Logic and Cognition Workshop, ICLA 2019, March 2, 2019 Logic and cognition: Sujata Ghosh Towards an interdependent ISI Chennai sujata@isichennai.res.in methodology
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 other 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 order theory of mind Courtesy: Rineke Verbrugge
Orders of theory of mind p: Captain Bluntschli is the chocolate cream soldier ❖ 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”
Let’s start with the toddlers ! Courtesy: Nicole Baars Toddlers do have trouble thinking about other people’s beliefs
Theory of mind in children Where would Milana think that Karna will look for the chocolate ? Courtesy: Avik Kumar Maitra ❖ 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) H. Wimmer and J. Perner, Beliefs about beliefs, Cognition 13 (1), 1983, 103 - 128
Theory of mind in teenagers Courtesy: Rineke Verbrugge Mother Connie, her 16 year old son Jeremy and his friend Pierce (Zits: Jerry Scott and Jimmy Borgman, April 16, 2016) ToM develops in the stage of adolescence as well
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: After the third question, If you know which number you have please step forward. Alice steps forward. Third question: If you know which number you have please step 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” Courtesy: Rineke Verbrugge B. Kooi, H. van Ditmarsch en W. van der Hoek, Dynamic Epistemic Logic . Springer, Berlijn, 2007. !
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
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