Syllogistic reasoning is one of the oldest domains of reasoning research and has made great advances in understanding and modeling human reasoning processes. However, the field was mostly focused on a traditional set of quantifiers originating in first-order logic, thereby neglecting the large variety of quantifiers humans use when engaging in reasoning in their everyday life. The present work makes three main contributions: (I) we conducted a study yielding a dataset covering all traditional syllogisms and tasks containing generalized quantifiers ``most'' and ``most not'', providing a starting point for existing theories and models to transition to generalized quantifiers. (II) based on the dataset, we analyze the impact that the additional quantifiers have on the reasoning behavior. (III) We investigated the reasoning behavior with respect to the difference between traditional and generalized quantifiers, gaining insights into some of the peculiarities of the domain of generalized syllogisms.

Humans seem to arbitrate between automatic and controlled processing by optimizing a trade-off between cognitive effort and performance. Previous research has described ways of how these costs and benefits can be quantified and how the trade-off between them can be performed. However, it remains unclear how the costs should be weighed relative to the benefits and how the cost of the arbitration mechanism itself factors in. Here, we derive measures for these separate factors from a single objective: the variational free energy. We demonstrate that by minimizing this objective, the trade-off between automatic and controlled processing as well as meta-control is optimized implicitly. As a proof of concept, we show that the congruency and proportion congruency effects in the Stroop task directly result from this optimization, given an environment with specific statistical regularities.