Self-Introduction 2016 Japanese academic year (April 2016 to March 2017) in Europe For 11 months I live in Paris and then the last month in London. Jean Baratgin at CHArt (EPHE, Paris 8) Cognitive psychology of probability judgment and reasoning Mike Oaksford at UL Birkbeck Cognitive psychology of reasoning and argumentation Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹ Visiting Scholar at University of London, Birkbeck Observational causal induction as independence test under rarity assumption 2017-01-18 Wed 7 / 73
❖ proportion of assumed-to-be rare instances [2]: ྆ऀͷ࿈ݴ(AND) ❖ ༧ଌ݅จʮC ͳΒEʯ ❖ அ݅จʮE ͳΒCʯ ҼՌਪͷ݅֬ ʢ݅จͷ֬ʣ !20 ɹɹɹ " [2] Takahashi, T., Kohno, Y., and Oyo, K.: in Proc. of ICCS2010, pp. 361–362 (2010) effect (E) No effect(¬E) पลස cause (C) N(C, E) N(C, ¬E) N(C) no cause (¬C) N(¬C, E) N(¬C, ¬E) N(¬C) पลස N(E) N(¬E) N(Ω) C E Causal Induction pARIs (proportion of assumed-to-be rare instan (Takahashi, Oyo, & Kohno, 2010; Takahashi et al., in prep.) Shares the rarity assumption with DFH. pARIs: the probability of "if C then E, and if E then C" (biconditional probability of C and E) pARIs = P(C ∧ E|C ∨ E) = P(C, E) P(C ∨ E) = N(C, E) N(C ∨ E) We will get back to this index later in terms of conditionals and i relationship to other indices.
ɹਓೳֶձୈճ كগੑԾఆͷ্Ͱͷಠཱੑݕఆ ❖ CͱE͕ಠཱͰ͋ΔͱԾఆ͢Δͱɺ(P(C), P(E) > 0) ❖ ۃكগੑԾఆN(¬C,¬E) → ∞ ❖ ୈҰࣜɺୈೋ͕ࣜ0ʹऩଋ͢Δۙͮ͘ ❖ ୈࡾࣜۃݶૢ࡞ޙෆมʢܭࢉՄೳʣ ❖ ୈࡾ͕ࣜ0ʹ͚ۙΕɺಠཱʹ͍ۙͱݴ͑Δ ❖ ୈࡾ͕ࣜ0͔Βԕ͚ΕɺඇಠཱੑΛ࣋ͭͱݴ͑Δ !29 We assume that people try to judge if C and E are independent, i.e. see whether the following equation holds or not: P(C, E) = P(C)P(E) = P(C|E)P(E|C). (8) In terms of frequencies, N(C, E) N(Ω) = N(C) N(Ω) · N(E) N(Ω) = N(C, E) N(E) · N(C, E) N(C) . (9) Under the extreme rarity assumption (XRA), N(¬C, ¬E) → ∞, the first and second converge to 0, while the third remains the same. So, as much as the third, P(C|E)P(E|C) is close to 0, C and E are independent. Otherwise, i.e. if P(C|E)P(E|C) is large (close to 1), C and E are somehow dependent. Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹ Visiting Scholar at University of London, Birkbeck and Observational causal induction as independence test under rarity assumption 2017-01-18 Wed 48 / 73 Statistical Independence indep under XRA We assume that people try to judge if C and E are independent, i.e see whether the following equation holds or not: P(C, E) = P(C)P(E) = P(C|E)P(E|C). (8 n terms of frequencies, N(C, E) N(Ω) = N(C) N(Ω) · N(E) N(Ω) = N(C, E) N(E) · N(C, E) N(C) . (9 Under the extreme rarity assumption (XRA), N(¬C, ¬E) → ∞, the first and second converge to 0, while the third remains the same. So, as much as the third, P(C|E)P(E|C) is close to 0, C and E ar ndependent. Otherwise, i.e. if P(C|E)P(E|C) is large (close to 1) C and E are somehow dependent. uji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹ Visiting Scholar at University of London, Observational causal induction as independence test under rarity assumptio 2017-01-18 Wed 36
References • Hattori, M., Oaksford, M., 2007. Adaptive Non-Interventional Heuristics for Covariation Detection in Causal Induction: Model Comparison and Rational Analysis. Cogn. Sci. 31, 765–814. doi: 10.1080/03640210701530755
• Wason, P. C. (1966). “Reasoning,” in New Horizons in Psychology, ed B. Foss (Harmondsworth: Penguin Books), 135– 151.
• Over, D. E., and Baratgin, J. (2017). “The ”defective“ truth table: its past, present, and future,” in The Thinking Mind: A Festschrift for Ken Manktelow, eds N. Galbraith, E. Lucas, and D. E. Over (London: Psychology Press), 15–28.
References • Baratgin, J., Politzer, G., Over, D.E., Takahashi, T., 2018. The Psychology of Uncertainty and Three-Valued Truth Tables. Front. Psychol. 9, 1479. doi:10.3389/fpsyg.2018.01479
• Hattori, M., Over, D.E., Hattori, I., Takahashi, T., Baratgin, J., 2016. Dual frames in causal reasoning and other types of thinking. The Thinking Mind: A Festschrift for Ken Manktelow, 98–114. doi: 10.4324/9781315676074
• Hattori, M., Over, D.E., Hattori, I., Takahashi, T., Baratgin, J., 2016. Dual frames in causal reasoning and other types of thinking. Think. Mind A Festschrift Ken Manktelow 98–114. doi:10.4324/9781315676074
• Hattori, I., Hattori, M., Over, D.E., Takahashi, T., Baratgin, J., 2017. Dual frames for causal induction: the normative and the heuristic. Think. Reason. 23, 292–317. doi:10.1080/13546783.2017.1316314
• Nakamura, H., Shao, J., Baratgin, J., Over, D.E., Takahashi, T., Yama, H., 2018. Understanding conditionals in the east: A replication study of Politzer et al. (2010) With Easterners. Front. Psychol. 9, 505. doi:10.3389/ fpsyg.2018.00505
• Takahashi, T., Kohno, Y., & Oyo, K. (2010). Causal induction heuristics as proportion of assumed-to-be rare Instances (pARIs). In Proceedings of the 7th International Conference on Cognitive Science (ICCS2010) (pp. 361–362)
• Takahashi, T., Oyo, K., Tamatsukuri, A. Correlation Detection with and without the Theory of Conditionals: A model update of Hattori & Oaksford (2007). A book chapter proposed, on BioRxiv, doi:10.1101/247742.
Papers in preparation • Higuchi, K., Oyo, K., Yokokawa, J., Takahashi, T., (in prep.). Adaptive rationality of the pARIs rule in observational causal induction (tentative).
• Sato, A., Takahashi, T., (in prep.). Compounds of conditionals in probability judgments (tentative).
• Observational Causal Induction as Independence Test Under Rarity Assumption
• Takarada, Y., Oyo, K., Yokokawa, J., Takahashi, T., (in prep.) Causal induction with defective data and defective biconditionals (tentative).
• Yoshizawa, H., Takahashi, T., (in prep.). Logical property of Japanese conditionals (tentative).
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