Abstract
Previous research (Oberauer & Wilhelm, 2000) has shown an inherent directionality between the two terms linked in premises of typical deductive reasoning tasks. With three experiments we investigated the effect of inherent directionality on the time to integrate two premises and for the derivation of a conclusion. We varied figure (i.e., order of terms in the premises) and direction of inference (i.e., order of terms in the conclusion) in deduction tasks from various domains (propositional reasoning, syllogisms, spatial, temporal, and linear order reasoning). Effects of figure on premise reading times varied with the directionality of the relations. Effects of direction of inference reflected the same directionality for a subset of relations. We propose that two factors are jointly responsible for a large part of observed directionality effects in premise integration: the inherent directionality of relational statements and a general advantage for a given–new order of terms in the second premise. Difficulty of deriving a conclusion is affected by the directionality or relations if and only if the relation is semantically asymmetric, so that the directionality must be preserved in the integrated mental model.
Acknowledgments
This work was supported by Grant FOR 375/1-1 of Deutsche Forschungsgemeinschaft (DFG). We thank Karina Schimanke, Artur Schneider, and Petra Grüttner for collecting the data of Experiments 2 and 3. We are indebted to Phil Johnson-Laird for his comments on a previous version of the paper and to Reinhold Kliegl for many thoughtful discussions.
Notes
Our approach to premise integration was inspired by the mental model theory, and therefore we call these representations mental models, acknowledging that our results are also compatible with other theories that assume relational representations to integrate several premises.
Oliver Wilhelm is now at Humboldt University, Berlin, Germany.
Note: Predicted directionality effects are based on the analysis of inherent directionality of various relations (Oberauer & Wilhelm, Citation2000). “Picture verif.” refers to findings from sentence–picture verification experiments (Oberauer & Wilhelm, Citation2000). “Premise integration” refers to effects of figure on reading times for the second premise in the present experiments. An advantage for (A–B, B–C) is the empirical signature of forward directionality (P → Q); an advantage for (B–A, C–B) indicates backward directionality (P ← Q). “Inference” refers to directionality effects at the inference stage, evidenced by Direction of Inference > Figure interactions on latencies of the third premise (Experiment 1) or conclusion evaluation times (Experiments 2–4). An advantage for direction A–C with (AB, BC) and for direction C–A with (BA, CB) indicates direc- tionality P → Q; the reverse interaction indicates directionality P ← Q. E1 to E3 refer to Experiments 1 to 3; P–Q indicates no directionality.
Note: In this schema, B refers to the middle term (i.e. the term that appears in both premises), A refers to the end term of the first premise, and C refers to the end term of the second premise.
For conditional inferences, four standard forms are defined depending on the second (“minor”) premise: Following “If A then B”, a second premise “A” licenses the conclusion “B” by modus ponens (MP), and a second premise “not B” licenses the conclusion “not A” by modus tollens (MT). A second premise “not A” leads to the form denial of the antecedent (DA), and “B” results in acceptance of the consequent (AC); these two arguments are not valid with a standard conditional, but are valid with a biconditional.
Where a between-subjects factor was involved, homogeneity of variance was tested by Levene’s test, and in the case of a significant deviation from homogeneity, the contrast in question was tested by a Kruskal–Wallis test. This nonparametric test led to the same conclusion as did the ANOVAs in all cases.
When the biconditional is read as “If A then B and if B then A”, we expect no overall directionality effect, because the two conditionals have opposite directionalities. If the biconditional is read as “If A then B and if not A then not B”, we expect directionality from the A term to the B term.
Adherents of the syntactic principle could try to apply it to our experiment in the following way (suggested by Mike Oaksford): People are looking for an end term in the subject role to use it as the subject of the conclusion. After reading the first premise, they already pick its subject as a candidate subject of the end term. In (AB, BC), the second premise confirms this choice, whereas in (BA, CB), the second premise enforces a revision: The subject of the first premise (B) turns out to be the middle term, and the subject of the second premise (C) needs to be chosen as subject of the conclusion. This can explain the advantage for in reading times. People could then formulate a relational conclusion for themselves according to the syntactic principle, with the subject mentioned first, and if the order of terms in the third premise and conclusion match that order, they process them faster. This could explain the effects in the inference stage. Such an account, however, works if and only if the first term in a premise, but not the second term, is a grammatical subject. This is the case for the quantifier “all” and the spatial relation, but not for the conditionals and the disjunction. Hence, this application of the syntactic account predicts the wrong interaction between term order effects and relation.
Notes: > means “is larger than”; > means “is smaller than”. Examples are for the condition with comparatives; in the spatial condition relations were “is on the left of ” and “is on the right of ”, and in the temporal condition, “was before” and “was after”, respectively. “Same” and “Reversed” refer to how the relation in the conclusion relates to the relation in the first premise.