Deriving a conclusion from relational premises

Deriving a Conclusion From Relational Premises Jean-Baptiste Van der Henst (jvanderhenst@hotmail.com) Laboratory of Experimental Psychology, K.U. Leuven, Tiensestraat 102 Leuven, 3000 Belgium Walter Schaeken (Walter.Schaeken@psy.kuleuven.ac.be) Laboratory of Experimental Psychology, K.U. Leuven, Tiensestraat 102 Leuven, 3000 Belgium Abstract Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of “mental models” compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyse the relational terms that people use in drawing conclusions from spatial relation problems (A is to the left of B, B is to the left C, D is in front of A, E is in front C, What is the relation between D and E?). We show that the linguistic form of premises, the presentation format, the orientation of the question and the internal inspection of the mental model are important factors in determining the wording of conclusions. Our study shows that the type of conclusion produced provides a key to identifying the mental processes involved in solving these problems. Introduction Consider problem: the following relational reasoning A is to the left of B B is to the left of C D is in front of A E is in front of C What is the relation between D and E? How might this problem be solved? One possibility consists of building in one’s mind an analogical representation, which exhibits the relation between D and E: A D B C E Another is to use inference rules and apply these rules to the propositional form of the premises to derive the required relation. During the last forty years, numerous studies have attempted to discriminate between these two approaches. In the sixties and seventies, they were respectively labelled the ‘analogical’ approach (DeSoto, London & Handel, 1965; Huttenlocher, 1968) and the ‘linguistic’ approach (Clark, 1969a; b) and related to representational processes. In the eighties and nineties, they were labelled the “mental model” (Johnson-Laird, 1983; Byrne & Johnson-Laid, 1989) and the “mental logic” approaches (Hagert, 1984; Rips, 1994; Braine & O’Brien; 1998) and related to inferential processes. To compare these two approaches, researchers have relied on performance results (see Evans, Newstead & Byrne, 1993 for review). They either consider the correctness of the conclusion or the response time. However, no study has ever investigated the type of conclusions that people formulate. It is rather surprising that psychologists of reasoning have ignored this question since in another field of deductive reasoning, namely reasoning involving quantifiers like “all”, “none”, and “some”, this issue was one of the first to be investigated under the guise of the ‘atmosphere’ effect (Woodworth & Sells, 1935). This effect, which has since been extensively explored (see Evans, Newstead and Byrne, 1993 for review) refers to the fact that universal premises (All A are B) prompt universal conclusions, particular premises (Some A are B) prompt particular conclusions, affirmative premises prompt affirmative conclusions and negative premises prompt negative conclusions. The question we will address is that of the wording of conclusions in relational reasoning. In the above example, the answers “D is to the left of E” and “E is to the right of D” are both correct. But which of these two conclusions do people actually draw? In this article, we want to show that taking into account the wording of the conclusions can reveal several important mechanisms that occur in representing and in reasoning from spatial relational descriptions. We now present several factors that may influence the wording of conclusions. The linguistic form of the premises According to mental model theory, there are two stages in representing the premises. The first stage, which is compatible with a linguistic approach, consists of forming a propositional representation that is close to the surface form of the sentence. The second stage consists of using this propositional representation as a basis for constructing a mental model that is analogous to the situation described in the premises. Once the model is built, the linguistic details of the premises and their propositional representation tend to be forgotten (Mani & Johnson-Laird, 1982). The formulation of the