A Constraint Satisfaction Model of Causal Learning and Reasoning

Abstract

CogSci02 A Constraint Satisfaction Model of Causal Learning and Reasoning York Hagmayer (york.hagmayer@bio.uni-goettingen.de) Department of Psychology, University of Gottingen Gosslerstr. 14, 37073 Gottingen, Germany Michael R. Waldmann (michael.waldmann@bio.uni-goettingen.de) Department of Psychology, University of Gottingen Gosslerstr. 14, 37073 Gottingen, Germany Abstract Following up on previous work by Thagard (1989, 2000) we have developed a connectionist constraint satisfaction model which aims at capturing a wide variety of tasks involving causal cognitions, including causal reasoning, learning, hy- pothesis testing, and prediction. We will show that this model predicts a number of recent findings, including asymmetries of blocking, and asymmetries of sensitivity to structural im- plications of causal models in explicit versus implicit tasks. Introduction Causal reasoning has been widely investigated during the last decade, which has led to a number of interesting novel findings (see Shanks, Holyoak, & Medin, 1996; Hagmayer & Waldmann, 2001, for overviews). For example, it has been shown that participants’ causal judgments are sensitive to the contingency between the cause and the effect, and that people’s judgments reflect the causal models underlying the observed learning events (see Hagmayer & Waldmann, 2001; Waldmann, 1996). Moreover, causal reasoning has been studied in the context of a number of different tasks, such as learning, reasoning, categorization, or hypothesis testing. Most psychological theories and computational models of causal learning and reasoning are rooted in two traditions. They are either based on associationistic or on probabilistic or Bayesian models (see Shanks et al., 1996; Thagard, 2000). Both kinds of models have been criticized. Associa- tionistic learning networks have proven unable to capture the fundamental semantics of causal models because they are insensitive to the differences between learning events that represent causes versus effects (see Waldmann, 1996). By contrast, Bayesian networks are perfectly capable of rep- resenting causal models with links directed from causes to effects (see Pearl, 2000). However, although the goal of these networks is to reduce the complexity of purely prob- abilistic reasoning, realistic Bayesian models still require fairly complex computations, and they presuppose compe- tencies in reasoning with numerical probabilities which seem unrealistic for untutored people (see Thagard, 2000, for a detailed critique of these models). The aim of this paper is to introduce a more qualitatively oriented, connectionist constraint satisfaction model of causal reasoning and learning. Our model is inspired by Thagard’s (2000) suggestion that constraint satisfaction models may qualitatively capture many insights underlying normative Bayesian network models in spite of the fact that constraint satisfaction model use computationally far sim- pler, and therefore psychologically more realistic processes. The model differs from standard associationist learning models (e.g., Rescorla & Wagner, 1972) in that it is capable of expressing basic differences between causal models. Our model embodies a uniform mechanism of learning and rea- soning, which assesses the fit between data and causal mod- els. This architecture allows us to model a wide range of different tasks within a unified model, which in the literature have so far been treated as separate, such as learning and hypothesis testing. Constraint Satisfaction Models Constraint satisfaction models (Thagard, 1989, 2000) aim at capturing qualitative aspects of reasoning. Their basic as- sumption is that people hold a set of interconnected beliefs. The beliefs pose constraints on each other, they either sup- port each other, contradict each other, or are unrelated. Co- herence between the beliefs can be achieved by processes which attempt to honor these constraints. Within a constraint satisfaction model beliefs are repre- sented as nodes which represent propositions (e.g., “A causes B”). The nodes are connected by symmetric relations. The numerical activation of the nodes indicates the strength of the belief in the proposition. A belief that is highly acti- vated is held strongly, a belief that is negatively activated is rejected. The activation of a node depends on the activation of all other nodes with which it is connected. More pre- cisely, the net input to a single node j from all other nodes i is defined as the weighted sum of the activation a of all re- lated nodes (following Thagard, 1989, p.466, eq.5): Net j = ∑ i w ij a i (t) The weights w represent the strength of the connection of the beliefs. In our simulations, they are generally pre-set to default values which are either positive or negative and re- main constant throughout the simulation. At the beginning of the simulations, the activation of the nodes representing hy- potheses are set to a low default value. However, nodes rep- resenting empirical evidence are connected to a special acti- vation node whose activation remains constant at 1.0. This architecture allows us to capture the intuition that more faith is put into empirical evidence than into theoretical hypothe- ses (see Thagard, 1989). To update the activation in each