COMPUTATION MEETS COGNITION

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COMPUTATION MEETS COGNITION
CSCA Colloquium, 19 november 2003

• Johan van Benthem http//staff.science.uva.nl/joh
  an/
• Institute for Logic, Language and Computation ILLC

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De Kunst van het Kennis Maken

• Lite version on September 1st
• Now a little bit more classic.
• But also CSCA formula encourage meeting of
  ideas from computation and cognition.

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Turing Machines and Humans

• Turing machine, ambiguity of computer
• Computational paradigm for reasoning,
• hardware/machine-language oriented...
• Turing Test mimick linguistic competence
• AI human intelligence in machines?
• (But birds flie, other than Tweety, ? planes)
• Computer science software, high-level process
  specifications, various implementations

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Questions and Answers

• Communication basic cognitive ability, in
  addition to reasoning dynamic, social
• Minimal episode
• Q Is this the road to the Colosseum?
• A Yes
• What information is conveyed
• facts, but also epistemic overtones
• information about others information
• Important in action plundering your account.
• Attunement to levels of knowledge in action
  general knowledge, common knowledge,...

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The Cards

• Three cards red, white, blue for players 1, 2, 3.
• Each sees his own card, not that of the others.
• Actual distribution 1red, 2white, 3blue.
• Player 2 asks 1 Do you have the blue card?"
• Truthful answer "No.
• Who knows what about the cards?
• Which information in questions and answers?
• Need information states and updates.

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The Correct Solution

• Player 2 knows how the cards lie.
• Player 3 knows that 2 has found out.
• Player 1 only knows that 2 or 3 knows.
• How to compute? Initial state
• rwb 1 rbw
• 2 3 2
• bwr 3
  wbr
• 1 3 1
• brw 2 wrb

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The Update

• 1's answer eliminates all points starting with
  'b'
• rwb 1 rbw
• 2
• 3 wbr
• 1
• wrb
• All knowledge facts can now be read off.
• Common knowledge reached at just rwb

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Other Scenarios

• Informative question 2 does not know
• Other presuppositions real question?
• First update to
• rwb
• 2
• bwr 3 1
• brw 2 wrb
• Answer to rwb
• 3
• Read off knowledge wrb

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Logical Systems

• Ka f a knows that f
• Kaf, ltagtf a thinks f possible
• Kaf Ú Kaf a knows if f
• Ka Kb f a knows that b doesnt know f
• Question answer before
• KQf KQf, ltQgt(KAf Ú KAf)
• after e.g. KQKAf,
• and even common knowledge
• CQ, A f

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Epistemic Logic

• Valid principles, true in all information models
• Kaf f Truth
• Ka(f y) (Kaf Kay) Distribution
• Kaf KaKaf Positive Introspection
• Kaf KaKaf Negative Introspection
• CG f f EG CG f Equilibrium
• (f CG (f EG f)) CG f Induction
• Used in modern multi-agent systems.
• Much-discussed plausible for humans?

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Public Update Mechanism

• Public announcement of A
• eliminate all worlds where A is not true
• from to
• s s
• A A
• A 1
• 2

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Muddy Children

• Three children are playing outside,and two got
  mud on their foreheads. They see each other, not
  themselves. Everyone knows there is at least one
  muddy child. Now their Father comes along, and
  says At least one of you is dirty.
• Now he asks Who knows if he is dirty?
• Children answer truthfully. Father keeps asking.
• What will happen?
• History of such puzzles...

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Updates for Puzzles

• 1 VVV 3
• SVV 2 VVS
• 3 VSV 1
• 2 1 3 2
• SVS
• SSV 2 VSS
• 3 SSS 1
• Updates remove parts of the diagram.
• Stabilisation common knowledge.

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Updates for Puzzles

• 1 VVV 3
• SVV 2 VVS
• 3 VSV 1
• 2 1 3 2
• SVS
• SSV 2 VSS
• 3 SSS 1
• New feature program structure, iteration!

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Update with Privacy

• Read my own card but not show what it is...
• from to
• f you f you
• me
• Update with actions new states are pairs
• (s, read Lecture), (t, read Nightclub)
• Precondition action must succeed in s.
• Can make models more complex!
• I tell you something, but dont know if you heard
• I show you my card, but do not read it myself.

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Secrecy and Security

• Other extreme as much secrecy as possible.
• Security in communication or transactions.
• Misleading, lying, cheating. Increase complexity.
• Other forms of update beliefs, expectations,...
• New practices Games analysis moves Cluedo
• (Reaction of the firm...)
• Email as a new laboratory for communication
  effects of plain addreds, cc, bcc...

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Logic of Programs, 1

• Conversation is program changing information
  states of others. Analogy computer science
• A! f after public update with A, f will
• hold in the new information model
• Logic connects pre and postconditions
• A!Kaf Ka(A A!f)
• Techniques of program analysis now apply.
• Formula A!Kaf brings together philosophy,
  linguistics, mathematics, computer science, ...

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Logic of Programs, 2

• Note that A! can also be a complex program
• with constructions , IF THEN, WHILE
• Complexity again base logic decidable, with
• iteration undecidable. Bad news good news.
• Conversation realizes all Turing computation!
• Program analysis versus synthesis
• what to say, design new procedures.
• Moscow Puzzle how inform each other publicly
  about the cards, without letting the others in?

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Social Software

• Analysis of existing social procedures with
  programming methods conversation, auctions,
  email, voting procedures (selecting the Doge).
• Also design of new ones. Emerge all the time!
• Sint Nicolaas. We want to draw lots for
  surprise gifts so
• that (a) no one knows anything about who has
  whom,
• (b) no one draws himself. Public procedure, no
  probability.
• Programming task for Turing machine,
• but now with knowledge requirements.
• More examples (Parikh) fair division, subsidies.

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Games

• Games add further temporal dimension
• strategic longer-term behaviour.
• In linguistics meaning of question-answer
• also driven by purpose, and game context.
• Game theory signalling, beliefs, probability,
• social software mechanism design.
• Current meeting logic and game theory add
  fine-structure of knowledge and updates to
  standard mathematics of Nash Equilibrium.
• Computer science systematic process analysis.

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The Latest in Design

• http//www.mysteryoftheabbey.com/
• 24 different cards represent 24 monks. One card
  is laid face down, for the killer. The rest
  distributed over the players, with left overs in
  a special pile. Purpose figure out who the
  killer is. Possible moves
• 1. ask another player a question about his
• observations (all answer truthfully)
• 2. pick a random card from another player
• 3. pick up one of the left over cards
• After every 4 rounds, players must give n of
  his cards to the player to his left. n
  increases by one on every round.

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Cognitive Issues

• Status of the information diagrams,
• knowledge axioms, and algorithms.
• High-level specification or reality?
• Are we really so good in communication?
• Coping with complexity Cluedo score cards.
• Complexity reduction, why (?) reliable?
• Which games click and are playeable?
• Can we design natural cognitive practices?
• What does this resonance tell us?

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Conclusion

• Turing revisited philosophy of this talk
• Not fruitful grand over-all Claims about
• (non-)identity computation and cognition.
• Contact 1 Exchange of ideas, models
• Contact 2 Interplay high-level algorithms,
• cognitive implementation, approximation
• Contact 3 Fact mixtures of cognition and
  computation, explain why these work...