Understanding quantified categorical expressions

Abstract

A model of categorical inference (Revlis, 1975b) claims that a conversion operation participates in the encoding of quantified, categorical expressions. As a consequence, a reasoner is said to interpret such sentences as "All A are Boo in a way that permits it to also be the case that "All B are A." The present study examines this conception of encoding using a sentence-picture verification task. In two experiments, students were asked to judge whether one of five possible Euler diagrams was true or false of a categorical expression (e.g., All A are B, No A are B, Some A are B, Some A are not B). Verification errors support a three-stage verification model whose major component is access to a "meaning stack" representing the progressive analysis of categorical relations; at the top of that stack is a converted reading of the input sentence. These findings have implications for current conceptions of categorical inference and semantic retrieval.Some of the recent models of syllogistic reasoning make strong and largely unsupported claims concerning our understanding of the categorical relations we are asked to reason about (e.g., Erickson, 1974; JohnsonLaird, 1975; Revlis, 1975b). One such model, the conversion model (Revlis, 1975b), although accurate in predicting reasoners' decisions, makes a particularly counterintuitive claim regarding our representation of quantified relations; to wit, a conversion operation is said to participate in the encoding of such relations, so that when a reasoner is told that all A are B, he/she interprets this proposition to mean that the converse is also true (all B are A). In summary, the reasoner is said to make decisions from an interpretation, which, if expressed as a sentence, would be markedly different from the sentence as actually presented and intended by the experimenter. The purpose of the present study is to test for the operation of conversion in the encoding of quantified, categorical expressions using a sentence-picture verification task rather than an extended inference task. The findings have implications for models of syllogistic reasoning, as well as for conceptions of categorization and semantic retrieval (e.g., Just, 1974;Meyer, 1970). Conversion OperationThe presence of conversion was first noted as a psychologically relevant variable by Wilkins (1928), but she was at a loss to account for its presence. More recent findings in psycholinguistics and categorical reasoning suggest that conversion of quantified relations may be based on one or both of the following two factors:

The belief-bias effect in formal reasoning: The influence of knowledge on logic

“…It makes the strong claim that a conversion operation participates in the encoding of each quantified, categorical expression: When the reasoner is told "All A are B," he or she interprets this proposition to mean that both the intended inclusion relation and its converse, "All B are A," are true. The presence of conversion in encoding is found in the verification errors of adults (Revlin & Leirer, 1980), is consistent with the developmental sequence in the comprehension of quantified, categorical expressions described by Bucci (1978), and may reflect a heuristic assumption of symmetry in "is a" relations (i.e., "All A are B" and "All B are A"; cf. Tsal, 1977).…”

Transitive inferences from narrative relations.

“…These are traditionally labeled as false (though without semantic constraints on symmetry these relations could be interpreted as true). Acceptance of false relations has been found in studies of narratives (e.g., Griggs & Osterman, 1980a, 1980b) as well as in sentence verification studies (e.g., Bucci, 1978; Revlin & Leirer, 1980).…”

The Interpretation of Classically Quantified Sentences: A Set-Theoretic Approach

“…In effect, the conversion of A propositions has been frequently described (see Begg & Denny, 1969;Revlin & Leirer, 1980; and studies of immediate inference). We believe that the view that [A] is represented by SUBSET while it may be represented by EQUIVALENCE as a limiting case is normatively incorrect and descriptively wrong.…”

“…In brief, according to this analysis, we can expect a systematic increase in errors for the evaluation of A and O sentences applied to SUBSET and SUPERSET diagrams. Interestingly, a few studies of A sentences using a sentence-picture verification task or a truth judgment task have reported a greater rate of errors for SUPERSET (Just, 1974, Experiment 3;Meyer, 1970) or for both SUPERSET and SUBSET (Just, 1974, Experiment 1; Revlin & Leirer, 1980) than for the other set relations. In fact, this kind of error is pervasive in all the relevant literature; it is sometimes much higher than for the other relations and can reach 25%.…”