Exploring Pragmatic Factors on the Logical Relationships of Conditional Reasoning: A Study of Counterfactual and Hypothetical Conditionals

Previous theories have established the mental model activation of processing different types of conditionals, stating that counterfactual conditionals expressing events that contradict known facts (e.g., "If it had rained, then they would not go to the park.") are considered to trigger two mental models: (1) a hypothetical but factually wrong model (e.g., "rain" and "did not go to the park") and (2) a corresponding real-world model (e.g., "did not rain" and "went to the park"). This study aimed to investigate whether pragmatic factors differentially influence readers' comprehension and distinction between counterfactual and hypothetical conditional sentences in Mandarin Chinese. Participants were required to read and judge the comprehensibility of Chinese hypothetical and counterfactual conditionals, which were different in temporal indicators (past vs. future temporal indicators) in the antecedent. Different polarities (with vs. without negators) and different moving directions (different directional verbs: lai2 [come] vs. qu4 [go]) in the consequent were also manipulated. Linear mixed-effects models (LMEM) revealed that hypothetical conditionals (with future temporal indicators) were more comprehensible than counterfactual conditionals (with past temporal indicators). The semantic similarities within the subordinate clause revealed future temporal indicators had higher lexical-semantic co-occurrence than past indicators, suggesting that temporal indicators impact comprehension partly through lexical semantics in the premise, and hypothetical conditionals are more easily processed. However, the semantic similarity analysis of the main and the subordinate clauses showed no effect of temporal indicators, suggesting that lexical-semantic co-occurrence across clauses may not substantially contribute to the distinction between hypothetical conditionals and counterfactual conditionals. In conclusion, this study offers insights into the comprehension of Chinese conditional sentences by shedding light on the pragmatic factors influencing the activation of different mental models.

How people think about the truth of hypothetical impossibilities

People can think about hypothetical impossibilities and a curious observation is that some impossible conditionals seem true and others do not. Four experiments test the proposal that people think about impossibilities just as they do possibilities, by attempting to construct a consistent simulation of the impossible conjecture with its suggested outcome, informed by their knowledge of the real world. The results show that participants judge some impossible conditionals true with one outcome, for example, "if people were made of steel, they would not bruise easily" and false with the opposite outcome, "if people were made of steel they would bruise easily", and others false with either outcome, for example, "if houses were made of spaghetti, their engines would (not) be noisy". However, they can sometimes judge impossible conditionals true with either outcome, for example, "if Plato were identical to Socrates, he would (not) have a small nose", or "if sheep and wolves were alike, they would (not) eat grass". The results were observed for judgments about what could be true (Experiments 1 and 4), judgments of degrees of truth (Experiment 2), and judgments of what is true (Experiment 3). The results rule out the idea that people evaluate the truth of a hypothetical impossibility by relying on cognitive processes that compare the probability of each conditional to its counterpart with the opposite outcome.

Can counterfactual explanations of AI systems' predictions skew lay users' causal intuitions about the world? If so, can we correct for that?

Counterfactual (CF) explanations have been employed as one of the modes of explainability in explainable artificial intelligence (AI)-both to increase the transparency of AI systems and to provide recourse. Cognitive science and psychology have pointed out that people regularly use CFs to express causal relationships. Most AI systems, however, are only able to capture associations or correlations in data, so interpreting them as casual would not be justified. In this perspective, we present two experiments (total n = 364) exploring the effects of CF explanations of AI systems' predictions on lay people's causal beliefs about the real world. In Experiment 1, we found that providing CF explanations of an AI system's predictions does indeed (unjustifiably) affect people's causal beliefs regarding factors/features the AI uses and that people are more likely to view them as causal factors in the real world. Inspired by the literature on misinformation and health warning messaging, Experiment 2 tested whether we can correct for the unjustified change in causal beliefs. We found that pointing out that AI systems capture correlations and not necessarily causal relationships can attenuate the effects of CF explanations on people's causal beliefs.

Alternatives or syntactic negation? Adults’ and children’s preferences for constructing counterfactual possibilities

Reasoning with counterfactuals such as “if his sister had entered silently, the child would have been awake”, requires considering what is conjectured (“his sister entered silently”) and what is the counterfactual possibility (“his sister did not enter silently”). In two experiments, we test how both adults (Study 1) and children from 8 to 12 years (Study 2) construct counterfactual possibilities about the cause of an effect (“the child was awake because…”). We test specifically whether people construct the counterfactual possibility by recovering alternatives, for example, “the alarm clock sounded” or by using the syntactic negation using propositional symbols (“his sister did not enter silently”). Moreover, as children show difficulty in thinking with abstract contents, we test whether they construct the counterfactual possibility more readily by recovering concrete alternatives (“the alarm clock sounded”) rather than abstract alternatives (“he had trouble sleeping”). Results showed that children, as well as adults, recovered the alternative as the cause of the effect rather than the negation. Moreover, children, unlike adults, created the counterfactual possibility more frequently by recovering concrete situations rather than abstract situations.

Indicatives, Subjunctives, and the Falsity of the Antecedent

It is widely held that there are important differences between indicative conditionals (e.g., "If the authors are linguists, they have written a linguistics paper") and subjunctive conditionals (e.g., "If the authors had been linguists, they would have written a linguistics paper"). A central difference is that indicatives and subjunctives convey different stances toward the truth of their antecedents. Indicatives (often) convey neutrality: for example, about whether the authors in question are linguists. Subjunctives (often) convey the falsity of the antecedent: for example, that the authors in question are not linguists. This paper tests prominent accounts of how these different stances are conveyed: whether by presupposition or conversational implicature. Experiment 1 tests the presupposition account by investigating whether the stances project-remain constant-when embedded under operators like negations, possibility modals, and interrogatives, a key characteristic of presuppositions. Experiment 2 tests the conversational-implicature account by investigating whether the stances can be cancelled without producing a contradiction, a key characteristic of implicatures. The results provide evidence that both stances-neutrality about the antecedent in indicatives and the falsity of the antecedent in subjunctives-are conveyed by conversational implicatures.

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 children and adults keep track of real information when thinking counterfactually

Thinking about counterfactual conditionals such as “if she had not painted the sheet of paper, it would have been blank” requires us to consider what is conjectured (She did not paint and the sheet was blank) and what actually happened (She painted and the sheet was not blank). In two experiments with adults (Study 1) and schoolchildren from 7 to 13 years (Study 2), we tested three potential sources of difficulty with counterfactuals: inferring, distinguishing what is real vs conjectured (epistemic status) and comprehending linguistic conditional expressions (“if” vs “even if”). The results showed that neither adults nor schoolchildren had difficulty in the comprehension of counterfactual expressions such as “even if” with respect to “if then”. The ability to infer with both of these develops during school years, with adults showing great ability. However, the third source factor is critical: we found that the key to young children’s difficulty with counterfactual thinking was their inability to differentiate real and conjectured information, while adults showed little difficulty with this.

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.

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.

Counterfactual Thinking: From Logic to Morality

People create counterfactual alternatives to reality when they imagine how things would have turned out differently “if only. . . .” They understand counterfactuals by constructing models that correspond to the conjecture, and to the presupposed facts. The dual meaning of counterfactuals leads people to make more inferences from them compared to ordinary conditionals. People create counterfactuals by changing an aspect of reality that has been represented explicitly in their models, and they zoom in on a “fault line,” such as an exceptional event. However, knowledge can modulate what is represented in models and so the fault lines can shift. Counterfactuals permeate much of mental life, including judgments about morality, such as blame or praise, and assessments of emotions, such as regret or relief.

Understanding Counterfactuality: A Review of Experimental Evidence for the Dual Meaning of Counterfactuals

Cognitive and linguistic theories of counterfactual language comprehension assume that counterfactuals convey a dual meaning. Subjunctive-counterfactual conditionals (e.g., 'If Tom had studied hard, he would have passed the test') express a supposition while implying the factual state of affairs (Tom has not studied hard and failed). The question of how counterfactual dual meaning plays out during language processing is currently gaining interest in psycholinguistics. Whereas numerous studies using offline measures of language processing consistently support counterfactual dual meaning, evidence coming from online studies is less conclusive. Here, we review the available studies that examine online counterfactual language comprehension through behavioural measurement (self-paced reading times, eye-tracking) and neuroimaging (electroencephalography, functional magnetic resonance imaging). While we argue that these studies do not offer direct evidence for the online computation of counterfactual dual meaning, they provide valuable information about the way counterfactual meaning unfolds in time and influences successive information processing. Further advances in research on counterfactual comprehension require more specific predictions about how counterfactual dual meaning impacts incremental sentence processing.

Hip fracture in the elderly: a re-analysis of the EPIDOS study with causal Bayesian networks

Objectives

Hip fractures commonly result in permanent disability, institutionalization or death in elderly. Existing hip-fracture predicting tools are underused in clinical practice, partly due to their lack of intuitive interpretation. By use of a graphical layer, Bayesian network models could increase the attractiveness of fracture prediction tools. Our aim was to study the potential contribution of a causal Bayesian network in this clinical setting. A logistic regression was performed as a standard control approach to check the robustness of the causal Bayesian network approach.

Setting

EPIDOS is a multicenter study, conducted in an ambulatory care setting in five French cities between 1992 and 1996 and updated in 2010. The study included 7598 women aged 75 years or older, in which fractures were assessed quarterly during 4 years. A causal Bayesian network and a logistic regression were performed on EPIDOS data to describe major variables involved in hip fractures occurrences.

Results

Both models had similar association estimations and predictive performances. They detected gait speed and mineral bone density as variables the most involved in the fracture process. The causal Bayesian network showed that gait speed and bone mineral density were directly connected to fracture and seem to mediate the influence of all the other variables included in our model. The logistic regression approach detected multiple interactions involving psychotropic drug use, age and bone mineral density.

Conclusion

Both approaches retrieved similar variables as predictors of hip fractures. However, Bayesian network highlighted the whole web of relation between the variables involved in the analysis, suggesting a possible mechanism leading to hip fracture. According to the latter results, intervention focusing concomitantly on gait speed and bone mineral density may be necessary for an optimal prevention of hip fracture occurrence in elderly people.

Marking the counterfactual: ERP evidence for pragmatic processing of German subjunctives

Counterfactual conditionals are frequently used in language to express potentially valid reasoning from factually false suppositions. Counterfactuals provide two pieces of information: their literal meaning expresses a suppositional dependency between an antecedent (If the dice had been rigged…) and a consequent (… then the game would have been unfair). Their second, backgrounded meaning refers to the opposite state of affairs and suggests that, in fact, the dice were not rigged and the game was fair. Counterfactual antecedents are particularly intriguing because they set up a counterfactual world which is known to be false, but which is nevertheless kept to when evaluating the conditional's consequent. In the last years several event-related potential (ERP) studies have targeted the processing of counterfactual consequents, yet counterfactual antecedents have remained unstudied. We present an EEG/ERP investigation which employed German conditionals to compare subjunctive mood (which marks counterfactuality) with indicative mood at the critical point of mood disambiguation via auxiliary introduction in the conditional's antecedent. Conditional sentences were presented visually one word at a time. Participants completed an acceptability judgment and probe detection task which was not related to the critical manipulation of linguistic mood. ERPs at the point of mood disambiguation in the antecedent were compared between indicative and subjunctive. Our main finding is a transient negative deflection in frontal regions for subjunctive compared to indicative mood in a time-window of 450–600 ms. We discuss this novel finding in respect to working memory requirements for rule application and increased referential processing demands for the representation of counterfactuals' dual meaning. Our result suggests that the counterfactually implied dual meaning is processed without any delay at the earliest point where counterfactuality is marked by subjunctive mood.

Encouraging Children to Think Counterfactually Enhances Blocking in a Causal Learning Task

According to a higher order reasoning account, inferential reasoning processes underpin the widely observed cue competition effect of blocking in causal learning. The inference required for blocking has been described as modus tollens (if p then q, not q therefore not p). Young children are known to have difficulties with this type of inference, but research with adults suggests that this inference is easier if participants think counterfactually. In this study, 100 children (51 five-year-olds and 49 six- to seven-year-olds) were assigned to two types of pretraining groups. The counterfactual group observed demonstrations of cues paired with outcomes and answered questions about what the outcome would have been if the causal status of cues had been different, whereas the factual group answered factual questions about the same demonstrations. Children then completed a causal learning task. Counterfactual pretraining enhanced levels of blocking as well as modus tollens reasoning but only for the younger children. These findings provide new evidence for an important role for inferential reasoning in causal learning.

Processing counterfactual and hypothetical conditionals: an fMRI investigation

Counterfactual thinking is ubiquitous in everyday life and an important aspect of cognition and emotion. Although counterfactual thought has been argued to differ from processing factual or hypothetical information, imaging data which elucidate these differences on a neural level are still scarce. We investigated the neural correlates of processing counterfactual sentences under visual and aural presentation. We compared conditionals in subjunctive mood which explicitly contradicted previously presented facts (i.e. counterfactuals) to conditionals framed in indicative mood which did not contradict factual world knowledge and thus conveyed a hypothetical supposition. Our results show activation in right occipital cortex (cuneus) and right basal ganglia (caudate nucleus) during counterfactual sentence processing. Importantly the occipital activation is not only present under visual presentation but also with purely auditory stimulus presentation, precluding a visual processing artifact. Thus our results can be interpreted as reflecting the fact that counterfactual conditionals pragmatically imply the relevance of keeping in mind both factual and supposed information whereas the hypothetical conditionals imply that real world information is irrelevant for processing the conditional and can be omitted. The need to sustain representations of factual and suppositional events during counterfactual sentence processing requires increased mental imagery and integration efforts. Our findings are compatible with predictions based on mental model theory.

The rewarding value of good motor performance in the context of monetary incentives

Whether an agent receives positive task feedback or a monetary reward, neural activity in their striatum increases. In the latter case striatal activity reflects extrinsic reward processing, while in the former, striatal activity reflects the intrinsically rewarding effects of performing well. There can be a "hidden cost of reward", which is a detrimental effect of extrinsic on intrinsic reward value. This raises the question how these two types of reward interact. To address this, we applied a monetary incentive delay task: in all trials participants received feedback depending on their performance. In half of the trials they could additionally receive monetary reward if they performed well. This resulted in high performance trials, which were monetarily rewarded and high performance trials that were not. This made it possible to dissociate the neural correlates of performance feedback from the neural correlates of monetary reward that comes with high performance. Performance feedback alone elicits activation increases in the ventral striatum. This activation increases due to additional monetary reward. Neural response in the dorsal striatum on the other hand is only significantly increased by feedback when a monetary incentive is present. The quality of performance does not significantly influence dorsal striatum activity. In conclusion, our results indicate that the dorsal striatum is primarily sensitive to optional or actually received external rewards, whereas the ventral striatum may be coding intrinsic reward due to positive performance feedback. Thus the ventral striatum is suggested to be involved in the processing of intrinsically motivated behavior.

Eye movements reveal rapid concurrent access to factual and counterfactual interpretations of the world

Imagining a counterfactual world using conditionals (e.g., If Joanne had remembered her umbrella …) is common in everyday language. However, such utterances are likely to involve fairly complex reasoning processes to represent both the explicit hypothetical conjecture and its implied factual meaning. Online research into these mechanisms has so far been limited. The present paper describes two eye movement studies that investigated the time-course with which comprehenders can set up and access factual inferences based on a realistic counterfactual context. Adult participants were eye-tracked while they read short narratives, in which a context sentence set up a counterfactual world ( If … then …), and a subsequent critical sentence described an event that was either consistent or inconsistent with the implied factual world. A factual consistent condition ( Because … then …) was included as a baseline of normal contextual integration. Results showed that within a counterfactual scenario, readers quickly inferred the implied factual meaning of the discourse. However, initial processing of the critical word led to clear, but distinct, anomaly detection responses for both contextually inconsistent and consistent conditions. These results provide evidence that readers can rapidly make a factual inference from a preceding counterfactual context, despite maintaining access to both counterfactual and factual interpretations of events.

Inferences From Counterfactual Threats and Promises

We examine how people understand and reason from counterfactual threats, for example, “if you had hit your sister, I would have grounded you” and counterfactual promises, for example, “if you had tidied your room, I would have given you ice-cream.” The first experiment shows that people consider counterfactual threats, but not counterfactual promises, to have the illocutionary force of an inducement. They also make the immediate inference that the action mentioned in the “if” part of the counterfactual threat and promise did not occur. The second experiment shows that people make more negative inferences (modus tollens and denial of the antecedent) than affirmative inferences (modus ponens and affirmation of the consequent) from counterfactual threats and promises, unlike indicative threats and promises. We discuss the implications of the results for theories of the mental representations and cognitive processes that underlie conditional inducements.

Executive control and the experience of regret

The experience of regret rests on a counterfactual analysis of events. Previous research indicates that regret emerges at around 6 years of age, marginally later than the age at which children begin to answer counterfactual questions correctly. We hypothesized that the late emergence of regret relative to early counterfactual thinking is a result of the executive demands of simultaneously holding in mind and comparing dual representations of reality (counterfactual and actual). To test this hypothesis, we administered two regret tasks along with four tests of executive function (two working memory tasks, a switch task, and an inhibition task) to a sample of 104 4- to 7-year-olds. Results indicated that switching, but not working memory or inhibition, was a significant predictor of whether or not children experienced regret. This finding corroborates and extends previous research showing that the development of counterfactual thinking in children is related to their developing executive competence.

An investigation into the online processing of counterfactual and indicative conditionals

The ability to represent conditional information is central to human cognition. In two self-paced reading experiments we investigated how readers process counterfactual conditionals (e.g., If Darren had been athletic, he could probably have played on the rugby team) and indicative conditionals (e.g., If Darren is athletic, he probably plays on the rugby team). In Experiment 1 we focused on how readers process counterfactual conditional sentences. We found that processing of the antecedent of counterfactual conditionals was rapidly constrained by prior context (i.e., knowing whether Darren was or was not athletic). A reading-time penalty was observed for the critical region of text comprising the last word of the antecedent and the first word of the consequent when the information in the antecedent did not fit with prior context. In Experiment 2 we contrasted counterfactual conditionals with indicative conditionals. For counterfactual conditionals we found the same effect on the critical region as we found in Experiment 1. In contrast, however, we found no evidence that processing of the antecedent of indicative conditionals was constrained by prior context. For indicative conditionals (but not for counterfactual conditionals), the results we report are consistent with the suppositional account of conditionals. We propose that current theories of conditionals need to be able to account for online processing differences between indicative and counterfactual conditionals.

'If' and the problems of conditional reasoning

'If' is a puzzle. No consensus has existed about its meaning for over two thousand years. Here, we show how the main psychological theories deal with the seven crucial problems that it raises. These competing explanations treat 'if' as though it was a term in a formal logic, or as eliciting the construction of a mental model of the world, or as an instruction to suppose that a proposition holds. The solution to 'if' would be a major step towards understanding how people reason, and towards implementing a computer program that can reason in a human way. We argue that the mental model theory is closer to resolving the puzzle of 'if' than its competitors.

Comparisons, mental models, and the action effect in judgments of regret

People tend to attribute more regret to a character who has decided to take action and experienced a negative outcome than to one who has decided not to act and experienced a negative outcome. For some decisions, however, this finding is not observed in a between-participants design and thus appears to rely on comparisons between people's representations of action and their representations of inaction. In this article, we outline a mental models account that explains findings from studies that have used within- and between-participants designs, and we suggest that, for decisions with uncertain counterfactual outcomes, information about the consequences of a decision to act causes people to flesh out their representation of the counterfactual states of affairs for inaction. In three experiments, we confirm our predictions about participants' fleshing out of representations, demonstrating that an action effect occurs only when information about the consequences of action is available to participants as they rate the nonactor and when this information about action is informative with respect to judgments about inaction. It is important to note that the action effect always occurs when the decision scenario specifies certain counterfactual outcomes. These results suggest that people sometimes base their attributions of regret on comparisons among different sets of mental models.

Counterfactual and Semifactual Conditionals Prime Alternative Possibilities

The authors examined in 3 experiments the comprehension of counterfactuals, such as "If it had rained, the plants would have bloomed," and semifactuals, such as "Even if it had rained, the plants would have bloomed," compared with indicative conditionals, "If it rained, the plants bloomed." The first experiment showed that people read the negative conjunction, "not p and not q" faster when it was primed by a counterfactual than when it was primed by an indicative conditional. They read the affirmative conjunction, "p and q" equally quickly when it was primed by either conditional. The 2nd experiment showed that people read the negated-antecedent conjunction, "not p and q" faster when it was primed by a semifactual conditional. The 3rd experiment corroborated these results in a direct comparison of counterfactuals and semifactuals. The authors discuss the implications of the results for the mental representations of different conditionals.

The emergence of consequential thought: evidence from neuroscience

The ability to think counterfactually about the consequence of one's actions represents one of the hallmarks of the development of complex reasoning skills. The legal system places a great emphasis on this type of reasoning ability as it directly relates to the degree to which individuals may be judged liable for their actions. In the present paper, we review both behavioural and neuroscientific data exploring the role that counterfactual thinking plays in reasoning about the consequences of one's actions, especially as it pertains to the developing mind of the adolescent. On the basis of assimilation of both behavioural and neuroscientific data, we propose a brain-based model that provides a theoretical framework for understanding the emergence of counterfactual reasoning ability in the developing mind.

Counterfactual thinking: the temporal order effect

People often think about how things might have happened differently. Their counterfactual thoughts tend to mentally undo the most recent event in an independent sequence. Consider a game in which two players must each pick the same color card, both red or both black. The first picks black and the second picks red and so they lose. People think, "If only the second player had picked black." Our study tested the idea that the ways in which the players could have won provide counterfactual alternatives to the facts. In three experiments, the same set of facts (both players picked black cards), and the same winning conditions (to win in this new game they must pick different color cards) were presented, but the description of the winning conditions varied (e.g., "if one or the other but not both picks a red card" vs. "if one or the other but not both picks a black card"). The results showed that the temporal order effect can be produced or reversed by different descriptions. The descriptions make accessible different elements of the winning possibilities. A theory of the mental representations and cognitive processes underlying counterfactual thinking in the temporal order effect is described.