Co-reference and reasoning

CLARE R. WALSH 0 0 Brown University , Providence, Rhode Island Co-reference occurs when two or more noun phrases refer to the same individual, as in the following inferential problem: Mark is kneeling by the fire or he is looking at the TV but not both. / Mark is kneeling by the fire. / Is he looking at the TV? In three experiments, we compared co-referential reasoning problems with problems referring to different individuals. Experiment 1 showed that co-reference improves accuracy. In Experiment 2, we replicated that finding and showed that co-reference speeds up both reading and inference. Experiment 3 showed that the effects of co-reference are greatest when the premises and the conclusion share co-referents. These effects led the participants to make illusory inferencesthat is, to draw systematically invalid conclusions. The results are discussed in terms of the mental model theory of reasoning. - Rachel is not climbing up the stairs. Is she cooking at the stove? [Answer: yes.] The inference is valid, because if its premises are true then its conclusion must be true too. This is an example of an inference with a co-referential actor, because readers understand that Rachel and she refer to the same person. What effect does such a co-reference have on deductive reasoning? No definite answer is to be found in At the time most of this research was conducted, the first author was supported by an Enterprise Ireland PhD fellowship, a Government of Ireland Scholarship from the Council for Humanities and Social Sciences, a Dublin University Postgraduate Award, and a postdoctoral fellowship from the Educational Testing Service. The second author was supported by Grant BCS 0076287 from the National Science Foundation for investigation of strategies in reasoning. Some of the results were presented at the 23rd meeting of the Cognitive Science Conference in Edinburgh in August, 2001. We thank Ruth Byrne, Sam Glucksberg, Uri Hasson, Markus Knauff, Mike Oaksford, Yingrui Yang, Lauren Ziskind, and two anonymous reviewers for their helpful comments on this research. Correspondence concerning this article should be addressed to C. Walsh, Department of Cognitive and Linguistic Sciences, Brown University, Box 1978, Providence, RI 02912 (e-mail: ). the psychological literature, and the present article aims to remedy this deficiency. If individuals use formal rules of inference in reasoning, then they should possess the following rule for disjunctions: They can make the inference above by applying this rule to the logical form of the premises, setting A equal to Rachel is climbing up the stairs and B equal to Rachel is cooking at the stove (see, e.g., Braine & OBrien, 1998; Rips, 1994). The use of the rule should be the same whether or not clauses A and B are co-referential. In contrast, the mental model theory postulates that individuals with no training in logic use the meaning of assertions and their general knowledge to construct mental models of the possibilities that are compatible with the premises (Johnson-Laird & Byrne, 1991). Each mental model represents a possibility. A conclusion is judged to be valid if it holds in all the mental models of the premises. Conversely, it is judged as invalid (i.e., not necessarily the case) if reasoners find a counterexample that is, a model of the premises in which the conclusion is false. Because working memory is limited, mental models are governed by the principle of truth: by default, they represent only true possibilities and, within them, the clauses in the premises only when they are true (JohnsonLaird & Byrne, 2002). If a clause is false in a possibility, then it will not be represented in a mental model of the possibility. For instance, given an exclusive disjunction of the form A or B but not both, several experiments have shown that individuals list as possible just the following two cases (see, e.g., Barres & Johnson-Laird, 2003; Johnson-Laird & Savary, 1996): According to the theory, individuals make a mental note of what is false in each of these possibilities. If they retain these notes, then they can in principle use them to flesh out the mental models into fully explicit models: where denotes negation. Otherwise, they will be vulnerable to various sorts of illusory inferences that seem compelling but are in fact invalid (see, e.g., JohnsonLaird & Savary, 1996). We will return to these illusions in the account of Experiment 3. To make an inference of the sort A or B but not both. A or B but not both. reasoners can match the categorical information in the second premise with the first of the models above and then flesh out the model to draw the conclusion not-B. In contrast, to make an inference of this sort with a negative categorical premise, such as reasoners must use the categorical information to eliminate a modelthe first in the set aboveand must find the second model and assert the information that it contains. In general, the process of matching a premise to a model is easier than that of mismatching a premise to a model (i.e., using a premise to negate a model). Hence, the theory predicts that the first sort of inference should be easier than the second sort, and the results of previous experiments have corroborated this prediction (see, e.g., Johnson-Laird & Byrne, 1991). A biconditional of the form If and only if not-A then B has exactly the same fully explicit models as the preceding disjunction does. Most people, however, do not immediately realize the equivalence. They consider instead the mental models of the biconditional: The first model represents the salient possibility in which the antecedent, not-A, and the consequent, B, are both true. The second model, denoted by the ellipsis, is a placeholder with no explicit content. It represents the possibilities in which the antecedent and the consequent are both false. If individuals retain the mental note of this information, they can use it to construct fully explicit models of the biconditional, which are the same as those for the exclusive disjunction A or B but not both. The meaning of a premise, co-reference, and background knowledge can all modulate the basic meanings of sentential connectives (Johnson-Laird & Byrne, 2002). Modulation occurs, for example, when knowledge prevents the construction of a mental model. Thus, a disjunction such as Rachel ate salmon for dinner or she ate fish would ordinarily be compatible with the possibility in which she ate salmon but not fish. However, this possibility is ruled out by the co-reference of Rachel and she and by the knowledge that salmon is fish. The recovery and representation of co-reference is central to comprehension. Indeed, the ease of establishing co-referential relations enhances the understanding and memory of discourse (see, e.g., Garnham, Oakhill, & Johnson-Laird, 1982). A noun phrase can lead to the introduction of a new entity into a mental model of discourse, and subsequent references (...truncated)