Abstract
The Bayesian model was recently proposed as a normative reference for psychology studies in deductive reasoning. This new paradigm supports that individuals evaluate the probability of an indicative conditional if A then C in the natural language as the conditional probability \(P(\textit{C given A})\) (P(C|A) according to Bayes’ rule). In this paper, we show applying an eye-tracking methodology that if the cognitive process for both probability assessments (\(P(\textit{if A then C})\) and P(C|A)) is really identical, it actually doesn’t match the traditional focusing situation of revision corresponding to Bayes’ rule (change of reference class in a static universe). Individuals appear to revise their probability as if the universe was evolving. They use a minimal rule in mentally removing the elements of the worlds that are not A. This situation, called updating, actually seems to be the natural frame for individuals to evaluate the probability of indicative conditional and the conditional probability.
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Notes
- 1.
- 2.
The two usual forms of Bayes’ rule are the conditional probability:
$$\begin{aligned} P(H|D) = \frac{P(H \wedge D)}{P(D)}=\frac{P(H \wedge D)}{P(H \wedge D)+P(\lnot H \wedge D)} \nonumber \end{aligned}$$and the Bayes’ identity:
$$\begin{aligned} P(H|D) = \frac{P(H)P(D|H)}{P(D)}=\frac{P(H)P(D|H)}{P(H)P(D|H)+P(\lnot H)P(D|\lnot H)} \nonumber \end{aligned}$$with P(H) the prior probability of hypothesis H, P(H|D) the posterior probability after the knowledge of data D, P(D|H) the likelihood and P(D) the probability of D.
- 3.
- 4.
- 5.
With \(\wedge _{k}\) for the Kleene-Łukasiewicz-Heiting conjunction.
- 6.
- 7.
The minimal rule is isomorphic to redistributing the weights of removed world(s) proportionally to the remaining world(s). For the type 1 problem, it mathematically corresponds to Bayes’ rule:
- 8.
These colors were better discriminated.
- 9.
The viewing angle of the stimuli was 9.6 on a \(1920 \times 1080\) resolution computer screen.
- 10.
To avoid a possible order effect, the participants were randomly allocated to six groups which all answered five questions (two controls and the three conditionals in different orders).
- 11.
The gaze behavior were also recorded for scan path and visual strategy (VS) investigation.
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Baratgin, J., Ocak, B., Bessaa, H., Stilgenbauer, JL. (2017). Updating Context in the Equation: An Experimental Argument with Eye Tracking. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_4
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