Logic and cognition: Sujata Ghosh Towards an interdependent ISI - - PowerPoint PPT Presentation

Logic and Cognition Workshop, ICLA 2019, March 2, 2019

Logic and cognition: Towards an interdependent methodology

Sujata Ghosh ISI Chennai sujata@isichennai.res.in

What is logic ?

What is logic ?

‘Contrariwise,’ continued Tweedledee, ‘if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.’

• Lewis Caroll, Through the looking-glass, and what Alice found there, 1871

From encyclopaedia britannica ……

❖

Logic the study of correct reasoning, especially as it involves the drawing of inferences

From encyclopaedia britannica ……

❖ Logic

the study of correct reasoning, especially as it involves the drawing of inferences

❖ Psychology

scientific discipline that studies mental states and processes and behaviour in humans and

• ther animals

❖ Cognition

the states and processes involved in knowing which in their completeness include perception and judgement

An overview of the talk

❖

Part I: A brief look at the history of logic and psychology, moving on to logic and cognition

❖

Part II: Studies in social cognition with a focus on higher-order theory of mind

❖

Part III: A meeting of methods: Logics, experiments and computational cognitive models

A brief look at the history of logic and psychology, moving on to logic and cognition (19th century onwards ….)

Mid to late 19th century

❖

Beneke [1842]: The evaluation of human mind can be influenced only in accord with the law of the mind; and while the ascertainments of these laws belong to psychology, in psychology has to be seen the basic science, not only for all other sciences, but for logic too.

❖

Boole [1845]: […] to investigate the fundamental laws of those operations of the mind by which reasoning is performed […], to collect […] some probable intimations concerning the nature and constitution of the human mind.

❖

de Morgan [1847]: the branch of inquiry (be it called science or art), in which the act of the mind in reasoning is considered, particularly with reference to the connection of thought and language.

❖

Mill [1858]: the science of the operations of the understanding which are subservient to the estimation of evidence: both the process itself of advancing from known truths to unknown, and all other intellectual operations in so far as auxiliary to this.

❖

Erdmann [1892]: The judgements, conclusions […] are the processes of consciousness which stand in lawful connection […] to other processes of the imagination and of the sensation and the will. […] Logic remains with the question, how they should be in order to become universally valid propositions about the imagined.

Logic and Psychology went hand in hand

Late 19th to early 20th century

❖

Frege: Neither logic nor mathematics has the task of investigating minds and the contents of consciousness whose bearer is an individual person. The logicians […] are too much caught up in psychology […] Logic is in no way a part of

• psychology. Thoughts are not psychic structures, and thinking is not an inner producing

and forming, but an apprehension of thoughts which are already objectively given.

❖ Husserl:

To refer to a number as a mental construct is thus an absurdity, an offence against the perfectly clear meaning of arithmetic discourse, which can be be at anytime be perceived as valid […] If concepts are mental constructs, then such things as our numbers are not

• concepts. But if they are concepts, then concepts are not mental constructs.

Logic and Psychology got divorced

Sympathetic attitudes in late 20th century

❖

Haack [1978] Strong psychologism: logic is descriptive of how humans in fact think; Weak psychologism: logic is prescriptive of how we should think; Antipsychologism: logic has nothing to do with mental processes at all

❖

Macnamara [1986] The psychological study of logic is largely neutral in ontological matters and seeks merely to study how logical intuition is grounded in properties of mind

• M. Kusch, Psychologism, Routledge, New York, 1995
• W. Stelzner, Psychologism, universality and the use of logic, In: J. Faye et al. (eds.),

Nature’s Principles, Springer, The Netherlands, 2005, 269 - 288 F.J. Pelletier, R. Elio and P. Hanson, Is logic in all our heads?From naturalism to psychologism, Studia Logica 86, 2008, 1-65

21st century: The practical turn in logic

21st century: The practical turn in logic

❖

Michiel van Lambalgen and Keith Stenning (2008) Human Reasoning and Cognitive Science

❖

Johan van Benthem (2008) Logic and reasoning: Do the facts matter?

❖

Rineke Verbrugge (2009) Logic and social cognition: The facts matter, and so do computational models

❖ Rohit Parikh (2011)

Is there a logic of society?

Studies in social cognition with a focus on higher-order theory of mind

What is theory of mind ?

“As humans we assume that others want , think, believe and the like, and thereby infer states that are not directly observable, using these states anticipatorily predict the behaviour of others as well as our own. These inferences, which amount to a theory of mind, are to our knowledge universal in human adults.”

• D. Premack & G. Woodruff (1978)
• D. Premack and G. Woodruff, Does the chimpanzee have a theory of mind?, BBS 1 (4), 1978, 515 - 526

What is theory of mind ?

❖ The ability to reason about mental

states of others

❖ This may concern their beliefs,

thoughts, knowledge, intentions

❖ People use it to explain, predict and

manipulate behaviours of others

❖ People apply it recursively: Higher

• rder theory of mind

Courtesy: Rineke Verbrugge

Orders of theory of mind

❖ 1st order attribution:

“Sergius knows that p”

❖ 2nd order attribution:

“Raina does not know that Sergius knows that p”

❖ 3rd order attribution:

“Sergius knows that Raina does not know that Sergius knows that p”

p: Captain Bluntschli is the chocolate cream soldier

Let’s start with the toddlers !

Toddlers do have trouble thinking about other people’s beliefs

Courtesy: Nicole Baars

Theory of mind in children

Where would Milana think that Karna will look for the chocolate ?

❖ 3 year old children: The TV stand (zero-order: the actual location of the chocolate) ❖ 4-5 year old children: The toy box (first-order: Karna’s belief about the location) ❖ 6-7 year old children: The drawer (second-order: Milana’s false belief about

Karna’s belief)

Courtesy: Avik Kumar Maitra

• H. Wimmer and J. Perner, Beliefs about beliefs, Cognition 13 (1), 1983, 103 - 128

Theory of mind in teenagers

ToM develops in the stage of adolescence as well

Mother Connie, her 16 year old son Jeremy and his friend Pierce (Zits: Jerry Scott and Jimmy Borgman, April 16, 2016)

Courtesy: Rineke Verbrugge

Theory of mind in adults

Even the adults find it difficult to apply second-order theory of mind

The Camp David Accords, 1978

Second order ToM is good for creating win-win solutions in mixed-motive situations like negotiation

Enters logic: Idealized ToM agents

! "

Consecutive number puzzle

First question: If you know which number you have please step forward. Second question: If you know which number you have please step forward. Third question: If you know which number you have please step forward. After the third question, Alice steps forward.

First question

After the first question, nobody stepped forward.

Second question

After the second question, nobody stepped forward.

“ ” “ ” “ ” “ ”

Third question: Alice steps forward “I have 3”

• B. Kooi, H. van Ditmarsch en W. van der Hoek, Dynamic Epistemic Logic. Springer, Berlijn, 2007.!

Courtesy: Rineke Verbrugge

Dynamic epistemic logic

• B. Kooi, H. van Ditmarsch en W. van der Hoek, Dynamic Epistemic Logic. Springer, Berlijn, 2007.!
• W. van der Hoek and R. Verbrugge, Epistemic Logic: A Survey, In: V. Mazalov and L. Petrosjan (eds.), Game Theory and

Applications, Volume 8, Nova Science Publishers, New York, 2002, 53-94

• H. van Ditmarsch, W. van der Hoek and B. Kooi, Dynamic Epistemic Logic, Springer, Berlin, 2007
• H. van Ditmarsch, J. Halpern, W. van der Hoek and B. Kooi (eds.), Handbook of Epistemic Logic,

College Publications, London, 2015

Experiments on adults with regard to higher-order theory of mind

Can training help to improve second-order reasoning ?

" " " "

Marble Drop Game

❖ A turn-taking game between the participant (orange) and a computer (blue). ❖ A white marble drops down. Players control the course of the marble by opening the left or right

trap door of their colour.

❖ The participant wants the marble to drop into a bin in which the left marble is as dark orange as

possible.

❖ The computer wants the marble to drop into a bin in which the left marble is as dark blue as

possible.

• B. Meijering, L. van Maanen, H. van Rijn and R. Verbrugge, The facilitative effect of context on second order social reasoning,

In: R. Catrambone and S. Ohlsson (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society, 2010, 1423-1428

Zero-order marble drop game

Courtesy: Ben Meijering

First-order marble drop game

Courtesy: Ben Meijering

Second-order marble drop game

Courtesy: Ben Meijering

Findings of the experiment

Effect of step-wise training on correct decisions on marble drop games: The proportion of correct decisions increased a lot by step-wise training

• from 65% to 94% !

Other such training experiments on marble drop games continued ……

• R. Verbrugge, B. Meijering, S. Wierda, H. van Rijn and N.A. Taatgen, Step-wise training supports strategic second-order theory of

mind in turn-taking games, Judgement and Decision Making 13 (1), 2018, 79-98

Facts do matter, so does computational models

human behaviour experiments model behaviour cognitive models Using a computational cognitive model allows to make specific predictions about accuracy, reaction times, points of attention, active brain regions.

Computational cognitive models

ACT-R

❖ memory for text or list of words ❖ multi-tasking ❖ high school algebra ❖ air traffic control ❖ children’s learning of irregular verbs ❖ children’s pronoun interpretation

• ACT-R is a cognitive architecture: A theory

about how human cognition works ACT-R has been used for many different tasks:

J.R. Anderson, How can the human mind occur in the physical universe?, Oxford University Press, 2007

How does ACT-R work ?

How does ACT-R work?!

Perception! Action! Cognition!

How does ACT-R work ?

How does ACT-R work?!

Perception! Action! Cognition!

Factual knowledge represented in chunks

How does ACT-R work ?

How does ACT-R work?!

Perception! Action! Cognition!

Procedural Knowledge

Production rules

Symbolic representation of procedural knowledge

(p Name list of buffer tests ====> list of buffer changes )

IF Goal buffer is empty If the model does not yet have a goal, Problem State buffer is empty and does not yet have a representation of game state, Visual buffer is empty and has not yet attended any payoffs, THEN Goal is to compare Player 1’s then set the goal to compare Player 1’s payoffs at locations δ and γ payoffs at δ and γ .

ACT-R model for Marble Drop

!"#$%&%'()" *(+,%$

• .%/(0%$

1%0,%$ 2&3#"4,&%$

5'%&' #3.6%&(+30

ACT-R model for Marble Drop

!"#$%&%'()" *(+,%$

• .%/(0%$

1%0,%$ 2&3#"4,&%$

5"'&(")"6$3#%'(306 (073&.%'(30 8''"046 9%:377 ;'3&"6#,&&"0'6 #3.9%&(+30 ;'%&' #3.9%&(+30

ACT-R model for Marble Drop

!"#$%&%'()" *(+,%$

• .%/(0%$

1%0,%$ 2&3#"4,&%$

5"'&(")"6$3#%'(306 (073&.%'(30 8''"046 9%:377 ;'3&"6#,&&"0'6 #3.9%&(+30 5"'&(")"6)%$,"6376 9%:377 ;'%&' #3.9%&(+30

ACT-R model for Marble Drop

!"#$%&%'()" *(+,%$

• .%/(0%$

1%0,%$ 2&3#"4,&%$

5"'&(")"6$3#%'(306 (073&.%'(30 8''"046 9%:377 ;'3&"6#,&&"0'6 #3.9%&(+30 5"'&(")"6)%$,"6376 9%:377 5"'&(")"6$3#%'(306 (073&.%'(30 ;'3&"69%:3776)%$," ;'%&' #3.9%&(+30

ACT-R model for Marble Drop

!"#$%&%'()" *(+,%$

• .%/(0%$

1%0,%$ 2&3#"4,&%$

5''"046 7%8399 :"'&(")"6)%$,"6396 7%8399 :"'&(")"6$3#%'(306 (093&.%'(30 5''"046 7%8399 ;'3&"6#,&&"0'6 #3.7%&(+30 :"'&(")"6)%$,"6396 7%8399 :"'&(")"6$3#%'(306 (093&.%'(30 ;'3&"67%83996)%$," ;'%&' #3.7%&(+30 <3.7%&"6 )%$,"+

ACT-R model for Marble Drop

Declarative Visual Imaginal Manual Procedural

Attend payoff Retrieve value of payoff Retrieve new comparison Press button Retrieve location information Attend payoff Store current comparison Retrieve value of payoff Retrieve location information Store payoff value Start comparison Compare values

ACT-R model for Marble Drop

Declarative Visual Imaginal Manual Procedural

Attend payoff Retrieve value of payoff Retrieve new comparison Press button Retrieve location information Attend payoff Store current comparison Retrieve value of payoff Retrieve location information Store payoff value Start comparison Compare values

• L. van Maanen and R. Verbrugge, A computational model of second-order social

reasoning, In: D. Salvucci and G. Gunzelmann (eds.), Proceedings of the 10th International Conference of Cognitive Modeling, 2010, 259-264

Can we do away with these ad hoc model building ?

human behaviour experiments model behaviour cognitive models formal modelling

A meeting of methodologies: Reasoning in adults while playing turn-taking games

Experiments

• S. Ghosh, A. Heifetz and R. Verbrugge, Do players reason by forward induction in dynamic perfect information games?,

In: R. Ramanujam (ed.), Proceedings of the 15th Conference of Theoretical Aspects of rationality and Knowledge (TARK 2015), EPTCS 215, 2016, 159-175

• S. Ghosh, A. Heifetz, R. Verbrugge and H. de Weerd, What drives people’s choices in turn-taking games, if not game-theoretic

rationality?, In: J. Lang (ed.), Proceedings of the 16th Conference of Theoretical Aspects of rationality and Knowledge (TARK 2017), EPTCS 251, 2017, 265-284

Research questions

❖

Are people inclined to use forward induction reasoning when they play certain turn-taking games ?

❖

If not, what are they actually doing ? What roles are played by risk attitudes and cooperativeness versus competitiveness ?

❖

Do people take the perspective of the opponents and make use of theory of mind ?

❖

Can they reasonably be divided into types of players ?

Marble drop game

The computer decides here. The computer decides here. You decide here. You decide here.

The games

C C P P

a b c d e f g h

(4,1) (1,2) (3,1) (1,4) (6,3)

Game 1

C C P P

a b c d e f g h

(2,1) (1,2) (3,1) (1,4) (6,3)

Game 2 C C P P

a b c d e f g h

(4,1) (1,2) (3,1) (1,4) (6,4)

Game 3

C C P P

a b c d e f g h

(2,1) (1,2) (3,1) (1,4) (6,4)

Game 4

The games

C P P

c d e f g h (1,2) (3,1) (1,4) (6,4)

Game 3’ C P P

c d e f g h (1,2) (3,1) (1,4) (6,3)

Game 1’

Experimental details

❖ computer vs. human ❖ 50 participants (Bachelor and Masters students) ❖ instruction sheet ❖ 14 practice games; 8 rounds of 6 experiment games ❖ deviation from BI strategy; response examined ❖ two groups A and B ❖ some question rounds ❖ questions at the end of the experiment on behaviour at each node of a game

Findings of the experiment

❖

a very low extent of game-theoretic strategic reasoning - be it BI or EFR (FI)

❖

the higher pay-off of 6 for the computer at the end of each game might have motivated the participants to think that the computer would take more risk

Final question

Final answer analysis

Behavior Risk-taking (self) Risk-taking (opponent) Risk-averse (self) Risk-averse (opponent) Participants (Group A)

A0, A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A14, A15, A18, A19, A20, A21, A22, A23, A24 A1, A2, A3, A4, A5, A6, A7, A8, A9, A11, A12, A14, A15, A17, A18, A19, A20, A21, A22, A23, A24 A10, A13, A16, A17 A0, A4, A8, A9, A10, A13, A16, A17, A22

Participants (Group B)

B0, B1, B2, B3, B7, B9, B10, B12, B13, B15, B16, B18, B19, B20, B21, B22, B23, B24 B0, B2, B3, B7, B9, B10, B11, B12, B13, B15, B16, B18, B19, B20, B21, B22, B23, B24 B4, B5, B6, B8, B11, B17 B0, B1, B4, B5, B6, B8, B10, B11, B12, B14, B17, B18, B20, B21

Final answer analysis

Behavior Zeroth order theory

• f mind

First order theory

• f mind

Second order theory of mind Participants (Group A)

A0, A1, A3, A5, A8, A13, A15, A19, A20, A22 A2, A4, A7, A9, A10, A12, A14, A16, A17, A21, A23 A6, A11, A18, A24

Participants (Group B)

B3, B11, B14, B15, B16, B20 B0, B2, B4, B5, B6, B7, B8, B9, B10, B12, B13, B17, B18, B19, B21, B22, B24 B1, B23

Final answer analysis

Behavior Competitive Cooperative Neither Participants (Group A)

A0, A1, A2, A3, A10, A14, A15, A16, A19, A20, A21 A5, A7, A11, A17, A23, A24 A4, A6, A8, A9, A12, A13, A18, A22

Participants (Group B)

B3, B5, B14, B22 B0, B1, B2, B7, B8, B9, B11, B13, B16, B18, B19, B21, B23, B24 B4, B6, B10, B12, B15, B17, B20

Salient factors in people’s choices

❖

Game-theoretic motivations

❖

Risk-taking and risk-averse behaviour

❖

Theory of mind

❖

Competitiveness and cooperativeness

❖

Instinctive and contemplative behaviour

Logic

• S. Ghosh, B. Meijering and R. Verbrugge, Strategic reasoning: Building cognitive models from logical formulas,

Journal of Logic, Language and Information 23 (1), 2014, 1-29

• S. Ghosh and R. Verbrugge, Studying strategies and types of players: Experiments, logics and cognitive models,

Synthese 195 (10), 2018, 4265-4307

Syntactic representation of trees

1 a

}

b

!

x0 2 c1

⌃

d1

⇠

x1 2 c2

⌃

d2

⇠

x2 y1 y2 y3 y4

h = ((1, x0), a, t1) + ((1, x0), b, t2), where t1 = ((2, x1), c1, (2, y1)) + ((2, x1), d1, (2, y2)); t2 = ((2, x2), c2, (2, y3)) + ((2, x2), d2, (2, y4)).

b b b S Given h ∈ G(Nodes), let Nodes(h) denote the set of distinct pairs (i, x) that occur in the expression of h.

GpNodesq ::“ pi, xq | ΣamPJppi, xq, am, tamq

p q “ p q | pp q q where i P N, x P Nodes, Jpfiniteq Ñ Σ, and tam P GpNodesq. P Gp q

Syntax

BPFpXq ::“ x P X | ψ | ψ1 _ ψ2 | xa`yψ | xa´yψ,

where a P Σ, a countable set of actions.

For any countable set X, let X) be sets of formulas given formula Bpi,xq

z

ψ feel that it

p q For each z P GpNodesq and pi, xq P Nodespzq, a

Specifying behaviour (strategies)

Let Pi = {pi

0, pi 1, . . .} be a countable set of observables for i 2 N and P = S i2N Pi.

To this set of observables we add two kinds of propositional variables (u q ) to

S

i2N

ariables (ui = qi) that ‘the rational

and pr § qq syntax of strategy

î

iPN

denote “player i’s utility equal to the rational (or payoff) is qi”

2

î p i “

iq

that “the rational number r is less than or equal to the rational specifications is given by: number q”2

StratipPiq ::“ rψ fiÑ asi | η1 ` η2 | η1 ¨ η2, where ψ P BPFbpPiq.

to specify properties

• R. Ramanujam and S. Simon, A logical structure for strategies, In: G. Bonanno, W. van der Hoek and M. Woolridge (eds.), Logic and

the foundations of games and decision theory (LOFT 7), Text in Logic and Games, Volume 3, AUP, 2008, 183-208

Semantics

Let M “ pT, t› Ñx

i u, Vq

: frontier T N

Q

T “ pS, ñ, s0, p λ, Uq, utility function. For

p q ˆ elation › Ñx

i ⊆ S × S

Finally, V : S Ñ 2P

M, s | ù pui “ qiq iff Ups, iq “ qi. M, s | ù pr § qq iff r § q, where r,

| ù x y ñ | ù M, s | ù Bpi,xq

z

ψ iff the underlying game tree of TM is the same as Tz and for all s1 such that s › Ñx

i s1,

M, s1 | ù ψ.

Semantics

Let M “ pT, t› Ñx

i u, Vq

: frontier T N

Q

T “ pS, ñ, s0, p λ, Uq, utility function. For

p q ˆ elation › Ñx

i ⊆ S × S

Finally, V : S Ñ 2P

vrψ fiÑ asiwM “ Υ P 2ΩipTMq satisfying: µ P Υ iff µ satisfies the condition that, if s P Sµ is a player i node then M, s | ù ψ implies outµpsq “ a. vη1 ` η2wM “ vη1wM Y vη2wM vη1 ¨ η2wM “ vη1wM X vη2wM

Semantic function for strategies:

function v¨wM : StratipPiq Ñ 2ΩipTMq, strategy trees and ΩipTq denotes q Ñ and ΩipTq denotes the set of

all player i strategies in the game tree T.

i i

Example formulas

My5

P : rpxc`ypuP “ 2q ^ xd`yxe`ypuP “ 1q ^ p1 § 2q ^ rootq fiÑ csP

Op5

P : rpxc`ypuP “ 2q ^ xd`yxe`ypuP “ 1q ^ xd`yxf `yxg`ypuP “ 4q ^ xd`yxf `yxh`ypuP “ 3q^

p1 § 2q ^ p2 § 4q ^ p2 § 3q ^ p1 § 4q ^ p1 § 3q ^ p3 § 4q ^ rootq fiÑ csP

P C P (6,3) (1,2) (3,1) (1,4)

d f h c e g

Game 5

Computational cognitive models

• J. Top, R. Verbrugge and S. Ghosh, An automated method for building cognitive models for

turn-based games from a strategy logic, Games 9, 44, 2018

PRIMs

❖ manual module: perform actions ❖ visual module: perform eye movements,

retrieve and compare information from display

❖ working memory module: short term

storage of information

❖ declarative memory module: long term

storage and retrieval of information

❖ task control module: relevance of sequence

• f primitive elements

PRIMs is used to simulate and predict human behaviour in behavioural tasks PRIMs models can act as virtual participants.

N.A. Taatgen, The nature and transfer of cognitive skills, Psychological Review 120, 439, 2013

Translation: Formulas to model behaviour

xa`y and xa´y

root

turni

pui “ qiq

pr § qq

Sequence of the operators corresponds to the visual attention to the location Visual inspection of the specified node to determine the root A read of the player node and comparison with i Comparison of qi with a value in the visual input and storage in working memory Transfer of r and q from working memory to declarative memory

Translation: Formulas to model behaviour

Bpi,xq

z

and a

❖ Construction of beliefs about opponent strategies. ❖ Strategies are contained in the declarative memory. ❖ To verify a belief, a partial sequence of actions is sent to the declarative memory ❖ The attempt is to retrieve a full sequence of actions, which gives a strategy

Some issues

❖

Strategy formulas take the form of Horn clauses:

❖

Conjunctions in logic are unordered, but taken care of sequentially in PRIMs.

❖

Exhaustive strategy formulas are represented by a list of formulas

❖

Such a list is also unordered, but taken care of sequentially in PRIMs.

Verification experiments

My5

P : rpxc`ypuP “ 2q ^ xd`yxe`ypuP “ 1q ^ p1 § 2q ^ rootq fiÑ csP

Op5

P : rpxc`ypuP “ 2q ^ xd`yxe`ypuP “ 1q ^ xd`yxf `yxg`ypuP “ 4q ^ xd`yxf `yxh`ypuP “ 3q^

p1 § 2q ^ p2 § 4q ^ p2 § 3q ^ p1 § 4q ^ p1 § 3q ^ p3 § 4q ^ rootq fiÑ csP

P C P (6,3) (1,2) (3,1) (1,4)

d f h c e g

Game 5

Myopic, Game 5 Own-payoff, Game 5

Verification experiments

‚ Myopic, Game 5 My5

P : rpxc`ypuP “ 2q ^ xd`yxe`ypuP “ 1q ^ p1 § 2q ^ rootq fiÑ csP

‚ Own-payoff, Game 5 Op5

P : rpxc`ypuP “ 2q ^ xd`yxe`ypuP “ 1q ^ xd`yxf `yxg`ypuP “ 4q ^ xd`yxf `yxh`ypuP “ 3q^

p1 § 2q ^ p2 § 4q ^ p2 § 3q ^ p1 § 4q ^ p1 § 3q ^ p3 § 4q ^ rootq fiÑ csP

Exploratory experiments

C P C P (6,3) (4,1) (1,2) (3,1) (1,4)

b d f h a c e g

Game 1

‚ Zero-order theory-of-mind, Game 1 ToM-01

P : rpϕ ^ ψP ^ xb´yroot ÞÑ csP

ToM-01

P : rpϕ ^ ψP ^ xb´yroot ÞÑ dsP

‚ First-order theory-of-mind, Game 1 ToM-11

P : rpχ ^ Bpn2,Pq g1

xdyeq ÞÑ csP ToM-11

P : rpχ ^ Bpn2,Pq g1

xdyeq ÞÑ dsP ToM-11

P : rpχ ^ Bpn2,Pq g1

xdyfq ÞÑ csP ToM-11

P : rpχ ^ Bpn2,Pq g1

xdyfq ÞÑ dsP ‚ Second-order theory-of-mind, Game 1 ToM-21

P : rpχ ^ Bpn2,Pq g1

xdye ^ Bpn2,Pq

g1

xdyxfygq ÞÑ csP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdye ^ Bpn2,Pq

g1

xdyxfygq ÞÑ dsP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdyf ^ Bpn2,Pq

g1

xdyxfygq ÞÑ csP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdyf ^ Bpn2,Pq

g1

xdyxfygq ÞÑ dsP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdye ^ Bpn2,Pq

g1

xdyxfyhq ÞÑ csP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdye ^ Bpn2,Pq

g1

xdyxfyhq ÞÑ dsP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdyf ^ Bpn2,Pq

g1

xdyxfyhq ÞÑ csP ToM-21

P : rpχ ^ Bpn2,Pq g1

xdyf ^ Bpn2,Pq

g1

xdyxfyhq ÞÑ dsP

Exploratory experiments

Towards interdependence of methodologies

human behaviour experiments model behaviour cognitive models formal modelling

• S. Ghosh, Strategizing: A meeting of methods, In: B. Kim et al. (eds.)

Proceedings of the 14th and 15th Asian logic Conferences, World Scientific, 2019, 80-107

To conclude …..

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the computational level: identification of the goal and of the information processing task as an input-output function;

❖

the algorithmic and representation level: specification of an algorithm which computes the function;

❖

the implementation level: physical or neural implementation of the algorithm

Marr’s three levels of analysis of a task computed by a cognitive system Where do we stand ?

Second order ToM helps sometimes !

An adaptation of Shaw’s Arms and the man

Thanks to my collaborators !

Rineke Verbrugge Aviad Heifetz Tamoghna Halder Harmen de Weerd Jordi Top Khyati Sharma Ben Meijering