How do people learn from negative evidence? Non-monotonic generalizations and sampling assumptions in inductive reasoning

Abstract

A robust finding in category-based induction tasks is for positive observations to raise the willingness to generalize to other categories while negative observations lower the willingness to generalize. This pattern is referred to as monotonic generalization. Across three experiments we find systematic non-monotonicity effects, in which negative observations raise the willingness to generalize. Experiments 1 and 2 show that this effect emerges in hierarchically structured domains when a negative observation from a different category is added to a positive observation. They also demonstrate that this is related to a specific kind of shift in the reasoner's hypothesis space. Experiment 3 shows that the effect depends on the assumptions that the reasoner makes about how inductive arguments are constructed. Non-monotonic reasoning occurs when people believe the facts were put together by a helpful communicator, but monotonicity is restored when they believe the observations were sampled randomly from the environment.

Sampling Frames and Inductive Inference with Censored Evidence

“…This work complements recent studies that highlight the impact of social and pragmatic constraints on the sampling process in property inference (Hayes et al, under review;Ransom et al, 2016;Shafto et al, 2014;Voorspoels et al 2015). In everyday inference the samples of evidence that we observe are often likely to be subject to both types of constraints; frame-like limitations that systematically exclude certain types of data as well as data selected with a particular social goal (e.g., to teach or to mislead).…”

“…A growing body of evidence suggests that people's inductive inferences are guided by their understanding of the sampling processthe method by which observations were generated or selected (e.g., Navarro, Dry, & Lee, 2012;Shafto, Goodman, & Griffiths, 2014;Tenenbaum & Griffiths, 2001;Voorspoels, Navarro, Perfors, Ransom, & Storms, 2015;Xu & Tenenbaum, 2007). Much of the previous work in this area has examined sampling processes as a form of social cognition: people reason differently when they believe data were selected by a helpful teacher than when data are selected randomly, or when deception is involved.…”

“…The effect of sampling assumptions is captured in this framework by specifying different likelihoods for different sampling conditions: a helpful teacher does not select data d in a purely random way, for instance, so one should expect that the likelihood P(d|h) should be different when evidence is presented by a helpful teacher than when the same evidence arrives by a random sampling process (e.g., Navarro et al, 2012;Sanjana & Tenenbaum, 2003;Tenenbaum & Griffiths, 2001). In social reasoning contexts, the sampling model can be very complicated, insofar as it depends on the learner's theory of mind in respect of the teacher (Shafto et al, 2014, Voorspoels et al, 2015Xu & Tenenbaum, 2007). Sampling frames and induction In this paper we consider a class of Bayesian inductive reasoning models in which the data d are subject to a deterministic censoring mechanism defined by a simple survivor function S (d).…”

Inductive reasoning 2.0

“…A promising new approach views relevance theory in the context of people's beliefs about how and why premises have been sampled from the set of possible observations. These sampling assumptions are instantiated in a formal Bayesian model of belief revision (Ransom et al, ; Shafto, Goodman, & Griffiths, ; Voorspoels, Navarro, Perfors, Ransom, & Storms, ). A key insight is that reasoners often assume that the premises presented in an inductive argument have been selected intentionally by a helpful agent to highlight a salient property of the premises.…”

“…It has also been shown to predict novel phenomena involving negative evidence. For example, Voorspoels et al () showed that adding negative evidence to a premise set can increase belief in conclusions about how far a property can be generalized. For example, those who learned that “Mozart's music elicits alpha waves” but that “falling rocks do note elicit alpha waves” were more likely to conclude that “Metallica's music elicits alpha waves,” than those who were only given positive evidence.…”