THE SOCIAL SIDE OF COGNITIONTHE SOCIAL SIDE OF COGNITION

Johan van Benthem http://staff.science.uva.nl/~johan/

Stanford University & University of Amsterdam

Psychology Colloquium Amsterdam, 6 February 2006

History of LogicHistory of Logic Antiquity, reasoning

Frege, proofAnti-psychologism(vs. Wundt, Heymans)Language and meaning

Leibniz, Turing, computationBarwise, information (CSLI)

Dynamic Turn, actions (Gardenfors)Knowledge and many agents (Hintikka)Action + Knowledge --> Interaction

From Single Agents to GroupsFrom Single Agents to Groups

The usual cognitive skills: perception, memory, reasoning, learning, work for single agents.

But much of cognition involves many agents:communication, argumentation, interaction.

Irreducible complexity: 'many-mind problems' just as challenging as 'many-body problems'

Move in: linguistics, logic, computer science:many-agent settings are the normal situation!From Turing machines to networks of agents.

Logic: Proof or Conversation?Logic: Proof or Conversation?

Euclid’s Elements Plato’s Dialogues

Mathematical terminology from dialectics, the practice of ordinary argumentation?

Meaning and InterpretationMeaning and Interpretation

0 agents: classical logical truth conditions1 agent: dynamic semantics: meaning is information change potential for Hearer.2 agents: optimality theory: meaning requires game equilibrium between Speaker and Hearer

M EM - E, m - e

m e

Interactive reasoning required for getting this.Production - comprehension asymmetries (Petra Hendriks et al.)

Questions and AnswersQuestions and AnswersCommunication basic cognitive ability in addition to reasoning

Minimal episode:

Q “Is this the road to Criterion?”A “Yes.”

Information conveyed:

facts, but also epistemic overtones: information about others’ information

Q conveys that he does not know if , and that he thinks that A may know. A achieves that both know that , and they know it about each other, etc. End result: common knowledge in the group.

Basics of InteractionBasics of Interaction Communication is dynamic and social.

Speech acts and observations are crucial.

Iterated knowledge about others essential to real action: 'when can I plunder your bank account?’

Attunement to levels of knowledge in action: general knowledge, common knowledge, ...

Irreducible new forms of group knowledge – and even more, once we consider 'channels'.

Natural language: group knowledge, group action.

Logics of KnowledgeLogics of Knowledge

Need logic of knowledge:

Philosophy, Jaakko Hintikka

Logics of knowledge/belief

Ki i knows that

Complete axiom systems known since 1960s:

Ki & Ki ( ) Ki Omniscience(¬)Ki Ki(¬)Ki Introspection

Questions and Epistemic LogicQuestions and Epistemic Logic

Q asks "P?", A answered truthfully "Yes".

Truthful answer: A must know that P: KAP

Normal cooperative question presupposes • Q does not know if P: ¬KQP ¬KQ¬P

• Q thinks it possible that A knows if P:

<Q>(KAP KA¬P) After answer, P is common knowledge: C(Q, A}P

Information ChangeInformation Change • Information states: space of possible situations plus

uncertainties of the relevant agents:

PQ ¬P

• Information change/update:

PQ ¬P P

• Conversation: sequences of such steps.• Much more complex examples in games.

Update as ComputationUpdate as Computation

Leibniz logical reasoning as binary arithmetic, resolving disputes by “Calculemus”

Turing universal computing device can be defined mathematically

Computer science: models information flow, move toward interactive systems, ‘new reality’.

Programs and Dynamic LogicsPrograms and Dynamic LogicsComplete calculi of dynamic logic:

<1;2> <1><2><12> <1> <2><?> & <*> <><*>

ACM Turing Award winners:

Edsger Tony

Dijkstra Hoare

Logics of Knowledge plus ActionLogics of Knowledge plus ActionNow merge EL with CS logics of action![A!]after a truthful public announcement

of proposition A, holds

Typical uses: [A!]Ki[A!]CG philosophy + logic + computer science + linguistics

Complete logics discovered in the 1990s: [A!]p A p for atomic p

[A!]¬¬[A!] [A!]&[A!]&[A!] [A!]Ki A KiA!]

[A!]CG CG(A & [A!], [A!]

General Update MechanismsGeneral Update Mechanisms

• Communicative many-agent action in general: new phenomena beyond classical logic.

Incoming observations can make informationstates smaller by eliminating possibilities, orincrease the number of possibilities – whilekeeping track of what others know or don’t.

• Email: cc versus bcc.

• Example: parlour games like “Clue": info-spaces grow midway, decrease in end-game.

• Also, hiding and cheating are costly. Complexity thresholds from one practice to another

Games and LogicGames and Logic

But: the science of interaction par excellence:Game Theory? Natural marriage with logic.

Argumentation games: Middle Ages, Lorenzen, Abramsky (distributed processes)

Knowledge games: “be the first to know”

Also: logical analysis of player’s knowledge in games:‘rationality, Nobel prizes Nash, and this year: Auman.

ILLC Amsterdam, new Marie Curie project 2006: Centre for Logic, Games & Computation

Game Theory and Update LogicGame Theory and Update Logic

• Update evolution: when finite stabilization? Not finite in general, decidable from game definition?

• Finding equilibria: optimal strategy profiles• Detecting agent types: how complex?

Social Stance 1: Learning and TeachingSocial Stance 1: Learning and Teaching

Learning Theory models individual agents. But the typical setting is interactive, between two agents: Teacher and Student. Make them Learn!

S o S o

o * o *

Different theoretical and practical perspective: not merely information transport of textbook content, but strategic classroom equilibrium.Understand learning systems, not just single students.

Social Stance 2: Belief RevisionSocial Stance 2: Belief Revision

Simple belief update does not do it!

p ¬p

Announcing p leads to belief in everything:

p

So, must we follow AGM logic-free approach?

ESSLLI Workshop 2005, Edinburgh (Herzig & vD).Many solutions. E.g., product update can compute new plausibility values for worlds (Spohn, Aucher).

Diversity of agents again: different policies.

Multi-Agent Belief RevisionMulti-Agent Belief Revision

Standard belief revision theory is still autistic! We change our beliefs because of conflicting

agents/sources: if only ‘Me’ versus ‘Nature’.

Strategies for revising beliefs: wide repertoire:fight it out (game), priority (social ranking),

various probabilistic merges via reliability.

Issues not settled by our dynamic-epistemic logics: merging group beliefs, resolving conflicts among sources.

Should the basic Intuitions/Postulates be ‘interactive’?

Social Stance 3: Group StructureSocial Stance 3: Group StructureEmergent forms of group knowledge? common knowledge, implicit distributed knowledge, & other forms: e.g., limits of maximal communication in a network.

Even collective forms of belief revision: theories, research programs philosophy of science?

Bratman, Gardenfors: connections with group intention, and possibly collective action?

Still reductionism? Are there irreducible group-level phenomena beyond individual interaction?

But What about Reality?But What about Reality?

Logic, language, computation: natural triangle – the original ’ILLC formula'. Major isssues: meaning, inference, computation, complexity.

Little interaction with experimental cognitive science!

‘Anti-Psychologism’:

Encounters with Reality?Encounters with Reality?Experimental issues suggested by the above:

• What do people get out of various types of assertion?• Interactive strategies in conversation or learning? • How do they revise or merge beliefs and how do they resolve conflicts of opinion?• How do they cope with diversity of agents?

ILLC/CREED: Do computational 'complexity barriers' occur in human experience of 'difficulty'? Clue variants: add motive, one or more cheats

Creed, and/or: Greed

Evidence all around us: Sudoku, GSM puzzles, games

The TriangleThe Triangle

• Logic (theory, ideal model building)• Computer science (computational design)• Pyschology (the experimental facts)

Creative combination of stances:

natural practice, virtual reality into new mixed practices (e.g., Bennet’s new book)

From analysis (Venetian Elections) to design of behaviour (Social Software):

Games, Internet etc. are a free Cognitive Lab! NIAS Project “Social Software”: Verbrugge, van Eijck

Logic and Cognitive Pyschology, 1Logic and Cognitive Pyschology, 1Forthcoming issue of Journal Topoi, edited by: J. van Benthem, Helen Hodges & Wilfrid Hodges.

• Cristiano Castelfranchi & Emiliano Lorini, Deep Surprise, Incredulity, and Cascade Belief Revision• Robin Clark & Murray Grossman, Number Sense and Quantifier Interpretation• H. Wind Cowles, Matthew Walenski, and Robert KluenderLinguistic and Cognitive Prominence in Anaphor Resolution• Artur d'Avila Garcez, Dov Gabbay and John Woods,Abductive Reasoning in Neural-Symbolic Systems• Markus Knauff, The Logical Brain in Action• Hannes Leitgeb 'Belief Revision, Conditionals, and Cognition• Guy Politzer Reasoning with Conditionals•Robert van Rooij and Anton Benz Optimal Interpretation and Multi-Attribute Utilities• Keith Stenning and Michiel van Lambalgen Logic and Mental Illness

Logic and Cognitive Pyschology, 2Logic and Cognitive Pyschology, 2

Logic Made EasyHow to Know When Language Deceives Youby Deborah J. Bennett