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Mathematical fixation: Search viewed through a cognitive lens

Published online by Cambridge University Press:  24 May 2017

Steven Phillips  and
Yuji Takeda
Steven Phillips
Affiliation:
National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 6-11, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8566, Japan. [email protected]@aist.go.jphttps://staff.aist.go.jp/steven.phillipshttps://staff.aist.go.jp/yuji-takeda
Yuji Takeda
Affiliation:
National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 6-11, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8566, Japan. [email protected]@aist.go.jphttps://staff.aist.go.jp/steven.phillipshttps://staff.aist.go.jp/yuji-takeda
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Abstract

We provide a mathematical category theory account of the size and location of the authors' Functional View Field (FVF). Category theory explains systematic cognitive ability via universal construction, that is, a necessary and sufficient condition for composition of cognitive processes. Similarly, FVF size and location is derived from a (universal) construction called a fibre (pullback) bundle.

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 40 , 2017 , e152
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Copyright
Copyright © Cambridge University Press 2017 

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References

Aizawa, K. (2003) The systematicity arguments. Kluwer Academic.CrossRefGoogle Scholar
Duncan, J. & Humphreys, G. W. (1989) Visual search and stimulus similarity. Psychological Review 96:433–58. doi: 10.1037/0033-295X.96.3.433.Google Scholar
Fodor, J. A. & Pylyshyn, Z. W. (1988) Connectionism and cognitive architecture: A critical analysis. Cognition 28(1–2):3–71.Google Scholar
Gentner, D. (1983) Structure-mapping: A theoretical framework for analogy. Cognitive Science 7(2):47–59.Google Scholar
Husemoller, D. (1994) Fibre bundles, third edition. Springer-Verlag.CrossRefGoogle Scholar
Johnson, M., Rosebrugh, R. & Wood, R. (2012) Lenses, fibrations and universal translations. Mathematical Structures in Computer Science 22:25–42.Google Scholar
Mac Lane, S. (1998) Categories for the working mathematician, second edition. Springer.Google Scholar
Phillips, S. (2014) Analogy, cognitive architecture and universal construction: A tale of two systematicities. PLoS ONE 9(2):e89152.Google Scholar
Phillips, S., Takeda, Y. & Singh, A. (2012) Visual feature integration indicated by phase-locked frontal-parietal EEG signals. PLoS ONE 7(3):e32502.Google Scholar
Phillips, S. & Wilson, W. H. (2010) Categorial compositionality: A category theory explanation for the systematicity of human cognition. PLoS Computational Biology 6(7):e1000858.Google Scholar
Phillips, S. & Wilson, W. H. (2011) Categorial compositionality II: Universal constructions and a general theory of (quasi-)systematicity in human cognition. PLoS Computational Biology 7(8):e1002102.Google Scholar
Phillips, S. & Wilson, W. H. (2012) Categorial compositionality III: F-(co)algebras and the systematicity of recursive capacities in human cognition. PLoS ONE 7(4):e35028.Google Scholar
van Gelder, T. (1990) Compositionality: A connectionist variation on a classical theme. Cognitive Science 14:355–84.Google Scholar
Wolfe, J. M., Cave, K. R. & Franzel, S. L. (1989) Guided search: An alternative to the feature integration model for visual search. Journal of Experimental Psychology: Human Perception and Performance 15(3):419–33.Google Scholar
Zelinsky, G. J., Adeli, H., Peng, Y. & Samaras, D. (2013) Modelling eye movements in a categorical search task. Philosophical Transactions of the Royal Society of London B: Biological Sciences 368(1628):20130058.Google Scholar