The negated conditional: A litmus test for the suppositional conditional?

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability [P(q/p)]. In this paper, the authors examine a further implication of this analysis with respect to the wide-scope negation of conditional assertions, "it is not the case that if p then q." Under the suppositional account, nothing categorically follows from the negation of a conditional, other than a second conditional, "if p then not-q." In contrast, according to the mental model theory, a negated conditional is consistent only with the determinate state of affairs, p and not-q. In 4 experiments, the authors compare the contrasting predictions that arise from each of these accounts. The findings are consistent with the suppositional theory but are incongruent with the mental model theory of conditionals. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conditions for the Acceptance of Deontic Conditionals.

Recent psychological research has investigated how people assess the probability of an indicative conditional. Most people give the conditional probability of q given p as the probability of if p then q. Asking about the probability of an indicative conditional, one is in effect asking about its acceptability. But on what basis are deontic conditionals judged to be acceptable or unacceptable? Using a decision theoretic analysis, we argue that a deontic conditional, of the form if p then must q or if p then may q, will be judged acceptable to the extent that the p & q possibility is preferred to the p & not-q possibility. Two experiments are reported in which this prediction was upheld. There was also evidence that the pragmatic suitability of permission rules is partly determined by evaluations of the not-p & q possibility. Implications of these results for theories of deontic reasoning are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Distributions most nearly compatible with given families of conditional distributions

Consider a discrete bivariate random variable (X, Y) with possible values 1, 2, ...,I forX and 1, 2, ...J forY. Suppose that putative families of conditional distributions, forX given values ofY and ofY given values ofX, are available. After reviewing conditions for compatibiity of such conditional specifications of the distribution of (X, Y), attention is focussed on the incompatible case. The Kullback-Leibler information function is shown to provide a convenient measure of inconsistency. Using it, algorithms are provided for computing the joint distribution for (X, Y) that is least discrepant from the given inconsistent conditional specifications. Other discrepancy measures are briefly discussed.     

A simple algorithm for checking compatibility among discrete conditional distributions

A distribution is said to be conditionally specified when only its conditional distributions are known or available. The very first issue is always compatibility: does there exist a joint distribution capable of reproducing all of the conditional distributions? We review five methods-mostly for two or three variables-published since 2002, and we conclude that these methods are either mathematically too involved and/or are too difficult (and in many cases impossible) to generalize to a high dimension. The purpose of this paper is to propose a general algorithm that can efficiently verify compatibility in a straightforward fashion. Our method is intuitively simple and general enough to deal with any full-conditional specifications. Furthermore, we illustrate the phenomenon that two theoretically equivalent conditional models can be different in terms of compatibilities, or can result in different joint distributions. The implications of this phenomenon are also discussed.     

Theories of Conditional Reasoning: A Developmental Examination of Competing Hypotheses.

Children and adolescents were presented with problems that contained deontic (i.e., if action p is taken, then precondition q must be met) or causal (i.e., if event p occurs, then event q will transpire) conditionals and that varied in the ease with which alternative antecedents could be activated. Results showed that inferences were linked to the availability of alternative antecedents and the generation of "disabling" conditions (claims that the conditionals were false under specific circumstances). Age-related developments were found only on problems involving indeterminate inferences. Correlations among inferences differed for children and adolescents. The findings provide stronger support for domain-general theories than for domain-specific theories of reasoning and suggest, under some conditions, age-related changes in the roles of implicit and explicit processing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Semantics as a Foundation for Psychology: A Case Study of Wason's Selection Task

We review the various explanations that have been offered toaccount for subjects' behaviour in Wason's famous selection task. Weargue that one element that is lacking is a good understanding ofsubjects' semantics for the key expressions involved, and anunderstanding of how this semantics is affected by the demands the taskputs upon the subject's cognitive system. We make novel proposals inthese terms for explaining the major content effects of deonticmaterials. Throughout we illustrate with excerpts from tutorialdialogues which motivate the kinds of analysis proposed. Our long termgoal is an integration of the various insights about conditionalreasoning on offer from different cognitive science methodologies. Thepurpose of this paper is to try to draw the attention of logicians andsemanticists to this area, since we believe that empirical investigationof the cognitive processes involved could benefit from semanticanalyses.     

Efficient simulation of a bivariate exponential conditionals distribution

The bivariate distribution with exponential conditionals (BEC) is introduced by Arnold and Strauss [1988. Bivariate distributions with exponential conditionals, J. Amer. Statist. Assoc. 83, 522-527]. This work presents a simple and fast algorithm for simulating random variates from this density.     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Hohfeld in cyberspace and other applications of normative reasoning in agent technology

Two areas of importance for agents and multiagent systems are investigated: design of agent programming languages, and design of agent communication languages. The paper contributes in the above mentioned areas by demonstrating improved or novel applications for deontic logic and normative reasoning. Examples are taken from computer-supported cooperative work, and electronic commerce.