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The word “if” is everywhere in our language. Since conditionals make up a key factor of our reasoning and communication, it is important to know exactly how they are interpreted. A conditional has the grammatical structure ‘if Antecedent then Consequent’ (e.g., ‘If the letter is a B, then the number is a 7’). Permuting the truth value of the antecedent and the consequent, four truth table cases arise: two true-antecedent (TA) cases (TT: ‘a B’ and ‘a 7’ and TF: ‘a B’ and ‘not a 7’) and two false-antecedent (FA) cases (FT: ‘not a B’ and ‘a 7’ and FF: ‘not a B’ and ‘not a 7’). The truth table task paradigm has been the starting point for the debate between the two main theories accounting for human conditional reasoning: the Mental Models Theory (MMT; Johnson-Laird & Byrne, 2002) and the Suppositional Theory (ST; Evans & Over, 2004). Two general types of truth table task exist: In the possibilities task, participants indicate whether a situation is ‘possible’, ‘impossible’ or ‘irrelevant’ according to the conditional rule. In the truth task, they evaluate whether a situation makes the rule ‘true’, ‘false’, or is ‘irrelevant’ with respect to the truth of the rule. According to the MMT, people construct mental models of the possibilities compatible with the premises, but they initially do not represent what is false. When having sufficient cognitive ability, people flesh out this implicitly represented information into fully explicit models, also representing what is false. This leads to ‘two-valued’ answer patterns in which false-antecedent cases are judged to be ‘true’. According to the ST however, people evaluate conditionals running a Ramsey test. They ‘hypothetically add A to their stock of knowledge and evaluate their degree of belief in C given A’. They only process cases with a true antecedent, resulting in ‘three-valued’ answer patterns, in which false-antecedent cases are judged to be ‘irrelevant’. Examining the mental representation of conditionals, it is the aim of the present dissertation to identify exactly what are the processes underlying the answer patterns in truth table tasks. In two lines of research, a series of five large scale studies reveals both task characteristics (Study 1-3) and cognitive ability (Study 3-5) are a key factor in predicting the answer patterns. The first study consists of three between-subjects experiments. Comparing the classical two-option possibilities task with the truth task, we find two-valued answer patterns in the possibilities task, but three-valued patterns in the truth task. Adding irrelevant as a third option to the possibilities task results in a considerable amount of three-valued patterns, also in the possibilities task. Manipulating task-directionality, we observe that this accounts for a part of the differences between both tasks, since rule-to-situation tasks yield more two-valued answer patterns than do situation-to-rule tasks. It is concluded that both task-types are not comparable as such since number of answer alternatives, wording and directionality influence the results. In the second study we again manipulate directionality, but now making use of both implicit and explicit negations. Overall, we replicate the results of the first study: more two-valued patterns in the possibilities task, more three-valued patterns in the truth task but no effect of directionality. Concerning the negation-type, we find more three-valued patterns with implicit than with explicit negations, which is in line with the robust phenomenon of ‘matching bias’. In a third study we are interested in participants’ consistency across and between truth table tasks. In three within-subjects experiments, participants either receive the same task twice or are presented successively with both a possibilities task and a truth task in randomized order. Both experiments replicate the finding that two-valued answer patterns are mainly yielded by the possibilities task and three-valued patterns by the truth task. Within tasks, 60% of the participants show consistency, across tasks 20%. Next to task characteristics, individual differences seem to influence the results. In a fourth study we examine the influence of the ‘induction problem’ and cognitive ability. Schroyens (2010) attributes the three-valued answer patterns observed in the truth table task to the impossibility of establishing the truth of a universal claim on the basis of a single case. A truth table task with four options is administered and the correlation between participants’ judgments and their cognitive ability is inspected. A substantial part of the high intelligent participants indeed resists the induction problem by choosing the fourth ‘undetermined’ option but the major part of the most intelligent participants still judges the false-antecedent cases as ‘irrelevant’. These results support a suppositional representation of conditionals, but do not exclude that a part of the ‘irrelevant’ judgments in classical truth table tasks might indeed be caused by the induction problem. The relation between working memory and the answer patterns yielded by truth table tasks is the focus of the final and fifth study. In a dual task paradigm with working memory load manipulation, it is tested in three experiments whether differential load on participants’ working memory leads to different answer patterns on the truth table task. It is observed that false-antecedent cases are judged ‘irrelevant’ by those with the highest cognitive ability (~ST), and that the classification times for the false-antecedent cases equal those of the true-antecedent cases are revealed. Moreover, the mental load manipulations did not yield any effect, despite a positive correlation between cognitive ability and the three-valued answer patterns. We hypothesize that the overall pattern of results is caused by some kind of conflict-detection. To end the dissertation, the results of all studies are summarised and conclusions are formulated in terms of both theories on conditional reasoning, which are generally in favour of the ST. We point out that our findings are often problematic for the MMT, but that also the ST, as it stands, is

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