Probabilistic representation in syllogistic reasoning: A theory to integrate mental models and heuristics

Abstract

This paper presents a new theory of syllogistic reasoning. The proposed model assumes there are probabilistic representations of given signature situations. Instead of conducting an exhaustive search, the model constructs an individual-based "logical" mental representation that expresses the most probable state of affairs, and derives a necessary conclusion that is not inconsistent with the model using heuristics based on informativeness. The model is a unification of previous influential models. Its descriptive validity has been evaluated against existing empirical data and two new experiments, and by qualitative analyses based on previous empirical findings, all of which supported the theory. The model's behavior is also consistent with findings in other areas, including working memory capacity. The results indicate that people assume the probabilities of all target events mentioned in a syllogism to be almost equal, which suggests links between syllogistic reasoning and other areas of cognition.

Model fitting data from syllogistic reasoning experiments

“…In some experiments [1], [2], [4], [5], choice options were given to participants as instantiated above, while in other experiments [3], [6], [7], [8], participants were asked to generate their own conclusions.…”

“…Table 1, Table 2 show the comparison of the probabilistic representation theory (PRT) [1] with other models (the transitive-chain theory (TCT) [2] and the probability heuristic model (PHM) [3], respectively). Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9 show the comparison of three models (i.e., PRT, PHM, and a probabilistic extension of the mental model theory [pMM] [1], [4]) using data of Experiment 1 in [5], Experiment 2 in [5], Experiment 2, first Test in [4], Experiment 2, second Test in [4], Experiment 1 in [2], Experiment 3 in [6], Experiment with adult participants in [7], Experiment in [8], Experiment 1 in [1], and Experiment 2 in [1], respectively. Tables 13 and 14 show the comparison of PRT and PHM using data from syllogisms with generalized quantifiers, Experiment 1 in [3] and Experiment 2 in [3], respectively.…”

“…The data presented in this article are related to the research article entitled “Probabilistic representation in syllogistic reasoning: A theory to integrate mental models and heuristics” (M. Hattori, 2016) [1]. This article presents predicted data by three signature probabilistic models of syllogistic reasoning and model fitting results for each of a total of 12 experiments ( N =404) in the literature.…”

Mental Models or Probabilistic Reasoning or Both

“…The PHM is not without criticism: 'No valid conclusion' responses are not well explained by the model (Hattori, 2016); and there is some debate over the conclusions that should be produced (e.g., Elflein & Ragni, 2018;Hattori, 2016). Such issues could be avoided if the Probability Heuristic Model described a possible strategy rather than a fundamental reasoning mechanism.…”

Discounting and Augmentation in Causal Conditional Reasoning: Causal Models or Shallow Encoding?

“…It has recently been argued that mental models might provide the right kind of representation for recording the results of interrogating or sampling underlying probabilistic representations and that this might explain certain errors as people move from continuous to discrete representational formats [40, 41, 42]. This proposal means that some representational format like mental models would be required even if one takes a probabilistic view of the underlying deep logical structures over which people normally reason.…”