On the logic of nonmonotonic conditionals and conditional probabilities

I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, , in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, CB holds just in case P[B|C]r. Thus, each conditional in a given family behaves like conditional probability above some specific support level.Chris Swoyer provided very helpful comments on drafts of this paper.     

Indicative conditionals: probabilities and relevance

Philosophical Studies - We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the...     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

"The" interpretation(s) of conditionals

Recent studies indicate that a vast majority of people judge the probability of a conditional as equivalent to the conditional probability of . This means that in evaluating the applicability of a conditional people do not seem to take into account situations in which the antecedent is false. This has been taken as evidence against the model theory of Johnson-Laird and Byrne (2002). This theory, however, claims that the conditional interpretation in which false-antecedent cases are relevant is only one of many possible interpretations of "if." We present new evidence that confirms this flexibility of the interpretive system. When people are primed by thinking (1) about truth and the difference between the and or (2) are invited to judge which situations are consistent with the conditional, they are more likely to select a probability estimate that takes into account the false-antecedent cases.     

Illusory inferences from a disjunction of conditionals: a new mental models account

(Johnson-Laird, P.N., & Savary, F. (1999, Illusory inferences: a novel class of erroneous deductions. Cognition, 71, 191-229.) have recently presented a mental models account, based on the so-called principle of truth, for the occurrence of inferences that are compelling but invalid. This article presents an alternative account of the illusory inferences resulting from a disjunction of conditionals. In accordance with our modified theory of mental models of the conditional, we show that the way individuals represent conditionals leads them to misinterpret the locus of the disjunction and prevents them from drawing conclusions from a false conditional, thus accounting for the compelling character of the illusory inference.     

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

This article presents a developmental dual-process theory of the understanding of conditionals that integrates Evans’ heuristic–analytic theory within the revised mental model theory of conditional proposed by Barrouillet, Gauffroy, and Lecas (2008). According to this theory, the interpretation of a conditional sentence is driven by unconscious and implicit heuristic processes that provide individuals with an initial representation that captures its meaning by representing the cases that make it true. This initial model can be enriched with additional models (a process named fleshing out within the mental model theory) through the intervention of conscious and demanding analytic processes. Being optional, these processes construct representations of cases that are only compatible with the conditional, leaving its truth-value indeterminate when they occur. Because heuristic processes are relatively immune to developmental changes, while analytic processes strongly develop with age, the initial model remains stable through development whereas the number of additional models that can be constructed increases steadily. Thus, the dual-process mental model theory predicts in which cases conditionals will be deemed true, indeterminate, or false and how these cases evolve with age. These predictions were verified in children, adolescents and adults who were asked to evaluate the truth value and the probability of several types of conditionals. The results reveal a variety of developmental trajectories in the way different conditionals are interpreted, which can all be accounted for by our revised mental model theory.     

The use of conditional probabilities in applications of Holland's theory

The hexagon of J. L. Holland (1973, Making Vocational Choices: A Theory of Careers, Englewood Cliffs, NJ, Prentice-Hall) is a useful heuristic device for predicting congruency and consistency among the six personality/environment types specified by his theory. One limitation of the traditional hexagon is the implicit bidirectionality: the hexagon displays a single distance between two types. People in applied areas may assume a symmetry which does not exist. Examples are given of situations in which a consistent asymmetry occurs; e.g., in the illustrative data presented, C (Conventional) types are more likely to have E (Enterprising) as a secondary interest than E types are to have C as a secondary interest. Implications of such asymmetries are discussed and suggestions made concerning counseling and other applications.     

Reasoning with three types of conditional: Biases and mental models

Two experiments are reported which compare conditional reasoning with three types of rule. These consist of two types of rule that have been widely studied previously, if p then q and p only if q, together with a third type, q if p. In both experiments, the p only if q type of rule yields a different pattern of performance from the two other types of rule. Experiment 1 is an abstract rule-evaluation task and demonstrates differential effects of temporal order and of suppositional bias. Experiment 2 investigates rule generation, rephrasing, and comparison, and demonstrates differential effects of temporal order and of thematic content. An analysis of the results is offered in terms of biases and mental models. Effects of rule form and context can be explained as reflecting the different sequences in which mental models are created for each rule form. However, it is necessary to consider the internal structure of individual mental models to account for effects arising from temporal ordering of rules.     

Suppositions, extensionality, and conditionals: a critique of the mental model theory of Johnson-Laird And Byrne (2002)

P. N. Johnson-Laird and R. M. J. Byrne proposed an influential theory of conditionals in which mental models represent logical possibilities and inferences are drawn from the extensions of possibilities that are used to represent conditionals. In this article, the authors argue that the extensional semantics underlying this theory is equivalent to that of the material, truth-functional conditional, at least for what they term "basic" conditionals, concerning arbitrary problem content. On the basis of both logical argument and psychological evidence, the authors propose that this approach is fundamentally mistaken and that conditionals must be viewed within a suppositional theory based on what philosophical logicians call the Ramsey test. The Johnson-Laird and Byrne theory is critically examined with respect to its account of basic conditionals, nonbasic conditionals, and counterfactuals.     

On the nature of mental models of conditional: The case of If,If then,and Only if

It has recently been reported that forward inferences from if p then q sentences (i.e., from antecedent to consequent) were faster than backward inferences from consequent to antecedent (Barrouillet, Grosset, & Lecas, 2000). The standard mental model theory assumes that this directionality effect is a figural effect due to the order the information enters working memory, whereas we claim that it results from the nature of the mental models that represent oriented relations from hypothetical values introduced by the word If. We tested these hypotheses in an experiment in which adult participants evaluated conditional syllogisms from either if p then q, p only if q, or p if q statements. Contrary to the predictions resulting from the standard theory, the three forms of the conditional provoked a reversed directionality effect and denial inferences took longer to endorse than affirmative inferences for all the forms of conditionals. We argue from these results that mental models of the conditional represent oriented relations instead of mere co-occurrences between events.     

The online processing of only if and even if conditional statements: Implications for mental models

A sentential connective like only if or even if merges two simple propositions into a complex statement. This study used a visual world paradigm experiment to explore how this merging process proceeds online. We first presented participants with a short animation, illustrating different simple propositions that are possible to be merged by the sentential connectives. We then auditorily played an only if or an even if statement and recorded participants' eye movements on the concurrent test image. We observed that hearing the sentential connective results in more fixations on the tokens of the appropriate propositions that are eligible to be merged by the sentential connective. Each sentential connective elicited anticipatory effect suggests that once they heard the sentential connective, participants knew which propositions could be merged. We then discussed the implications of our results to the mental model theory of conditionals and the experimental studies reported in literature.     

Struggle with ultimate meaning: Nuanced associations with search for meaning,presence of meaning,and mental health

Struggle with ultimate meaning reflects concerns about whether one’s life has a deeper meaning or purpose. We examined whether this construct could be distinguished from presence of meaning in life and search for meaning. In two US samples – a web-based sample (N = 1047) and an undergraduate sample (N = 3978) – confirmatory factor analyses showed that struggle with ultimate meaning loaded on a factor that was distinct from but related to presence (negatively) and search (positively). Moderated regression analyses showed that people with low levels of presence combined with high levels of search for meaning were particularly likely to struggle with ultimate meaning. Additionally, when compared to presence and search, struggle with ultimate meaning related more strongly to depressive symptoms than presence or search. These results suggest that struggle with ultimate meaning represents a distinct component of how people grapple with meaning that has implications for mental health.     

The personal meaning of symbols: A method of investigation

In light of the inherent significance of symbols and their nevertheless manifold variety of meanings, we present a method for investigation. In the theory behind this method, the person is viewed as an organized process of self-reflection, always oriented from a particular point in time and space toward the past, present, and future. As this orientation varies, different valuations emerge, with avaluation being a unit of meaning seen by the person as particularly relevant in his or her own life. A distinction is made between symbolic valuations, which usually have a pictorial character (for example, I am impressed by the roots of a tree), and ordinary valuations, which typically have a conceptual character (for example, I have a strong bond with my family). These types of experiences are combined and organized in a system of valuations, from where the symbol receives its personal meaning. We present a method of self-investigation for studying the interrelation between the valuation of symbols and the valuation of daily life, the affective properties of these valuations, their motivational implications, and their long-term development. We illustrate the proposed methodology with the case study of a woman who incorporated the tree as a symbol of purification into her valuation system and show how this allowed her to reintegrate certain negative experiences out of her past in her actual self.The authors thank Wim van Gilst for writing the computer program, Roos Bos for placing all the data of the case study at their disposal, and Lee Ann Weeks for her detailed editorial comments.