The Effects of Negative Premises on Inductive Reasoning: A Psychological Experiment and Computational Modeling Study

The Effects of Negative Premises on Inductive Reasoning: A Psychological Experiment and Computational Modeling Study Kayo Sakamoto (SAKAMOTO@Nm.Hum.Titech.Ac.Jp) Tokyo Institute of Technology, 2-21-1 O-okayama, Meguro-ku, Tokyo, 152-8552 JAPAN Masanori Nakagawa (NAKAGAWA@Nm.Hum.Titech.Ac.Jp) Tokyo Institute of Technology, 2-21-1 O-okayama, Meguro-ku, Tokyo, 152-8552 JAPAN studies, such as causal learning (e.g., Buehner and Cheng, 2005). However, the effects of negative premises have rarely been discussed in any detail in the context of inductive reasoning studies concerned with the evaluation of arguments. Investigating the effects of negative premises can undoubtedly contribute to our understanding of inductive reasoning. For instance, cases where the entities in both negative and positive premises belong to the same category are clearly problematic for the category-based induction theory (Osherson et al., 1990) because it is impossible to distinguish between negative premises and positive premises from the categorical viewpoint. In contrast to the similarity and coverage model based on category-based induction theory, Sloman (1993) has proposed a feature- based model based on a simple perceptron. According to Sloman, knowledge of category structure is not required for the evaluation of arguments. Rather, he assumes that argument evaluation is based on a simple computation of feature similarities between the entities of the premises and the conclusion. Thus, Sloman’s feature-based model may be more effective at coping with negative premises than category-based induction theory. However, the psychological validity of Sloman’s model has yet to be tested in terms of processing negative premises. Accordingly, this study examines the validity of feature- based induction theory to handle these cases that are so problematic for category-based induction theory. In terms of model construction, what kind of model can adequately represent the cognitive process of feature-based induction, including negative premises? In addition to Sloman’s (1993) model, Sakamoto, Terai and Nakagawa (2005) have also proposed a feature-based model. While structurally similar, their model extends the learning algorithm in order to cope with negative premises. Moreover, their model utilizes corpus-analysis results to compute feature similarities, rather than the results of psychological evaluations used in Sloman’s model. This means that Sakamoto et al’s model is capable of simulating a far greater variety of entities than Sloman’s model (over 20,000 compared to just 46), because the corpus analysis provides information for an enormous quantity of words. However, when induction of the appropriate category is difficult, then the level of computation involved in the feature similarity comparisons will far exceed the computational capacity of simple perceptrons. This study therefore proposes a modified version of the Sakamoto et al Abstract Various learning theories stress the importance of negative learning (e.g., Bruner, 1959; Hanson, 1956). However, the effects of negative premises have rarely been discussed in any detail within theories of inductive reasoning (with the exception of Osherson et al., 1990). Although Sakamoto et al. (2005) have proposed some computational models that can cope with negative premises and verified their psychological validity, they did not consider cases where category-based induction theory is ineffective, such as when the entities in both negative and positive premises belong to the same category. The present study was conducted to test the hypothesis that, even when negative and positive premises involve same-category entities, people can estimate the likeliness of an argument conclusion by comparing feature similarities. Based on this hypothesis, two computational models are proposed to simulate this cognitive mechanism. While both these models were able to simulate the results obtained from the psychological experiment, a perceptron model could not. Finally, we argue that the mathematical equivalence (from Support Vector Machines perspective) of these two models suggests that they represent a promising approach to modeling the effects of negative premises, and, thus, to fully handling the complexities of feature-based induction on neural networks. Introduction This study is concerned with evaluating “arguments”, such as: Collies produce phagocytes. Horses produce phagocytes. Shepherds produce phagocytes. The propositions above the line are referred to as “premises” while the statement below is the “conclusion”. The evaluation of an argument involves estimating the likelihood of the conclusion based on the premises. Osherson, Smith, Wilkie, Lopez, and Shafir (1990) refer to this kind of argument as a “categorical” argument, because the predicate (e. g., “produce phagocytes”) in the premises and conclusion is attributed to one or more entities (e. g., “Collies”, “Shepherds”). The premises can also be negative in form (e. g., “Penguins do not produce phagocytes ”). Since classic studies, such as discrimination learning (e. g., Hanson, 1956) and concept learning (e.g., Bruner,1959), the importance of negative examples has been widely recognized, and has been demonstrated in more recent