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THE SOCIAL SIDE OF COGNITION

THE SOCIAL SIDE OF COGNITION. Psychology Colloquium Amsterdam, 6 February 2006. Johan van Benthem http://staff.science.uva.nl/~johan/ Stanford University & University of Amsterdam. History of Logic. Antiquity, reasoning Frege , proof Anti-psychologism (vs. Wundt, Heymans)

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THE SOCIAL SIDE OF COGNITION

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  1. THE SOCIAL SIDE OF COGNITION Psychology Colloquium Amsterdam, 6 February 2006 Johan van Benthemhttp://staff.science.uva.nl/~johan/ Stanford University & University of Amsterdam

  2. History of Logic Antiquity, reasoning Frege, proof Anti-psychologism (vs. Wundt, Heymans) Language and meaning Leibniz, Turing, computation Barwise, information (CSLI) Dynamic Turn, actions (Gardenfors) Knowledge and many agents (Hintikka) Action + Knowledge --> Interaction

  3. From 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.

  4. Logic: Proof or Conversation? Euclid’s ElementsPlato’s Dialogues Mathematical terminology from dialectics, the practice of ordinary argumentation?

  5. Meaning and Interpretation 0 agents: classical logical truth conditions 1 agent: dynamic semantics: meaning is information change potential for Hearer. 2 agents: optimality theory: meaning requires game equilibrium between Speaker and Hearer M E M - E, m - e m e Interactive reasoning required for getting this. Production - comprehension asymmetries (Petra Hendriks et al.)

  6. Questions and Answers Communication 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 f, and that he thinks that A may know. A achieves that both know that f, and they know it about each other, etc. End result: commonknowledge in the group.

  7. Basics of Interaction Communication is dynamicandsocial. 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.

  8. Logics of Knowledge Need logic of knowledge: Philosophy, Jaakko Hintikka Logics of knowledge/belief Ki i knows that f Complete axiom systems known since 1960s: Ki & Ki ()  KiOmniscience (¬)Ki Ki(¬)KiIntrospection

  9. Questions and Epistemic Logic Q asks "P?",Aanswered 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

  10. Information Change • Information states: space of possible situations plus uncertainties of the relevant agents: PQ ¬P • Information change/update: PQ ¬P Þ P • Conversation: sequences of such steps. • Much more complex examples in games.

  11. Update 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’.

  12. Programs and Dynamic Logics Complete calculi of dynamic logic: <p1;p2>f«<p1><p2>f <p1È p2>f«<p1>fÚ<p2>f <f?>y«f&y <p*>f«fÚ<p><p*>f ACM Turing Award winners: Edsger Tony Dijkstra Hoare

  13. Logics of Knowledge plus Action Now merge EL with CS logics of action! [A!]fafter a truthful public announcement of proposition A, f holds Typical uses: [A!]Kif , [A!]CGf philosophy + logic + computer science + linguistics Complete logics discovered in the 1990s: [A!]p « A  p for atomic p [A!]¬f « A ¬[A!]f [A!]f&y « [A!]f &[A!]y [A!]Kif « A  Ki[A!]f [A!]CG (f, y) « CG(A & [A!]f), [A!]y)

  14. General Update Mechanisms • Communicative many-agent action in general: new phenomena beyond classical logic. Incoming observations can make information states smaller by eliminating possibilities, or increase the number of possibilities – while keeping 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. Complexitythresholdsfrom one practice to another

  15. Games 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

  16. Game 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?

  17. Social 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.

  18. Social 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.

  19. Multi-Agent Belief Revision Standard belief revision theory is still autistic! We change our beliefs because of conflictingagents/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, resolvingconflicts among sources. Should the basic Intuitions/Postulates be ‘interactive’?

  20. Social Stance 3: Group Structure Emergent 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?

  21. 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’:

  22. 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

  23. The 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

  24. Logic and Cognitive Pyschology, 1 • Forthcoming 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 Kluender • Linguistic 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

  25. Logic and Cognitive Pyschology, 2 Logic Made Easy How to Know When Language Deceives You by Deborah J. Bennett

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