ORIGINAL ARTICLE Frank Rijmen Æ Paul De Boeck A latent class model for individual differences in the interpretation of conditionals Received: 22 August 2000 / Accepted: 20 March 2002 / Published online: 8 March 2003 Ó Springer-Verlag 2003 Abstract We investigated the hypothesis that there are three levels of performance associated with conditional reasoning: (1) Unsophisticated reasoners solve a modus tollens by accepting the invited inferences, treating the conditional as if it were a biconditional. (2) Reasoners of an intermediate level can resist the invited inferences, but cannot find the line of reasoning needed to endorse modus tollens. (3) Sophisticated reasoners do not draw the invited inferences either, but they do master the strategy to solve a modus tollens. On a first set of six problems, solved by 214 adoles- cents, an unrestricted latent class analysis revealed the existence of a large subgroup of reasoners with a bi- conditional interpretation of the conditional, and a smaller subgroup with a conditional interpretation. On a second set of 24 problems, solved by the same participants, a restricted latent class model corroborated the existence of a large subgroup of unsophisticated reasoners and a smaller subgroup of reasoners of an intermediate level. No evidence was found for the exis- tence of a subgroup of sophisticated reasoners. As expected, the class of biconditional reasoners was associated with the class of unsophisticated reasoners, and the class of conditional reasoners was associated with the class of reasoners of an intermediate level. Furthermore, the former showed a biconditonal re- sponse pattern on truth table tasks, whereas the latter showed a conditional response pattern. Reasoning with conditionals (if/then propositions) is a central topic in the study of deductive reasoning. Four classical conditional reasoning problems are: modus ponens (MP; ‘‘if p, then q’’ and ‘‘p’’, hence ‘‘q’’), modus tollens (MT; ‘‘if p, then q’’ and ‘‘not q’’, hence ‘‘not p’’), denial of the antecedent (DA; ‘‘if p, then q’’ and ‘‘not p’’, hence ‘‘not q’’) and affirmation of the consequent (AC; ‘‘if p, then q’’ and ‘‘q’’, hence ‘‘p’’). The latter two are fallacies; they are not valid arguments in classical logic. The empirical studies of reasoning with conditionals indicate that MP is endorsed by almost everyone (except very young children), in contrast with MT (for a review, see Evans, Newstead, & Byrne, 1993). Rule theories of propositional reasoning (e.g. Braine, 1978; Braine, Reiser & Rumain, 1984; Braine & O’Brien, 1991; Osh- erson, 1975; Rips, 1984, 1994) account for this empirical finding by assuming that a rule for MP is part of the repertory, but a rule for MT is not. Hence, solving a MT problem should be more difficult because it requires the application of several basic rules:  p ðsuppositionÞ  q ðmodus ponensÞ  incompatible ðcontradictionÞ  not p ðreductio ad absurdumÞ Also the mental model theory of propositional rea- soning (Johnson-Laird & Byrne, 1991; Johnson-Laird, Byrne & Schaeken, 1992) can account for the difference between MP and MT. MP can be solved using the initial representation of a conditional:  p ½ q so that MP requires only one explicit model, whereas MT requires that the initial representation is fleshed out to represent all three of the situations that are consistent with the conditional:  p q  not p q  not p not q Another empirical observation is that participants often do endorse the DA and AC inferences, although they are not valid in classical logic. Avoiding the Psychological Research (2003) 67: 219–231 DOI 10.1007/s00426-002-0092-7 Frank Rijmen was supported by the Fund for Scientific Research Flanders (FWO). F. Rijmen (&) Æ P. De Boeck University of Leuven, Tiensestraat, 102, 3000 Leuven, Belgium E-mail: frank.rijmen@psy.kuleuven.ac.be Tel.: +32-16-326123 Fax: +32-16-325988