons logicallyf is “Bob is standing in the rain”y is “Bob is getting wet”

Kf  f

An agent only knows true things

Kf  KKf

Positive introspection

¬Kf  K¬Kf

Negative introspection

Epistemic Logic Relies on 4 Axioms(f and y are facts)


Multiagent Knowledge 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’’

KAm: agent A knows m

A sends m to B

KAm ?

KBm ? Em ?

KAKB m?

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


Knowledge
Knowledge 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’’

: Monica and Chandler are ...

¬: they are just friends


Nested knowledge
Nested Knowledge 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’’

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
Rachel Finds Out … 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’’

Pre:

  • Kj, ¬Kr, Br

  • ¬KjKr, ¬Kj ¬Kr


Rachel found out
Rachel Found Out 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’’

Pre:

  • Kj, ¬Kr, Br

  • ¬KjKr, ¬Kj ¬Kr

Post:

  • Kj, Kr

  • KjKr, KrKj

  • E{j,r}, E{j,r} E{j,r} 


Phoebe found out
Phoebe Found Out 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’’

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), EF

and let {c, m, and j } be the Lovers team, EL : ¬EFEF and ¬ELEF


Phoebe found out1
Phoebe Found Out 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’’

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 e f
m and c Learn 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’’EF

Pre:

  • EFEF

  • ¬KmEF, ¬KcEF

  • ¬ELEF

    (Chandler tells Monica about the attempted seduction)


M and c learn e f1
m and c Learn 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’’EF

Pre:

  • EFEF

  • ¬KmEF, ¬KcEF

  • ¬ELEF

Post:

  • KmEF, KcEF

  • EL EF

  • ¬EF EL EF


P and r learn e l e f
p and r Learn 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’’EL EF

Pre:

  • KmEF, KcEF

  • EL EF

  • ¬EF EL EF, BF EL EF


P and r learn e l e f1
p and r learn 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’’EL EF

Pre:

  • KmEF, KcEF

  • EL EF

  • ¬EF EL EF, BF EL EF

Post:

  • EF EL EF

  • ¬E LEFELEF


E friends happy
E (Friends) Happy? 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’’


Common knowledge
Common Knowledge 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’’

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


Enemies
Enemies 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’’

“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


Secretary of defense
Secretary of Defense 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’’

  • “Despite Mr. Rumsfeld’s rather outlandish mode of speaking, fans of the tough-talking U.S. defense secretary argued that he was misunderstood.”


Knowledge rationality action
Knowledge, Rationality, Action 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’’

  • Knowledge

    • about world, other’s knowledge, & rationality

    • uncertainty, beliefs, suspicion

    • dynamic aspects: updating, learning

  • Rationality

    • An agent should do what is best for itself

  • Action

    • Emphasis on choice

    • Abilities: physical (robots), computational

    • Epistemic actions


ad