Orlando Espino

Conditionals and directionality: On the meaning of if vs. only if

The aim of this study was to test the predictions of the current theories of reasoning about the comprehension of conditional statements. We used two types of conditional statement that are logically equivalent: if p then q and p only if q. The model theory of reasoning considers that these conditional forms differ in their initial meaning, because the negative contingency is considered only in the p only if q form. Mental-rule theories maintain that the interpretation of p only if q depends on a rephrasing of the statement as: if not q then not p. Alternatively, a directional bias may explain the differences between if p then q and p only if q. We report three experiments that demonstrate the existence of a directional bias in the comprehension of the conditionals. The results were not predicted by either the mental-rules theories or the model theory; they could, however, be easily assimilated by the model theory.

People think about what is true for conditionals, not what is false: Only true possibilities prime the comprehension of if

We report the results of two priming experiments that examine the comprehension of conditionals—for example, “if there are apples then there are oranges”—and biconditionals—for example, “if and only if there are apples then there are oranges”. The first experiment showed that participants read a biconditional faster when it was primed by a true possibility, “there were apples and there were oranges” than when it was primed by a false possibility, “there were no apples and there were oranges”; a conditional was primed equally by both possibilities. The second experiment showed that participants read the negated-antecedent conjunction faster when it was primed by a conditional than when it was primed by a biconditional; the affirmative conjunction was primed equally by both connectives. The experiments show that (a) when people understand “if A then B”, they access the true possibilities, “A and B”, and “not-A and B”, and (b) when they understand “if and only if A then B” they access “A and B”, but they do not access “not-A and B”. We discuss their implications for current theories of reasoning.

Activation of end-terms in syllogistic reasoning

We report five experiments showing that the activation of the end-terms of a syllogism is determined by their position in the composite model of the premises. We show that it is not determined by the position of the terms in the rule being applied (Ford, 1994), by the syntactic role of the terms in the premises (Polk & Newell, 1995; Wetherick & Gilhooly, 1990), by the type of conclusion (Chater & Oaksford, 1999), or by the terms from the source premise (Stenning & Yule, 1997). In our first experiment we found that after reading a categorical premise, the most active term is the last term in the premise. In Experiments 2, 3, and 4 we demonstrated that this pattern of activity is due to the position of the concepts in the model of the premises, regardless of the delay after reading the premises (150 or 2000 msec) or the quantity of the quantifiers (universal or existential). The fifth experiment showed that the pattern switches around after participants evaluate a conclusion. We propose that the last element in the model maintains a higher level of activity during the comprehension process because it is generally used to attach the incoming information. After this process, the first term becomes more active because it is the concept to which the whole representation is referred. These results are predicted by the mental model theory (Johnson-Laird & Byrne, 1991), but not by the verbal reasoning theory (Polk & Newell, 1995), the graphical methods theory (Yule & Stenning, 1992), the attachment-heuristic theory (Chater & Oaksford, 1999), or the mental rules theory (Ford, 1994).

It is not the case that if you understand a conditional you know how to negate it

We report the results of an experiment to test the cognitive processes underlying inferences from negated conditionals, e.g., ‘it is not the case that if A then B’. The results show that people endorse not only the conditional conclusion ‘if A then not B’ but also ‘if not A then B’. We discuss the implications of the results for competing explanations of reasoning about negated conditionals.

Priming effect on the exceptive conditional ‘except if’

Here we report the results of one priming experiment that examines the comprehension of exceptive conditionals—for example, ‘Mary will go out tonight except if she has an exam tomorrow’—and indicative conditionals—for example, ‘Mary will not go out tonight if she has an exam tomorrow’. The experiment showed that participants read the true possibility ‘Mary is not going out tonight and she has an exam tomorrow’ faster when it was primed by an exceptive conditional than when it was primed by an indicative; other possibilities (‘Mary is going out tonight and she does not have an exam tomorrow’, ‘Mary is going out tonight and she has an exam tomorrow’ and ‘Mary is not going out tonight and she does not have an exam tomorrow’) were primed equally by both connectives. The experiments showed that (1) when people understand ‘B except if A’, they access the true possibilities ‘not-A & B’ and ‘A & not-B’, and (2) when they understand ‘B, if not-A’ they access ‘not-A & B’, but they do not access ‘A & not-B’. We discuss the implications of this for current theories of reasoning.

Directionality Effect in Double Conditionals.

Directionality effect in deductive reasoning is a very well-known phenomenon that shows that the percentage of forward or backward inferences that participants make depends on the conditional form used. A new extension of the semantic hypothesis (Oberauer & Wilhelm, 2000) is presented to explain the directionality effect in double conditionals with different directionality. This hypothesis claims that the directional effect depends on which term plays the role of relatum. It also makes several novel claims which have been confirmed in three experiments: Experiments 1 and 2 showed there were more forward than backward inferences when the end-term that played the role of relatum was in the first premise, experiment 1: t (45) = 2.73, p < .01, experiment 2: t (38) = 12.06, p < .05, but there were more backward than forward inferences when the end-term that played the role of relatum was in the second premise, experiment 1: t (45) = 2.84, p < .01, experiment 2: t (38) = 2.21, p < .04. Experiment 3 showed that there was no directional effect when both end-terms played the role of relatum, t (34) = 1.39, p = .17, or when both middle-terms (or neither of the end-terms) played the role of relatum, t (34) = .78, p = .44. These experiments confirmed the predictions of the new extension of the semantic hypothesis.

Theories of reasoning and the representational level: A reply to Oaksford

Oaksford (2001) considers that the findings of Espino, Santamaría, and García Madruga (2000a) could be explained by the Probability Heuristics Model (PHM) proposed by Chater and Oaksford (1999). He specifically voices three objections, the two main ones being based on the fact that PHM is not a theory about syllogism representation. If this is the case, we consider that PHM cannot explain our data, because most of them were registered before the participants evaluated the conclusion. We argue that only a theory at the representational level can property explain these data.

Priming effect in affirmative complex conditional connectives

ABSTRACT We report the results of an experiment that examined the mental representations underlying the comprehension of complex conditional connectives (such as “A, on condition that B”) and the conditional if (such as “A, if B”). The mental representations during the comprehension stage were analysed using a “priming methodology”. The experiment showed that participants read the possibility “A and not-B” faster when it was primed by “A, if B” than when it was primed by “A, on condition that B”. The finding suggests that people understand the sentence “A, on condition that B” as biconditional; other possibilities (“A and B”, “not-A and B”, “not-A and not-B”) were primed equally by both connectives. We discuss the implications of this for current theories of reasoning.

Usos cotidianos del condicional en el lenguaje escrito

This paper presents a normative study on the use of conditionals in written language. A sample of texts (total length 450.000 words) originally written in Spanish was used. A total of 408 conditionals were found. We analyzed the quality of the conditionals as simple indicative, biconditionals, counterfactual, deontic (obligations, permissions, etc.) or causal, and tested the frequency of use for each of these types of conditionals. For each of them, we also tested the order as direct (antecedent-consequent) or reverse (consequent-antecedent), and the use of negations in each of the components. The results were compared to the predictions of the main current theories of reasoning.

La activación de los términos durante la comprensión de proposiciones cuantificadas

ResumenSe han llevado a cabo dos investigaciones con el objeto de estudiar que terminos (sujeto o predicado) de las proposiciones cuantificadas estan mas activados durante el proceso de comprension. El objetivo de estas investigaciones radica en dar una explicacion en terminos de activacion del fenomeno “efecto de la figura” en tareas silogisticas. Actualmente las explicaciones existentes de este fenomeno se han hecho atendiendo a las limitaciones de la memoria de trabajo o bien al papel sintactico desempenado por los terminos.Los resultados de ambos experimentos, en los que se ha utilizado una tarea de activacion, indicaron que el primer termino de una proposicion afirmativa esta mas activado que el segundo, independientemente de la funcion sintactica que desempene en la proposicion (sujeto o predicado). Tales resultados apoyan la hipotesis de que el efecto de la figura en tareas de razonamiento silogistico podria explicarse por la activacion diferencial de los terminos durante la comprension del silogismo.