The cognitive adequacy of Allen's interval calculus for qualitative spatial representation and reasoning

Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible than conventional numerical approaches to spatial reasoning, because it copes with the indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge. The paper reports experimental results concerning the cognitive adequacy of an important approach used in QSR, namely the spatial interpretation of the interval calculus introduced by Allen (1983). Knauff, Rauh and Schlieder (1995) distinguished between the conceptual and inferential cognitive adequacy of Allen’s interval calculus. The former refers to the thirteen base relations as a representational system and the latter to the compositions of these relations as a tool for reasoning. The results of two memory experiments on conceptual adequacy show that people use ordinal information similar to the interval relations when representing and remembering spatial arrangements. Furthermore, symmetry transformations on the interval relations were found to be responsible for most of the errors, whereas conceptual neighborhood theory did not appear to correspond to cognitively relevant concepts. Inferential adequacy was investigated by two reasoning experiments and the results show that in inference tasks where the number of possible interval relations for the composition is more than one, subjects ignore numerous possibilities and interindividually prefer the same relations. Reorientations and transpositions operating on the relations seem to be important for reasoning performance as well, whereas conceptual neighborhood did not appear to affect the difficulty of reasoning tasks based on the interval relations

Necessity, Possibility and the Search for Counterexamples in Human Reasoning

Abstract Necessity, Possibility and the Search for Counterexamples in Human Reasoning Sylvia Mary Parnell Serpell This thesis presents a series of experiments where endorsement rates, latencies and measures of cognitive ability were collected, to investigate the extent to which people search for counterexamples under necessity instructions, and alternative models under possibility instructions. The research was motivated by a syllogistic reasoning study carried out by Evans, Handley, Harper, and Johnson-Laird (1999), and predictions were derived from mental model theory (Johnson-Laird, 1983; Johnson-Laird & Byrne, 1991). With regard to the endorsement rate data: Experiment 1 failed to find evidence that a search for counterexamples or alternative models took place. In contrast experiment 2 (transitive inference) found some evidence to support the search for alternative models under possibility instructions, and following an improved training session, experiment 3 produced strong evidence to suggest that people searched for other models; which was mediated by cognitive ability. There was also strong evidence from experiments 4, 5 and 6 (abstract and everyday conditionals) to support the search for counterexamples and alternative models. Furthermore it was also found that people were more likely to find alternative causes when there were many that could be retrieved from their everyday knowledge, and that people carried out a search for counterexamples with many alternative causes under necessity instructions, and across few and many causal groups under possibility instructions. .The evidence from the latency data was limited and inconsistent, although people with higher cognitive ability were generally quicker in completing the tasks