The mental representation and processes of spatial deductive reasoning with diagrams and sentences

Boudreau, Ginette; Pigeau, Ross

doi:10.1080/00207590042000001

Cited by 12 publications

(10 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The difculty of spatial reasoning increased systematically with the dimensional conditions although the formal derivations were the same across these conditions. These results corroborate earlier ndings according to which spatial deductions are systematically more dif cult to make from 3D mental models than from 2D ones (Boudreau & Pigeau, 2001).…”

Section: Discussionsupporting

confidence: 93%

See 1 more Smart Citation

The effects of formal order and spatial content on reasoning in three dimensions

Boudreau¹,

Pigeau²,

McCann³

2002

Int J Psychol

Self Cite

View full text Add to dashboard Cite

T his study investigates the effects of formal order and spatial content on reasoning in three dimensions in view of the Formal Rules theory and the Mental Models theory of spatial reasoning. Twenty-six subjects solved 144 spatial deductive problems that varied by the formal order of the entities (referential order, referential continuity) and the spatial content (dimension, orientation, and direction). There were two dependant variables: the correct responses and their response times. The number of mental models and the formal derivations underlying the deductions allowed comparison of opposite predictions made by the Formal Rules theory and the Mental Models theory of spatial reasoning.The results overwhelmingly supported the Mental Models theory's predictions. The effects of referential order showed that problems yielding two possible mental models were signi cantly more dif cult than problems based on one mental model, although the former problems involved a shorter formal derivation than the latter. The effects of referential continuity also generalized the Mental Models theory's prediction to reasoning in all three dimensions. The effects of referential continuity showed that problems that required independent layouts in memory were reliably more dif cult than problems that allowed the continuous integration of the entities in a mental model. We obtained these results despite the fact that the former condition required a shorter formal derivation than the latter. The effects of spatial content were also reliable despite the fact that the formal derivations were the same across spatial content. Thus, spatial deductions were signi cantly easier to make in 1D than in 2D and in 2D than 3D. Deductions were also signi cantly easier to make from left to right along the horizontal axis of a mental model, and from top to bottom along the vertical axis rather than from the respective opposite directions. The effects of spatial content suggest that mental models reproduce spatial relations relative to reference frames. C ette étude porte sur les effets de l'ordre formel et du contenu spatial sur le raisonnement en trois dimensions dans la perspective de la théorie des Règles Formelles et celle des Modèles Mentaux. Vingt-six adultes ont résolu 144 problèmes variant suivant l'ordre formel des entités (ordre référentiel, continuité référentielle) et le contenu spatial (dimensions, orientations, et directions). Les variables dépendantes étaient les bonnes réponses et les temps de réponses. Le nombre de modèles mentaux et les dérivations formelles sous-jacentes aux déductions ont permis de comparer les prédictions opposées faites par la théorie des Règles Formelles et celles des Modèles Mentaux.Les résultats con rment d'emblée les prédictions de la théorie des Modèles Mentaux. Les effets de l'ordre référentiel montrent que les problèmes à deux modèles mentaux étaient signi cativement plus dif ciles que les problèmes à un modèle mental malgré le fait que les premiers impliquaient des dérivations formelles plus courtes que l...

show abstract

Section: Discussionsupporting

confidence: 93%

“…Also, for twodimensional and three-dimensional problems, the premise that takes the longest time to process is the one that presents the multi-model characteristics of the problem even when the premise appears as the second one of a set of four (Boudreau & Pigeau, 2001).…”

Section: Discussionmentioning

confidence: 99%

The effects of formal order and spatial content on reasoning in three dimensions

Boudreau¹,

Pigeau²,

McCann³

2002

Int J Psychol

Self Cite

View full text Add to dashboard Cite

show abstract

“…The fascination for the tasks is primarily based on the fact that both types of problems lead to the same conclusion (the wrench is to the left of the saw) but reasoners have more difficulties with the second problem than with the first one (e.g., Boudreau and Pigeau 2001;Carreiras and Santamaria 1997;Roberts 2000;Schaeken et al 1998;Schaeken and Johnson-Laird 2000;Schaeken et al 1996a, b;Vandierendonck and de Vooght 1997).…”

Section: Relational Reasoningmentioning

confidence: 98%

How our brains reason logically

Knauff

2007

Topoi

View full text Add to dashboard Cite

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional ''if...then'', reasoning in the predicate calculus, i.e. inferences based on quantifiers such as ''all'', ''some'', ''none'', and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic.

show abstract

“…The mental model prediction linking problem difficulty to the number of models was initially supported by Byrne and Johnson-Laird's (1989) study and replicated by many others (Boudreau & Pigeau, 2001;Byrne & Johnson-Laird, 1989;Carreiras & Santamaria, 1997;Roberts, 2000;Schaeken, Girotto, & Johnson-Laird, 1998;Schaeken & Johnson-Laird, 2000;Schaeken, Johnson-Laird, & d'Ydewalle, 1996a, b;Vandierendonck & De Vooght, 1997. The reason why two-model problems are more difficult than single-model problems as in (A) is simply that it is harder to maintain two models in working memory than a single one.…”

Section: Introductionmentioning

confidence: 91%

Dealing with indeterminacy in spatial descriptions

Henst

Chevallier

Schaeken

et al. 2007

Psychological Research

View full text Add to dashboard Cite

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.

show abstract

The mental representation and processes of spatial deductive reasoning with diagrams and sentences

Cited by 12 publications

References 16 publications

The effects of formal order and spatial content on reasoning in three dimensions

The effects of formal order and spatial content on reasoning in three dimensions

How our brains reason logically

Dealing with indeterminacy in spatial descriptions

Contact Info

Product

Resources

About