The double disjunction task as a coordination problem

In this paper I present the double disjunction task as introduced by Johnson-Laird. This experiment is meant to show how mental model theory explains the discrepancy between logical competence and logical performance of individuals in deductive reasoning. I review the results of the task and identify three problems in the way the task is designed, that all fall under a lack of coordination between the subject and the experimenter, and an insufficient representation of the semantic/pragmatic interface. I then propose a reformulation of the task, that makes explicit the underlying semantic reasoning and emphasizes the difference of interpretation of the ddt between the experimenter and the subjects. 1 Introductory Remarks 1.1 The Double Disjunction Task The double disjunction task (ddt), introduced by Johnson-Laird et al. (1992), is an inferential task where subjects are asked to say “What, if anything, follows” from a set of two premises, typically of the form: Alice is in India or Barbara is in Pakistan [or both/but not bot] (P1) Barbara is in Pakistan or Cheryl is in Afghanistan [or both/but not bot] (P2) The optional parameters (in square brackets) are always covariant in premises. In the terminology introduced by Johnson-Laird et al. (1992), the authors determine an inclusive and an exclusive variant, when (resp.) the first and second values are chosen. These variants are called affirmative, as opposed to those obtained when (P2) is substituted with: Barbara is in Bangladesh or Cheryl is in Afghanistan [or both/but not bot] (P2) which are called negative, because of the incompatibility between (P1) and (P2), that gives rise to a contradiction. With subscript for inclusive or exclusive, and superscripts for positive and negative, one obtains four variants, ddti , ddt + e , ddt − i and ddt − e . The task was aimed at enforcing some predictions by the mental model theory (see below) according to which the more models an agent has to represent the less she is able to make correct inferences from the premises. Inclusive disjunctions should be therefore more difficult to cope with than exclusive ones, as well as disjunctions involving a contradiction in the premises. For matters of clarity, here is the truth table for the inclusive (noted ∨) and exclusive (noted ∨) disjunctions: