Abstract
How do people tackle indeterminate spatial descriptions, that is those descriptions for which several representations are possible? Take for instance the two following statements: B is to the left of A, C is to the left of A. This description is indeterminate because it is compatible with at least two possibilities: (1) C B A; (2) B C A. Studies on human reasoning have shown that people tend to reduce the complexity of such indeterminate descriptions by representing only one possibility. Which one do people favour? Is one possibility easier to work out than the other? Is one possibility more plausible than the other? Two competing hypotheses make different predictions about the representation people favour. If the building of the representation is driven by what we call manipulation difficulty, then (1) is more likely to be constructed than (2) because (2) results from reorganising the representation following the first statement where B is adjacent to A (i.e. B A) while (1) is just an extension of this initial representation. However, if the representation process is driven by pragmatic factors, then (2) is more likely to be built than (1) because the second statement could be interpreted as implicating “C is not to the left of B”. Indeed, if C had been to the left of B it would have been more appropriate to utter, “C is to the left of B” rather than “C is to the left of A”. Data from several experiments show that both manipulation difficulty and pragmatic factors play a role in determining participants’ representations.
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Notes
One of the hallmarks that provides Mental Model Theory with an “economical” dimension is the principle of truth. This principle guides the construction of mental models in propositional reasoning. It stipulates that reasoners tend to reduce the load on working memory by constructing mental models that only represent what is true but not what is false.
A linearization principle (“preferred solutions follow a linear order of start points and end points”); a regularization principle (“mental configurations of intervals incorporate point incidences in only those cases where they are unavoidable”) and a unification principle (“in the case of using the inverse of the first-premise-relation in the second premise, people prefer to equalize the end terms”).
The experimenter did not provide any indication about the way to solve indeterminate problems since this may have helped participants find the correct answer to such problems in the test phase (i.e. when the relation posed in the question is indeterminate) and may reduce the occurrence of wrong answers. As observed by Schaeken and Van der Henst (2005), informing participants that the answer “Nothing follows” (i.e. the relation is indeterminate) is correct for some problems leads to relatively high rates of correct performance for indeterminate problems. This arguably results from a strategy consisting in (a) looking for indeterminacy in the first place and in (b) not engaging fully in the construction of mental models. In this experiment, we were more interested in erroneous answers that reveal which model is built (and which one is neglected) than correct answers per se showing that indeterminacy was successfully identified. We did not provide any clue that may encourage the detection of indeterminacy. Hence, participants were not informed that some problems were indeterminate.
Except for Byrne and Johnson-Laird’s study which reports 18% of correct answers for the same kind of problems. However, in Byrne and Johnson-Laird’s study the premises were orally, and thus sequentially, presented. This easily explains the low level of performance in their study.
References
Bott, L., & Noveck, I. A. (2004). Some utterances are underinformative: The onset and time course of scalar inferences. Journal of Memory and Language, 51, 437–457.
Boudreau, G., & Pigeau, R. (2001). The mental representation and processes of spatial deductive reasoning with diagrams and sentences. International Journal of Psychology, 36, 42–52.
Byrne, R. M. J., & Johnson-Laird, P. N. (1989). Spatial reasoning. Journal of Memory and Language, 28, 564–575.
Cochran, W. G. (1954). Some methods for strengthening the common χ 2 tests. Biometrics, 10, 417–451.
Carreiras, C., & Santamaria, C. (1997). Reasoning about relations: Spatial and nonspatial problems. Thinking and Reasoning, 3, 309–327.
Castellan, N. Jr. (1965). On the partitioning of contingency tables. Psychological Bulletin, 64, 330–338.
De Soto, C. B., London, M., & Handel, S. (1965). Social reasoning and spatial paralogic. Journal of Personality and Social Psychology, 2, 293–307.
Goel, V., & Dolan, R. J. (2001). Functional neuroanatomy of three-term relational reasoning. Neuropsychologia, 39, 901–909.
Grice, H. P. (1975). Logic and conversation. In P. Cole, & J. L. Morgan (Eds.), Syntax and semantics, Vol 3: Speech acts (pp. 41–58). New York: Academic Press.
Horn, L. R. (1972). On the semantic properties of logical operators in English. Bloomington: Indiana University Linguistics Club.
Horn, L. R. (1989). A natural history of negation. Chicago: University of Chicago Press.
Huttenlocher, J. (1968). Constructing spatial images: A strategy in reasoning. Psychological Review, 75, 550–560.
Johnson-Laird, P. N. (1983). Mental models. Cambridge: Cambridge University Press.
Johnson-Laird, P. N., & Byrne, R. J. M. (1991). Deduction. Hove: Lawrence Erlbaum Associates.
Klauer, K. C., Stegmaier, R., & Meiser, T. (1997). Working memory involvement in propositional and spatial reasoning. Thinking and Reasoning, 3, 9–47.
Knauff, M., Mulack, T., Kassubek, J., Salih, H. R., & Greenlee, M. W. (2002). Spatial imagery in deductive reasoning: A functional MRI study. Cognitive Brain Research, 13, 203–212.
Knauff, M., Rauh, R., & Schlieder, C. (1995). Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen’s calculus. In Proceedings of the seventeenth annual conference of the Cognitive Science Society (pp. 200–205). Mahwah: Lawrence Erlbaum Associates.
Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65–100.
Newton, E. J., & Roberts, M. J. (2000) An experimental study of strategy development. Memory and Cognition, 28, 565–573.
Levinson, S. C. (1983). Pragmatics. Cambridge: Cambridge University Press.
Potts, G. R. (1972). Information processing strategies used in the encoding of linear orderings. Journal of Verbal Learning and Verbal Behaviour, 11, 727–740.
Rauh, R. (2000). Strategies of constructing preferred mental models in spatial relational inference. In W. Schaeken, G. De Vooght, A. Vandierendonck, & G. d’Ydewalle (Eds.), Deductive reasoning and strategies (pp. 177–190). Mahwah: Lawrence Erlbaum Associates.
Rauh, R., Hagen, C., Knauff, M., Kuss, T., Schlieder, C., & Strube, G. (2005): Preferred and alternative mental models in spatial reasoning. Spatial Cognition and Computation, 5(2&3), 239–269.
Roberts, M. J. (2000). Strategies in relational reasoning. Thinking and Reasoning, 6, 1–26.
Roberts, M. J., Gilmore, D. J., & Wood, D. J. (1997). Individual differences and strategy selection in reasoning. British Journal of Psychology, 88, 473–492.
Schaeken, W., & Johnson-Laird, P. N. (2000). Strategies in temporal reasoning. Thinking and Reasoning, 6, 193–219.
Schaeken, W., Girotto, V., & Johnson-Laird, P. N. (1998). The effect of irrelevant premise on temporal and spatial reasoning. Kognitionswissenchaft, 7, 27–32.
Schaeken, W., Johnson-Laird, P. N., & d’Ydewalle, G. (1996a). Mental models and temporal reasoning. Cognition, 60, 205–234.
Schaeken, W., Johnson-Laird, P. N., & d’Ydewalle, G. (1996b). Tense, aspect and temporal reasoning. Thinking and Reasoning, 2, 309–327.
Schaeken, W., & Van der Henst, J.-B. (2005). It’s good to be wrong: An analysis of mistakes in relational reasoning. In V. Dans Girotto, & P. N. Johnson-Laird (Eds.), The shape of reason (pp. 51–69). Psychology Press.
Schaeken, W., Van der Henst, J. B., & Schroyens, W. (2007). The mental model theory of relational reasoning: Premises’ relevance, conclusions’ phrasing and cognitive economy. In W. Schaeken, A. Vandierendonck, W. Schroyens, & G. d’Ydewalle (Eds.), The mental models theory of reasoning: Refinements and extensions (pp. 129–150). Mahwah: Lawrence Erlbaum Associates.
Siegel, S., & Castellan, N. Jr. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). New York: McGraw-Hill.
Van der Henst, J. B., & Schaeken, W. (2005). The wording of conclusions in relational reasoning. Cognition, 97, 1–22.
Vandierendonck, A., & De Vooght, G. (1997). Working memory constraints on linear reasoning with spatial and temporal contents. Quarterly Journal of Experimental Psychology, 50, 803–820.
Vandierendonck, A., & De Voogt, G. (1998). Mental models and working memory in temporal and spatial reasoning. In V. De Keyser, et al. (Eds.) Time and dynamic control of behaviour (pp. 383–402).
Vandierendonck, A., Dierckx, V., & De Vooght, G. (2004). Mental model construction in linear reasoning: Evidence for the construction of initial annotated models. Quarterly Journal of Experimental Psychology, 57A, 1369–1391.
Acknowledgments
We thank Karl Christoph Klauer, Maxwell Roberts and one anonymous reviewer for their thorough reading of our manuscript and for their helpful suggestions. We are indebted to Guy Politzer for having suggested us the pragmatic analysis we present in the paper. Finally, we are grateful to Frédéric Vermeulin for his help in collecting the data of Experiment 4.
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Van der Henst, JB., Chevallier, C., Schaeken, W. et al. Dealing with indeterminacy in spatial descriptions. Psychological Research 72, 553–566 (2008). https://doi.org/10.1007/s00426-007-0130-6
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DOI: https://doi.org/10.1007/s00426-007-0130-6