Illusory inferences in conditional expressions.

A robber points a gun at a cashier and says: "Only one of these two options is true: If you conceal the combination to the safe, then I kill you; otherwise, if you don´t conceal the combination to the safe, then I kill you." Hearing this statement, most people conclude that, in either case, "I kill you." This is an illusory response, in fact; the valid conclusion states "I don´t kill you." The research reported here studied the roles that different expressions of conditionals ("if-then," "only if," and "if and only if") play in the illusory response. Three experiments show that participants inferred the conclusion "I kill you" from the conditional "if-then" and "I may or may not kill you" from the conditional "only if," while selecting both options with similar frequency for the biconditional "if and only if." These results shed light on the main theories of deductive reasoning.

Inferences from the negation of counterfactual and semifactual conditionals.

Our goal was to study how people understand the negation of counterfactuals (such as "Antonio denied/said that it is false that if Messi had played, then Barcelona would have won") and semifactuals (such as "Antonio denied that even if Messi had played, Barcelona would have won"). Previous studies have shown that participants negated basic conditionals using small-scope interpretations by endorsing a new conditional with the negated consequent, but also by making large-scope interpretations, endorsing a conjunction with the negated consequent. Three experiments showed that when participants were asked whether the negation of a counterfactual (Experiments 1 and 2) or semifactual (Experiment 3) conditional was followed by a new conditional, they made a small-scope interpretation, endorsing the same conditional with the negated consequent (e.g., "if/even if Messi had played, Barcelona would not have won"). However, they also accepted the conditional with the negated antecedent for semifactuals (e.g., "even if Messi had not played, Barcelona would have won"). When participants were asked whether the negation of a counterfactual or semifactual conditional is followed by a conjunction, they endorsed the conjunction with both the negated antecedent and the consequent (e.g., "Messi did not play and Barcelona did not win"), but again they accepted the conjunction with the negated antecedent only for semifactuals (e.g., "Messi did not play and Barcelona did win"). These results have implications for the main theories of reasoning.

Similarities and differences in understanding negative and affirmative counterfactuals and causal assertions: Evidence from eye-tracking.

Two eye-tracking experiments compared affirmative and negative counterfactuals, "if she had (not) arrived early, she would (not) have bought roses" and affirmative and negative causal assertions, "Because she arrived (did not arrive) early, she bought (did not buy) roses." When participants heard a counterfactual, they looked on screen at words corresponding to its conjecture ("roses"), and its presupposed facts ("no roses"), whereas for a causal assertion, they looked only at words corresponding to the facts. For counterfactuals, they looked at the conjecture first, and later the presupposed facts, and at the latter more than the former. The effect was more pronounced for negative counterfactuals than affirmative ones because the negative counterfactual's presupposed facts identify a specific item ("she bought roses"), whereas the affirmative counterfactual's presupposed facts do not ("she did not buy roses"). Hence, when participants were given a binary context, "she did not know whether to buy roses or carnations," they looked primarily at the presupposed facts for both sorts of counterfactuals. We discuss the implications for theories of negation, the dual meaning of counterfactuals, and their relation to causal assertions.

How people keep track of what is real and what is imagined: The epistemic status of counterfactual alternatives to reality.

When people understand a counterfactual such as "if it had been a good year, there would have been roses," they simulate the imagined alternative to reality, for example, "there were roses," and the actual reality, as known or presupposed, for example, "there were no roses." Seven experiments examined how people keep track of the epistemic status of these possibilities, by priming participants to anticipate a story would continue about one or the other. When participants anticipated the story would continue about how the current reality related to the past presupposed reality, they read a target description about reality more rapidly than one about the imagined alternative, indicating they had prioritized access to their mental representation of reality; but when they anticipated the story would continue about how the current reality related to the imagined alternative to reality, they read a target description about the imagined alternative and one about reality equally rapidly, indicating they had maintained access to both (Experiment 1), unlike for stories with no counterfactuals (Experiments 2 and 3). The tendency is not invariant: it appears immune to remote experience (Experiments 4 and 5), but it is influenced by immediate experience (Experiments 6 and 7). The results have implications for theories of reality monitoring, reasoning, and imagination. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Possibilities and the parallel meanings of factual and counterfactual conditionals.

The mental model theory postulates that the meanings of conditionals are based on possibilities. Indicative conditionals-such as "If he is injured tomorrow, then he will take some leave"-have a factual interpretation that can be paraphrased as It is possible, and remains so, that he is injured tomorrow, and in that case certain that he takes some leave. Subjunctive conditionals, such as, "If he were injured tomorrow, then he would take some leave," have a prefactual interpretation that has the same paraphrase. But when context makes clear that his injury will not occur, the subjunctive has a counterfactual paraphrase, with the first clause: It was once possible, but does not remain so, that he will be injured tomorrow. Three experiments corroborated these predictions for participants' selections of paraphrases in their native Spanish, for epistemic and deontic conditionals, for those referring to past and to future events, and for those with then clauses referring to what may or must happen. These results are contrary to normal modal logics. They are also contrary to theories based on probabilities, which are inapplicable to deontic conditionals, such as, "If you have a ticket, then you must enter the show."

The Suppression of Inferences From Counterfactual Conditionals.

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, "if she watered the plants they bloomed," when beliefs about additional background conditions, for example, "if the sun shone they bloomed" decrease the frequency of inferences such as modus tollens (from "the plants did not bloom" to "therefore she did not water them"). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, "if she had watered the plants they would have bloomed," when beliefs about the known or presupposed facts, "she did not water the plants and they did not bloom" increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from "she did not water the plants" to "therefore they did not bloom") is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new "switched-suppression" effect for conditionals with negated components, for example, "if she had not watered the plants they would not have bloomed": modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning.

The Comprehension of Counterfactual Conditionals: Evidence From Eye-Tracking in the Visual World Paradigm.

Three experiments tracked participants' eye-movements to examine the time course of comprehension of the dual meaning of counterfactuals, such as "if there had been oranges then there would have been pears." Participants listened to conditionals while looking at images in the visual world paradigm, including an image of oranges and pears that corresponds to the counterfactual's conjecture, and one of no oranges and no pears that corresponds to its presumed facts, to establish at what point in time they consider each one. The results revealed striking individual differences: some participants looked at the negative image and the affirmative one, and some only at the affirmative image. The first experiment showed that participants who looked at the negative image increased their fixation on it within half a second. The second experiment showed they do so even without explicit instructions, and the third showed they do so even for printed words.

Thinking About the Opposite of What Is Said: Counterfactual Conditionals and Symbolic or Alternate Simulations of Negation.

When people understand a counterfactual such as "if the flowers had been roses, the trees would have been orange trees," they think about the conjecture, "there were roses and orange trees," and they also think about its opposite, the presupposed facts. We test whether people think about the opposite by representing alternates, for example, "poppies and apple trees," or whether models can contain symbols, for example, "no roses and no orange trees." We report the discovery of an inference-to-alternates effect-a tendency to make an affirmative inference that refers to an alternate even from a negative minor premise, for example, "there were no orange trees, therefore there were poppies." Nine experiments show the inference-to-alternates effect occurs in a binary context, but not a multiple context, and for direct and indirect reference; it can be induced and reduced by prior experience with similar inferences, and it also occurs for indicative conditionals. The results have implications for theories of counterfactual conditionals, and of negation.

Directional effect in double conditionals with a construction task: The semantic hypothesis.

The goal of this paper is to test the main predictions of the semantic hypothesis about the directional effect in double conditionals (such as, 'A only if B/only if C, B') with a construction task. The semantic hypothesis claims that directional effect can be explained by the inherent directionality of the relation between the relatum and the target object of the premises. According to this hypothesis, a directional effect should occur if only one of the end-terms of the premises takes the role of relatum: a) if the end-term that plays the role of relatum is in the first premise, a forward directional effect is predicted (from A to C); and b) if the end-term that plays the role of relatum is in the second premise, a backward directional effect is predicted (from C to A). On the other hand, it claims that there should be no directional effect when both end-terms take the role of relatum or when neither of the end-terms plays the role of relatum. Three experiments confirmed the main predictions of the semantic hypothesis in a construction task.

Priming effect in indicative and subjunctive exceptive conditionals.

We report the results of three experiments that examine the mental representations underlying the comprehension stages of negative exceptive conditionals using subjunctive mood ('B a menos que A', 'B a no ser que A'; 'B excepto que A'='B unless A') and indicative mood ('B excepto si A' and 'B salvo si A'='B except if A'). The mental representations during the comprehension stage were analyzed using a priming methodology. All experiments showed that participants read the true possibility 'not-B & A' faster when it was primed by exceptive conditionals requiring the subjunctive mood than when it was primed by exceptive conditionals requiring the indicative mood; other possibilities ('B & A', 'B & not-A', 'not-B & not-A') were primed equally by both connectives. The experiments showed that (a) when people understand negative exceptive conditionals using the subjunctive mood, such as 'B a menos que A'/'B a no ser que A'/'B excepto que A', they access the true possibilities 'not-B & A' and 'B & not-A', and (b) when they understand negative exceptive conditionals using the indicative mood, such as 'B excepto si A'/'B salvo si A', they access 'B & not-A', but not 'not-B & A'. 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.

The influence of verbal mood in exceptive conditional reasoning: indicative versus subjunctive / La influencia del modo verbal en el razonamiento de condicionales exceptivos: indicativo frente a subjuntivo

BACKGROUND: We report the results of two experiments that examine the mental representations underlying the comprehension and reasoning stages of negative exceptive conditionals requiring the subjunctive ('B a menos que A' and 'B a no ser que A' = 'B unless A') and the indicative mood ('B except si A' and 'B salvo si A' = 'B except if A'). METHOD: A truth table task was employed to infer the mental representation that people have in mind when they reason with negative exceptive conditionals. RESULTS: Both experiments showed that participants selected the possibility 'B & not-A' more frequently than the possibility 'not-B & A' when the conditional required the indicative mood, but they selected the possibilities 'B & not-A' and 'not-B & A' equally frequently when the conditional required the subjunctive mood. CONCLUSIONS: Exceptive conditionals in the subjunctive mood lead people to think in terms of dual possibilities, whereas the indicative mood leads people to consider just one possibility

ANTECEDENTES: se presentan dos experimentos que examinan la representación mental que subyace a la comprensión y el razonamiento de condicionales exceptivos negativos en subjuntivo ('B a menos que A' y 'B a no ser que A') y en indicativo modo ('B excepto si A' y 'B salvo si A'). MÉTODO:se usó una tarea de tabla de verdad para inferir la representación mental que las personas tienen en mente cuando razonan con condicionales exceptivos negativos. RESULTADOS: ambos experimentos mostraron que los participantes seleccionaban la posibilidad 'B & no A' más frecuentemente que la posibilidad 'no B & A' cuando el condicional exceptivo negativo estaba en indicativo, pero ellos seleccionaban igual de frecuente las posibilidades 'B & no A' y 'no B & A' cuando el condicional exceptivo negativo estaba en subjuntivo. CONCLUSIONES: los condicionales exceptivos negativos en modo subjuntivo llevan a las personas a pensar en términos de dos posibilidades, mientras que los condicionales exceptivos negativos en modo indicativo les llevaría a considerar solo una posibilidad

The influence of verbal mood in exceptive conditional reasoning: indicative versus subjunctive.

BACKGROUND: We report the results of two experiments that examine the mental representations underlying the comprehension and reasoning stages of negative exceptive conditionals requiring the subjunctive ('B a menos que A' and 'B a no ser que A' = 'B unless A') and the indicative mood ('B excepto si A' and 'B salvo si A' = 'B except if A'). METHOD: A truth table task was employed to infer the mental representation that people have in mind when they reason with negative exceptive conditionals. RESULTS: Both experiments showed that participants selected the possibility 'B & not-A' more frequently than the possibility 'not-B & A' when the conditional required the indicative mood, but they selected the possibilities 'B & not-A' and 'not-B & A' equally frequently when the conditional required the subjunctive mood. CONCLUSIONS: Exceptive conditionals in the subjunctive mood lead people to think in terms of dual possibilities, whereas the indicative mood leads people to consider just one possibility.

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 (AU)

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The compatibility heuristic in non-categorical hypothetical reasoning: inferences between conditionals and disjunctions.

A new theory explains how people make hypothetical inferences from a premise consistent with several alternatives to a conclusion consistent with several alternatives. The key proposal is that people rely on a heuristic that identifies compatible possibilities. It is tested in 7 experiments that examine inferences between conditionals and disjunctions. Participants accepted inferences between conditionals and inclusive disjunctions when a compatible possibility was immediately available, in their binary judgments that a conclusion followed or not (Experiment 1a) and ternary judgments that included it was not possible to know (Experiment 1b). The compatibility effect was amplified when compatible possibilities were more readily available, e.g., for 'A only if B' conditionals (Experiment 2). It was eliminated when compatible possibilities were not available, e.g., for 'if and only if A B' bi-conditionals and exclusive disjunctions (Experiment 3). The compatibility heuristic occurs even for inferences based on implicit negation e.g., 'A or B, therefore if C D' (Experiment 4), and between universals 'All A's are B's' and disjunctions (Experiment 5a) and universals and conditionals (Experiment 5b). The implications of the results for alternative theories of the cognitive processes underlying hypothetical deductions are discussed.

Presentation format and syllogistic reasoning

El efecto de la figura es un sesgo de respuesta que depende de la disposición de los términos en los silogismos. El resultado más usual, en una tarea de construcción, es que los participantes tienden a dar la respuesta en la dirección A-C cuando los silogismos son de la figura 4 (A-B/B-C), mientras que la mayoría de sus conclusiones son en la dirección opuesta (C-A) en la figura 1 (B-A/C-B). Presentamos un experimento que estudia el papel del tipo de formato de las premisas (presentación en dos líneas versus presentación en una línea) en silogismos categóricos. Los resultados obtenidos muestran que cuando la presentación de las premisas fue en el formato de una línea, los participantes generaban más respuestas A-C que respuestas C-A en todas las figuras silogísticas. Sin embargo, cuando la presentación de las premisas fue en dos líneas, los participantes generaban más respuestas A-C en los silogismos de la figura 4 y más respuestas C-A en los silogismos de la figura 1, pero no se encontraron diferencias significativas ni en los silogismos de la figura 2 (A-B/C-B) ni en los de la figura 3 (B-A/B-C). En este artículo discutimos las implicaciones de los resultados para las distintas teorías de razonamiento(AU)

Figural effect is a response bias that depends on the arrangement of the terms in syllogisms. The usual pattern in construction tasks is that participants tend to give A-C responses when the syllogisms are in figure 4(A-B/B-C), while the majority of their conclusions are in the opposite direction (C-A) for syllogisms in figure 1 (B-A/C-B). We report on one experiment that examines the role of the presentation format of premises (two-line presentation vs. one-line presentation) in categorical syllogisms. The experiment showed that when premises were presented in one-line presentation format, participants generated more A-C than C-A conclusions in all syllogistic figures. However, when premises were presented in twoline presentation format, participants generated more A-C conclusions in figure 4 and more C-A conclusions in figure 1, while there were no reliable differences for either figure 2 (A-B/C-B) or figure 3(B-A/B-C). We discuss the implications of these results for different theories of reasoning(AU)

Sequential effects in deduction: vost of inference switch

El paradigma de cambio de tarea ha ayudado a los psicólogos a conocer los procesos involucrados en el cambio de una actividad a otra. La literatura aporta resultados consistentes sobre la reconfiguración necesaria para el cambio de tarea (desaparición abrupta del coste cuando el cambio es predecible vs. reducción gradual del coste en condiciones de cambio impredecible; componentes endógeno y exógeno del coste; asimetría del coste…). En la investigación que presentamos aquí mostramos los resultados de varios experimentos en los que estudiamos el proceso de reconfiguración que se produce al alternar entre Modus Ponens y Modus Tollens. Los resultados muestran que el cambio de una inferencia a otra produce un empeoramiento en el número de errores de los participantes, así como un aumento en los tiempos de reacción (coste por interferencia del cambio). Además, encontramos una mejora gradual en el Modus Tollens en secuencias no predecibles y con intervalos respuesta-estímulo largos, en los ensayos de repetición de tarea. Ambos resultados son compatibles con la hipótesis de la reconfiguración de tarea(AU)

The task-switch paradigm has helped psychologists gain insight into the processes involved in changing from one activity to another. The literature has yielded consistent results about switch cost reconfiguration (abrupt offset in regular task-switch vs. gradual reduction in random task-switch; endogenous and exogenous components of switch cost; cost asymmetry...). In this study we present several experiments in which we investigated the reconfiguration process elicited by task switching between Modus Ponens and Modus Tollens. We found that the switch from one inference to a new one produces impairment in accuracy as an increase in reaction time (cost of inference switch). Moreover, with random sequences and a long response stimulus interval we found a gradual improvement in Modus Tollens repetitions. Both results are compatible with the task reconfiguration hypothesis(AU)

Efectos de direccionalidad en condicionales / Effect of directionality in conditionals

Se presentan dos experimentos en los que se demuestra que la dificultad delcondicional (una premisa o dos premisas) genera distintos tipos de efecto de direccionalidad. En el primer experimento, en el que se utilizó una premisa condicional, se encontraron efectos de direccionalidad sólo para el condicional "si p, entonces q". En este condicional las personas seleccionaron más inferencias hacia delante (desde p a q) que hacia atrás (desde q a p). En el segundo experimento, en el que se utilizaron dos premisas condicionales, se encontraron efectos de direccionalidad hacia delante para el condicional "si p, entonces q", efectos de direccionalidad hacia atrás para el condicional "p sólo si q" y ausencia de efectos de direccionalidad para el condicional "p si q". Los autores proponen que los efectos de direccionalidad en estos condicionales, son consecuencia de la actuación conjunta del principio de la "primera mención" (Gernsbacher,1990) y de la Hipótesis del Valor Hipotético (Evans, 1993; Grosset and Barrouillet, 2003) (AU)

Two experiments showed that the degree of difficulty of conditionals (conditionals with one premise versus conditionals with two premises) produces different kinds of directional effect. In experiment 1, where the difficulty was low, there was a directional effect for the conditional "if p, then q": participants select more forward (from p to q) than backward inferences (from q to p). In experiment 2, where the difficulty was high, there was a forward directional effect for the conditionals "if p, then q", a backward directional effect for the conditional "only if q" and no directional effects for the conditional "p if q". We propose that the directional effects in these conditionals are a result of application of the principle of "first mention" (Gernsbacher, 1990) and of the "Hypothesis of the hypothetical value" (Evans, 1993; Grosset and Barrouillet, 2003) (AU)

Efectos de direccionalidad en condicionales / Effect of directionality in conditionals

Se presentan dos experimentos en los que se demuestra que la dificultad delcondicional (una premisa o dos premisas) genera distintos tipos de efecto de direccionalidad. En el primer experimento, en el que se utilizó una premisacondicional, se encontraron efectos de direccionalidad sólo para elcondicional "si p, entonces q". En este condicional las personas seleccionaron más inferencias hacia delante (desde p a q) que hacia atrás(desde q a p). En el segundo experimento, en el que se utilizaron dos premisas condicionales, se encontraron efectos de direccionalidad haciadelante para el condicional "si p, entonces q", efectos de direccionalidadhacia atrás para el condicional "p sólo si q" y ausencia de efectos dedireccionalidad para el condicional "p si q". Los autores proponen que losefectos de direccionalidad en estos condicionales, son consecuencia de la actuación conjunta del principio de la "primera mención" (Gernsbacher,1990) y de la Hipótesis del Valor Hipotético (Evans, 1993; Grosset andBarrouillet, 2003) (AU)

Two experiments showed that the degree of difficulty of conditionals (conditionals with one premise versus conditionals with two premises) produces different kinds of directional effect. In experiment 1, where the difficulty was low, there was a directional effect for the conditional "if p, then q": participants select more forward (from p to q) than backward inferences (from q to p). In experiment 2, where the difficulty was high, there was a forward directional effect for theconditionals "if p, then q", a backward directional effect for the conditional "only if q" and no directional effects for the conditional "p if q". We propose that the directional effects in these conditionals are a result of application of the principle of "first mention" (Gernsbacher, 1990) and ofthe "Hypothesis of the hypothetical value" (Evans, 1993; Grosset and Barrouillet, 2003) (AU)

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.