I wrote a paper with Phil Johnson-Laird and Geoff Goodwin that reviews recent developments in theories of human reasoning. It seeks to explain how logic and probability fit together with cognitive processes of inference. You can download it here, and here’s the abstract:

This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn – not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction.

I published a computational model of immediate quantification inferences in QJEP with my co-authors, Max Lotstein, Greg Trafton, and Phil Johnson-Laird. You can download it here, and here’s the abstract:

We propose a theory of immediate inferences from assertions containing a single quantifier, such as: All of the artists are bakers; therefore, some of the bakers are artists. The theory is based on mental models and is implemented in a computer program, mReasoner. It predicts three main levels of increasing difficulty: (a) immediate inferences in which the premise and conclusion have identical meanings; (b) those in which the initial mental model of the premise yields the correct conclusion; and (c) those in which only an alternative to the initial model establishes the correct conclusion. These levels of difficulty were corroborated for inferences to necessary conclusions (in a reanalysis of data from Newstead, S. E., & Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning and Verbal Behavior, 22, 535–546), for inferences to modal conclusions, such as, it is possible that all of the bakers are artists (Experiment 1), for inferences with unorthodox quantifiers, such as, most of the artists (Experiment 2), and for inferences about the consistency of pairs of quantified assertions (Experiment 3). The theory also includes three parameters in a stochastic system that predicted quantitative differences in accuracy within the three main sorts of inference.

Max Lotstein, Phil Johnson-Laird and I published a paper in Cognitive Science on how people estimate unique probabilities, like the probability that Jeb Bush will be elected US President in 2016. The theory hinges on how mental models of beliefs are used to update iconic representations of probability. Here’s a link and here’s the abstract:

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory’s predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.

I recently gave a talk on the conditional probabilities of unique events (Khemlani, Lotstein, & Johnson-Laird, 2014) at the 8th London Reasoning Workshop at Birkbeck College. You can download the presentation here.
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I recently published a paper on kinematic mental simulations in PNAS. The paper is with Monica Bucciarelli, Robert Mackiewicz, and Phil Johnson-Laird, and it examines how reasoners without any background in computer science or logic can construct mental “algorithms” in a systematic way, akin to recipes or driving directions.
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