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From what I understand there is (or was) a controversy whether humans reason deductively by constructing mental models and surveying them or by following built-in inference rules of mental logic (usually logical, but perhaps content-specific too). The former is associated with Johnson-Laird and Byrne and the latter with Braine and O'Brien, to name a few prominent proponents.

I was trying to find a survey of the current state of the art, but did not have much luck. Most hits date back to 1990s or 2000s. This is confirmed by the Google Ngram, which shows mental logic peaking in the late 1990s and mental models in the early 2000s, and both dropping dramatically by 2010. Wikipedia does not help much either beyond "scientific debate continues" with references also predating 2010. After 2010 there seem to be (anecdotally) more papers with mental models, but they are narrowly focused, and even 2020 survey by Cárdenas-Figueroa and Navarro does not address the competing theory. Was there ever a resolution? Were they integrated, did both fall out of favor after something new emerged? I am particularly interested in cognitive aspects of mathematical reasoning.

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In essence, the mental model theory "won" the debate, but this was mostly a hollow victory, as both theories have become largely irrelevant.

For in-depth reviews, see for example: Holyoak & Morrison (2012), Oaksford & Chater (2007), Ball & Thompson (2017), Over (2020). To summarize however, a few factors have led to this outcome:

  1. The mental models theory has been refined over the years, whereas mental logic (aka mental rules or formal rule approach) has fallen out of favour - eg, López-Astorga (2016), Evans (2012):

Within the psychology of reasoning, the view that there is an in-built mental logic in the form of inference rules is nowadays a minority position, and even these theorists propose substantial variation from standard logics as well as a host of performance factors.

  1. Much of the debate became immaterial when researchers attempted to extend these 2 models to logical reasoning and critical thinking more generally - eg, Evans (2012):

... experimental evidence has accumulated indicating that people were apparently poor at logical reasoning, highly influenced by irrelevant features of the content and subject to a number of other cognitive biases. As a result, the paradigm has shifted in the past 10-15 years, and while deduction is still studied, it is allied to a number of other methods. Theoretically, there is now also a lot more interest in human reasoning as a probabilistic and pragmatic, rather than deductive process.

  1. This eventually lead to the popularity of much more comprehensive, and empirically successful, dual-process and (Bayesian) probabilistic theories, that subsume the mental logic and model theories, and created what is now known as the "new paradigm psychology of reasoning", integrating the psychology of reasoning with the study of judgement and decision-making.

Bonnefon (2013):

During the late 1990s and the early twenty-first century, the psychology of reasoning slowly moved towards a broader range of problems than deduction, ... which eventually coalesced into what some call the New Paradigm psychology of reasoning. ... It became increasingly common for psychologists to observe that people did very little deducing in everyday life, and that the study of deduction was accordingly unlikely to deliver general insights about how people reasoned.

Elqayam & Over (2012):

A Bayesian approach is indisputably a core element of this new paradigm—any approach within this paradigm takes into account degrees of belief and uncertainty. In this paper, we argued that dual processing is just as much a part of the new paradigm. ... Bayesianism, in turn, constrains the way dual processing is theorised, precluding the older mental logic or mental models interpretation.

Oaksford & Chater (2019):

The two most prominent old-paradigm theories make different assumptions about mental representations and processes. Mental logic proposes that the mind mirrors syntactic representations and the application of logical rules, as above. By contrast, mental models theory (MMT) assumes that people reason over representations that attempt to capture what the premises mean. ... The new paradigm in the psychology of reasoning, by contrast, attempts to explain argumentation, deduction, and induction in a probabilistic framework, in continuity with models that have become widespread in the cognitive and brain sciences.

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    $\begingroup$ Thank you for taking time to write this up, I did not realize that cognitive scientists soured so thoroughly on the binary logic as a model of reasoning. $\endgroup$
    – Conifold
    May 25, 2023 at 5:29

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