Academic journal article Memory & Cognition

Reasoning from Connectives and Relations between Entities

Academic journal article Memory & Cognition

Reasoning from Connectives and Relations between Entities

Article excerpt

Abstract This article reports investigations of inferences that depend both on connectives between clauses, such as or else, and on relations between entities, such as in the same place as. Participants made more valid inferences from biconditionals-for instance, Ann is taller than Beth if and only if Beth is taller than Cath-than from exclusive disjunctions (Exp. 1). They made more valid transitive inferences from a biconditional when a categorical premise affirmed rather than denied one of its clauses, but they made more valid transitive inferences from an exclusive disjunction when a categorical premise denied rather than affirmed one of its clauses (Exp. 2). From exclusive disjunctions, such as Either Ann is not in the same place as Beth or else Beth is not in the same place as Cath, individuals tended to infer that all three individuals could be in different places, whereas in fact this was impossible (Exps. 3a and 3b). The theory of mental models predicts all of these results.

Keywords Deductive reasoning . Sentential connectives . Relations . Mental models

(ProQuest: ... denotes formulae omitted.)

Consider the following inferential problem:

Either Ann is taller than Beth or else Beth is taller than Cath, but not both.

So, is it possible that Beth is the tallest of the three?

The logically correct answer is yes, and the validity of the inference depends both on the sentential connective or else, which interrelates the two clauses, and on the relations is taller than and is the tallest of, which interrelate entities. Previous studies have investigated how people understand connectives and make inferences from them, and how people understand and make inferences from relations. But no empirical studies have examined reasoning that hinges both on connectives and on relations, and this novel domain challenges theories of reasoning. The present article addresses this challenge and reports some new phenomena concerning such inferences.

Relations in everyday discourse have various logical properties, of which perhaps the three most important are transitivity, symmetry, and reflexivity (Tarski, 1965, chap. V). A relation such as is in the same place as is transitive because if A is in the same place as B and B is in the same place as C, then A is in the same place as C. It is symmetric because if A is in the same place as B, then B is in the same place as A. And it is reflexive because A is in the same place as A. A relation such as is taller than is transitive, but it is asymmetric because if A is taller than B, then B is not taller than A, and it is also irreflexive because A is not taller than A. Relations do have other logical properties (see Tarski, 1965), but these properties are recondite and seldom, if ever, relevant to everyday discourse. Indeed, most relational terms in language have no important logical properties-for instance, A loves B is neither transitive nor intransitive, neither symmetric nor asymmetric, and neither reflexive nor irreflexive.

Previous psychological studies have investigated how individuals make inferences from transitive relations-for instance, A is bigger than B and B is bigger than C; therefore, A is bigger than C (e.g., Clark, 1969; Huttenlocher, 1968). Transitive inferences occur in everyday life, in intelligence tests, and in inferring economic preferences (Tversky & Kahneman, 1986). The difficulty of such inferences depends on the number of relations that must be integrated (Viskontas, Morrison, Holyoak, Hummel, & Knowlton, 2004), the distance between queried elements (Mynatt & Smith, 1977), and the elicitation of extraneous visual images (e.g., Knauff, Fangmeier, Ruff, & Johnson- Laird, 2003). Previous studies have also examined inferences based on two-dimensional spatial relations, temporal relations, and relations between relations, and have shown that the difficulty of inferences also depends on the number of possibilities in which the premises hold (e. …

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