Two approaches to the formalisation of defeasible deontic reasoning

This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this method the language of Reiter's default logic is extended to include modal expressions, after which the argumentation framework in default logic of [20, 22] is used to give a plausible logical analysis of moral dilemmas and prima facie obligations.An earlier version of this article was written while the author was working at the Department of Computing, Imperial College London, supported by ESRC/MRC/SERC Joint Council Initiative Project G9212036. Work on the present version was supported by a research fellowship of the Royal Netherlands Academy of Arts and Sciences, and by Esprit WG 8319 Modelage. I thank one of the referees for his interesting comments. Also, many thanks are due to Marek Sergot for valuable discussions on the topic of this paper.     

Probabilistic factors in deontic reasoning

Abstract

Recent research on reasoning has resulted in a number of authors urging a convergence between ideas in the hitherto disparate fields of deduction and decision making. The deontic reasoning literature in particular refers increasingly to the decision-making constructs of subjective utility and subjective probability. Although the former construct has received some attention from experimenters, the latter has remained relatively unexplored. In this paper a set of experiments is reported in which a modified form of Wason's selection task using an enlarged array was used to investigate the role of a probabilistic factor in reasoning with conditional obligations. Results showed that this factor played a significant role in mediating this reasoning, when probabilistic information was added both to antecedent and to consequent items. Other results indicated that the effect occurred principally by suppressing selections of items with relatively low subjective relevance.     

Domain-general contributions to social reasoning: theory of mind and deontic reasoning re-explored

Using older adults and dual-task interference, we examined performance on two social reasoning tasks: theory of mind (ToM) tasks and versions of the deontic selection task involving social contracts and hazardous conditions. In line with performance accounts of social reasoning, evidence from both aging and the dual-task method suggested that domain-general resources contribute to performance of these tasks. Specifically, older adults were impaired relative to younger adults on all types of social reasoning tasks tested; performance varied as a function of the demands these tasks placed on domain-general resources. Moreover, in younger adults, simultaneous performance of a working memory task interfered with younger adults' performance on both types of social reasoning tasks; here too, the magnitude of the interference effect varied with the processing demands of each task. Limits placed on social reasoning by executive functions contribute a great deal to performance, even in old age and in healthy younger adults under conditions of divided attention. The role of potentially non-modular and modular contributions to social reasoning is discussed.     

Superordinate principles in reasoning with causal and deontic conditionals

We propose that the pragmatic factors that mediate everyday deduction, such as alternative and disabling conditions (e.g. Cummins et al., 1991) and additional requirements (Byrne, 1989) exert their effects on specific inferences because of their perceived relevance to more general principles, which we term SuperPs. Support for this proposal was found first in two causal inference experiments, in which it was shown that specific inferences were mediated by factors that are relevant to a more general principle, while the same inferences were unaffected by factors not relevant to the general principle. These results were extended to deontic inferences in two further experiments. Taken together, these findings show that unstated superordinate principles play a significant role in certain types of reasoning. Questions raised by the findings for the main theoretical approaches are discussed.     

Social roles and utilities in reasoning with deontic conditionals

A set of experiments is reported in which a new formulation of deontic thinking is tested. This is that people represent subjective utilities inherent in conforming to or violating deontic statements, along with the social dynamics of these statements. The experiments used Wason's selection task and tested people's understanding of conditional permission. In the first two experiments, familiar scenarios referring to family interactions were used. In the third, an imaginary business content was used. In both cases it was apparent that people's thinking depended on their representation of the utilities associated with the agent of a permission statement (the party who lays down the rule) and the actor (the party whose behaviour is its target). The results are discussed as favouring an explanation in terms of mental models, rather than the schema theories which have dominated this field hitherto.     

Evidence of deontic reasoning in 3- and 4-year-old children

Deontic reasoning is reasoning about what one may, ought, or ought not do in a given set of circumstances. Virtually all of our social institutions and child-rearing practices presume the capacity to reason about deontic concepts, such as what is permitted, obligated, or prohibited. Despite this, very little is known about the development of deontic reasoning. Two experiments were conducted that contrasted children’s reasoning performance on deontic and indicative reasoning tasks (i.e., the reduced array selection version of the Wason card selection task). Like adults, children as young as 3 years of age were found to adopt a violation-detecting strategy more often when reasoning about the deontic case than when reasoning about the indicative case. These results indicate that violation detection emerges as an effective deontic reasoning very early in human development.     

Domains of deontic reasoning: Resolving the discrepancy between the cognitive and moral reasoning literatures

Deontic reasoning has been studied in two subfields of psychology: the cognitive and moral reasoning literatures. These literatures have drawn different conclusions about the nature of deontic reasoning. The consensus within the cognitive reasoning literature is that deontic reasoning is a unitary phenomenon, whereas the consensus within the moral reasoning literature is that there are different subdomains of deontic reasoning. We present evidence from a series of experiments employing the methods of both literatures suggesting that people make a systematic distinction between two types of deontic rule: social contracts and precautions. The results call into question the prevailing opinion in the cognitive reasoning literature and provide further support for both an evolutionary view of deontic reasoning and the more domain-specific perspective found in the moral reasoning literature.     

Development of the deontic advantage in reasoning: Reply to Cummins

In response to Cummins’s report that comments on our article (Dack & Astington, Journal of Experimental Child Psychology, 2011, Vol. 110, pp. 94–114), this article clarifies our perspective on what constitutes the deontic advantage, and notes similarities and differences between Cummins’s perspective and our own. Like Cummins, we believe that young children are capable of deontic reasoning and that methodological factors alone cannot explain this ability. However, we maintain that it is important to be precise about methodology in order to facilitate investigation of how the deontic advantage changes over developmental time, and this question is our main interest, although as yet incompletely answered. Contrary to Cummins, we do not think that existing data can speak to the issue of the potential innateness of deontic reasoning. We also disagree with Cummins’s perspective on norm versus normative proposition and with some of her comparisons between deontic and epistemic phenomena.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.     

Two kinds of reasoning

According to one view of reasoning, people can evaluate arguments in at least two qualitatively different ways: in terms of their deductive correctness and in terms of their inductive strength. According to a second view, assessments of both correctness and strength are a function of an argument's position on a single psychological continuum (e.g., subjective conditional probability). A deductively correct argument is one with the maximum value on this continuum; a strong argument is one with a high value. The present experiment tested these theories by asking participants to evaluate the same set of arguments for correctness and strength. The results produced an interaction between type of argument and instructions: In some conditions, participants judged one argument deductively correct more often than a second, but judged the second argument inductively strong more often than the first. This finding supports the view that people have distinct ways to evaluate arguments.     

Cognitive and AI models of reasoning

Although relatively few in number, cognitive neuroscience studies of reasoning have two general implications for cognitive theories of deduction. First, an important distinction among these theories is whether they focus on the effect of personally relevant content on the processes and representations underlying deductive reasoning. Evidence is reviewed indicating that there is a neuroanatomical basis for both content-independent and content-dependent theories of deduction. Clinical and neuroimaging studies appear to show that content-independent reasoning is mediated by the left hemisphere, whereas content-dependent reasoning is mediated by regions in the right hemisphere and the bilateral ventromedial frontal cortex. In normal subjects, reasoning is likely to be based on contributions from both hemispheres. Second, clinical evidence indicates that the visuospatial processes used in deductive reasoning are mediated by the posterior areas of the left hemisphere, and that verbal and visuospatial reasoning representations overlap at the neuroanatomical level. This finding weighs against the claims of mental-model theory that deduction involves a significant nonverbal component. Further investigation, particularly with contemporary neuroimaging methods, is needed to test these preliminary conclusions.     

Generating initial models for reasoning

Much of the knowledge that children and adults have about the world resides in intuitive models. Previous work shows that intuitive models allow for computation of specific outcomes given information about the system, but little is known about how such models are acquired. The current study tested three hypotheses about how children and adults construct intuitive models when they encounter a new property: (1) intuitive models are constructed by transferring principles from familiar properties; (2) with development, children shift from applying a default model to constructing specialized models; and (3) younger children's model construction is constrained by the domain, but becomes increasingly domain independent with development. Participants from three age groups (10, 13, and 19 years) made a series of judgments about two familiar properties and one novel property. Causal models showed that all age groups transferred principles from the familiar properties to the novel property. None of the age groups used a default model. There was developmental change in the effect of domain; younger, but not older, children's models were affected by domain. These findings suggest that the transfer process is developmentally invariant but that constraints on the process (i.e., domain dependence and understanding of base models) change with development.     

Mental models in deductive reasoning

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.     

Interpersonal attraction and person perception: Two tests of three balance models

Two experiments tested the adequacy of three balance models (equal-weights tetrahedron model, unequal-weights tetrahedron model, Feather model) for the p?o?x triad. In the first experiment, involving a variation of Byrne's anonymous-stranger technique, a PDP-11 computer was used to provide feedback on five attitude issues for each of the cells of a design created by five levels of the p?x variable (?2, ?1, 0, +1, +2) and five levels of the o?x variable (?2, ?1, 0, +1, +2). The dependent variable was p?o, interpersonal attraction. In the second experiment there were five-level manipulations of both p?x and o?p with an o-x (person perception) dependent variable. The correlations between obtained results and the predicted values for each of the three models were quite high (.64, .65, .61, respectively, in the first experiment and .60, .59, and .58, respectively, in the second), but the Feather model was judged least adequate. The data in the first experiment were best described by the unequal-weights tetrahedron model, and the data in the second experiment were best described by the equal-weights tetrahedron model. It was argued that avoidance of mutual dislike was responsible for the relatively greater support for the unequal-weights than equal-weights tetrahedron model in the first experiment.     

Sharing-rule and detection of free-riders in cooperative groups: Evolutionarily important deontic reasoning in the Wason Selection task

Taking a Darwinian approach, we propose that people reason to detect free-riders on the Wason Selection task with the sharing-rule; If one receives the resource, one is an in-group member (standard), or If one is an in-group member, one receives the resource (switched). As predicted, taking the resource-provider's perspective, both undergraduates and children (11 to 12 years old) checked for the existence of out-group members taking undeserved resource. Changing the perspective to that of the resource-recipient did not alter the selection pattern in undergraduates, although the prediction was that another type of free-riding—failure to share by resource-provider—would be checked as well. However, by removing confounding factors in the materials, both undergraduates and children checked for both types of free-riding, which fully supports the prediction. These results indicate that the sharing-rule elicits a thematic content effect that cannot be explained by preceding deontic reasoning theories.