In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Stalnaker, 1968; Lewis, 1973). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted for by an alternative (...) hypothesis proposed by our reviewers. In Experiment 3, individual variation in truth assignments of indicative conditionals is investigated via Bayesian mixture models that classify participants as following one of several competing models. As a novelty of this study, it is found that a possible worlds semantics of Lewis and Stalnaker is capable of accounting for participants’ aggregate truth value assignments in this task. Applied to indicative conditionals, we show across three experiments, that the theory both captures participants’ truth values at the aggregate level (Experiments 1 and 2) and that it makes up the largest subgroup in the analysis of individual variation in our experimental paradigm (Experiment 3). (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...) remove an argumentative form from a logical system without getting entangled in an intricate logical web, since these revisions imply the removal of other parts of a system we want to maintain. Consequently, these revisions are incoherent and unwarranted. At the very least, the usual approach in the analysis of counter-examples of argumentative forms must be seriously reconsidered. (shrink)

Conditional information can be equally asserted in the forms if p, then q (e.g., ?if I am ill, I will miss work tomorrow?) and q, if p (e.g., ?I will miss work tomorrow, if I am ill?). While this type of clause order manipulation has previously been found to have no influence on the ultimate conclusions participants draw from conditional rules, we used self-paced reading to examine how it affects the real time incremental processing of everyday conditional statements. Experiment 1 (...) revealed that clause order interacts with presuppositional congruency as readers hypothetically represent counterfactual statements. When if p, then q counterfactuals contained a presupposition that was incongruent with prior context, these statements took longer to read than when the presupposition was congruent, but for q, if p conditionals there was no such congruency effect. Experiment 2 revealed that reading times were influenced by the subjective probability of an indicative conditional regardless of clause order, with a penalty observed for low-probability statements relative to high-probability statements in both conditional clause orders. These data reveal a dissociation whereby clause order mediates the effect of suppositional congruency on reading times, but does not mediate the effect of subjective probability. (shrink)

In this paper, we claim that the problem of conditionals should be dealt with by carefully distinguishing between thinking conditional propositions and conditional thinking, i.e. thinking on the basis of some supposition. This distinction deserves further investigation, if we are to make sense of some old and new experimental data concerning the understanding and the assertion of conditional sentences. Here we will argue that some of these data seem to refute the mental models theory of conditional reasoning, setting the ground (...) for a different approach to the cognitive study of conditionals. (shrink)

According to the weak version of linguistic relativity, also called the Sapir-Whorf hypothesis, the features of an individual’s native language influence his worldview and perception. We decided to test this hypothesis on the sufficient conditional and the necessary conditional, expressed differently in Chinese and French. In Chinese, connectors for both conditionals exist and are used in everyday life, while there is only a connector for the sufficient conditional in French. A first hypothesis follows from linguistic relativity: for the necessary conditional, (...) better logic performance is expected in Chinese participants rather than French participants. As a second hypothesis, for all participants, we expect performance on the sufficient conditional to be better than on the necessary conditional. Indeed, despite the isomorphism of the two conditionals, they differ in how information is processed for reasoning. We decided to study reasoning under uncertainty as it reflects reality more accurately. To do so, we analyzed the coherence of participants using de Finetti’s theory for deduction under uncertainty. The results of our study show no significant difference in performance between Chinese and French participants, neither on the sufficient conditional nor on the necessary conditional. Thus, our first hypothesis derived from the weak version of linguistic relativity is not confirmed. In contrast, our results confirm the second hypothesis in two out of three inference schemas. (shrink)

ABSTRACTThe probabilistic truth table task involves assessing the probability of "If A then C" conditional sentences. Previous studies have shown that a majority of participants assess this probability as the conditional probability P while a substantial minority responds with the probability of the conjunction A and C. In an experiment involving 96 participants, we investigated the impact on the rate of conjunctive responses of the context in which the task is framed. We show that a context intended to lead participants (...) to consider all the possible cases elicited more conjunctive responses than a context assumed not to have this effect. These results suggest that the step of inferring the probability can distort our assessment of participants' interpretation of conditional sentences. This might compromise the validity of the probabilistic task in studying conditional reasoning. (shrink)

The phenomenon known as matching bias consists of a tendency to see cases as relevant in logical reasoning tasks when the lexical content of a case matches that of a propositional rule, normally a conditional, which applies to that case. Matching is demonstrated by use of the negations paradigm that is by using conditionals in which the presence and absence of negative components is systematically varied. The phenomenon was first published in 1972 and the present paper reviews the history of (...) research and theorising on the problem in the subsequent 25 years. Theories of matching bias considered include those based on several broad frameworks including the heuristic-analytic theory, the mental models theory, the theory of optimal data selection, and relevance theory as well as the specific processing-negations account. The ability of these theories to account for a range of phenomena is considered, including the effects of linguistic form, realistic content, and explicit negation on the matching bias effect. Of particular importance are recent findings showing that the bias is observable on a wider range of linguistic forms than has generally been thought, and that it is almost entirely dependent on the use of implicit negation in the logical cases to which rules are applied. The reasons for the general suppression of matching when realistic content is used are, however, unclear and a need for further research is identified here. It is concluded that matching bias is a highly robust effect which is closely connected with the problem of understanding implicit negation. Most of the theories in the literature are unable to account for at least some of the major phenomena discovered in research on the bias. The accounts that fare best are those that posit local effects of negation, including the heuristic-analytic and processing negations theories. (shrink)

Matching bias refers to the non-normative performance that occurs when elements mentioned in a rule do not correspond with those in a test item. One aim of the present work is to capture matching bias via reaction times as participants carry out truth-table evaluation tasks. Experiment 1 requires participants to verify conditional rules, and Experiment 2 to falsify them as the paradigm employs four types of conditional sentences that systematically rotate negatives in the antecedent and consequent; and presents predominantly cases (...) having true antecedents. These experiments reveal that mismatching is linked to higher rates of incorrect responses and slower evaluation times. A second aim is to investigate the way not is processed. We compare a narrow view of negations, which argues that negation only denies information, to a search for alternatives view, which says that negations function to prime appropriate alternatives. Findings from both experiments support a narrow reading view. (shrink)

Johnson-Laird and Byrne present a theory of conditional inference based upon the manipulation of mental models. In the present paper, the theory is critically examined with regard to its ability to account for psychological data, principally with respect to the rate at which people draw the four basic inferences of modus ponens, denial of the antecedent, affirmation of the consequent and modus tollens. It is argued first that the theory is unclear in its definition and in particular with regard to (...) predictions of problem difficulty. Clarification and specification of principles are consequently provided here. Next, it is argued that there are a number of phenomena in the conditional reasoning literature for which the theory cannot account in its present form. Specifically, the relatively frequency of DA and AC inferences on affirmative conditionals is not as predicted by the theory, differences occur between inferences on if then and only if rules beyond the capacity of the theory to explain and there is no account of the “negative conclusion bias” observed when negated components are introduced into the rules. A number of revisions to the mental model theory of conditional reasoning are proposed in order to account for these findings. (shrink)