PosterPDF Available

Reasoning With Complex Relational Structures

Abstract

Our ability to integrate increasingly complex relationships underlies human reasoning (Holyoak & Thagard, 1995), relies on the prefrontal cortex (e.g., Christoff et al., 2001; Waltz et al., 1999), and correlates with intelligence (Marshalek, Lohman, & Snow, 1983). Kroger, Holyoak, and Hummel (2004) demonstrated that comparing increasingly complex relational structures resulted in increased processing demands as measured via reaction times for correctly solved problems. These increased processing demands were found even when controlling for iconic memory effects and working memory demands. However, the participants were trained on the relational structures prior to performing the task to reduce confounding processing demands in working memory with task learning rates. To explore these learning rates, we relaxed this training requirement and administered a similar relational match-to-sample task to undergraduate students. Stimuli were comprised of 2 x 2 matrices of non-semantic fractal pattern images and were arranged into three conditions of increasing relational complexity: perceptual-, analogical-, and system-mapping problems. Fractal pattern images reduced semantic memory influences and were never repeated throughout the experiment. Participants were instructed to choose whether the left or right target best matched the sample image by button press and received feedback after each trial. Problems were presented pseudorandomly across four blocks with 24 trials per block equally representing each condition (i.e., 8 trials of each condition). After completing the experiment, participants completed a brief questionnaire that evaluated task difficulty and possible solving strategies. The results demonstrate that changes in the participants’ accuracy and reaction time for correct solutions across blocks depended upon relational complexity. Perceptual matches were learned the fastest and were followed by analogical comparisons. However, it is unclear whether participants learned the relational structure of system mapping problems. Furthermore, the participants’ quantitative task performance and qualitative questionnaire responses were simultaneously analyzed using the multivariate technique of Multiple Factor Analysis (MFA; Abdi & Valentin, 2007; Pagès, 2015) and were explained across two orthogonal components. The first component contrasted the participants’ performance with solving strategies such that participants who endorsed matching based on differentness were more accurate. The second component contrasted self-reported task difficulty and participant strategies such that participants utilizing an incorrect perceptual strategy found the task more difficult than those utilizing more relational approaches. These results suggest that participant solving strategies are related to performance and perceived task difficulty. The participants who utilized relational strategies performed better and rated the task as becoming easier across blocks compared to those employing more perceptual based strategies. In summary, the participants’ block-wise performance was modulated by relational complexity in a non-semantic relational match-to-sample task. The participants showed performance improvements for perceptual and analogical mappings, but failed to demonstrate understanding of the relationally complex system-mapping problems, despite receiving feedback following each trial. Participants who employed more relational solving strategies (i.e., matching based on differentness), as opposed to perceptual strategies, were more accurate and rated the task as becoming easier across blocks. Future directions include exploring methods to increase performance on relationally complex analogical- and system-mapping problems. Keywords: relational match-to-sample, relational integration, multivariate statistics, system mapping, complex relational structures.
Reasoning With Complex
Relational Structures
Introduction
Performing relational comparisons with increasingly complex relational structures places greater processing demands in working memory1
We were interested in measuring the unguided learning rates of relational structures imposed upon match-to-sample problems devoid of semantics
Method
Participants solved relational match-to-sample problems across 3 conditions of increasing relational complexity: perceptual, analogical, and system
Stimuli were composed of fractal-like patterns to reduce the influence of semantic representations
Problems were presented pseudorandomly across 4 blocks with 24 trials per block that equally represented each condition (8 trials/condition/block)
Participants then completed a brief questionnaire that evaluated task difficulty, task progression, and possible solving strategies
37 participants (23 female; age M = 20.7 years, SD = 3.2) completed the experiment
References
1. Kroger, J., Holyoak, K. J., & Hummel, J. E. (2004). Varieties of sameness: the impact of relational complexity on perceptual comparisons. Cognitive
Science, 28(3), 335-358. doi:10.1016/j.cogsci.2003.06.003
2. Wickham, H. (2009). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York.
3. , S., Josse, J., & Husson, F. (2008). FactoMineR: An R package for multivariate analysis. Journal of Statistical Software, 25(1), 1-18.
4. Beaton, D., Chin Fatt, C. R., & Abdi, H. (2014). An ExPosition of multivariate analysis with the singular value decomposition in R. Computational
Statistics & Data Analysis, 72, 176-189.
Acknowledgements
Many thanks go to David Martinez, Pranali Kamat, Brandon
Pires, and Niki Allahyari for their help with data collection
and Monica Kulach for her help in designing this poster
Discussion
Participants showed performance improvements for perceptual-and analogical-, but did not demonstrate robust learning of system-mapping problems
Participants who employed relational solving strategies, as opposed to perceptual strategies, were more accurate and rated the task as becoming easier
Matthew J. Kmiecik1, Rudy Perez1, Harshita Dandu1& Daniel C. Krawczyk1,2
1The University of Texas at Dallas, 2University of Texas Southwestern Medical Center at Dallas
Analogy SystemPerceptual
Accuracy
Correct RT
Questionnaire
Results
0
2
4
6
8
10
12
1234
Block
Correct RT (s)
0.25
0.50
0.75
1.00
1234
Proportion Correct
0
5
10
15
20
1234567
Difficulty Rating
Least !Most
Number of Participants
0
5
10
15
20
25
Easier Same Harder
Task Progression Rating
Number of Participants
0
10
20
30
40
Solving Strategies
Yes No
Number of Participants
Component 1 Variance 19%
Component 2 Variance 9%
Questionnaire
Correct RT Accuracy
+
Time
Fixation Problem Feedback
Trial Timeline
Problem Type x Block Behavioral Analysis2Questionnaire Summary2Multiple Factor Analysis3,4
Perceptual Analogy System
Easier
Harder
Same
6
3
2
7
5
4
Verbalization-No
Color/Shape-No
Differentness-Yes
Appearance-Yes
1
Verbalization-Yes
Color/Shape-Yes
Appearance-No
Differentness-No
1
2
Perceptual
MatchIncorrect
Analogy
MatchIncorrect
System
Match Incorrect
Problem Types
Relational Complexity
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