A category theory explanation for systematicity: Universal constructions

The Architecture of Cognition: Rethinking Fodor and Pylyshyn's Systematicity Challenge

Volumn , Issue , 2014, Pages 227-250

  Phillips, Steven ^a   Wilson, William H ^b  

^a NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84944874709     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (36)

1. Aizawa, K. 2003. The Systematicity Arguments. New York: Kluwer Academic.
2. Arbib, M. A., and E. G. Manes. 1975. Arrows, Structures, and Functors: The Categorical Imperative. London: Academic Press.
3. Awodey, S. 2006. Category Theory. New York: Oxford University Press.
4. Baez, J. C., and M. Stay. 2011. Physics, topology, logic and computation: A Rosetta Stone. In New Structures in Physics, ed. B. Coecke, 95-172. New York: Springer.
5. Barr, M., and C. Wells. 1990. Category Theory for Computing Science. New York: Prentice Hall.
6. Bird, R., and O. de Moor. 1997. Algebra of Programming. Harlow: Prentice Hall.
7. Clark, S., B. Coecke, and M. Sadrzadeh. 2008. A compositional distributional model of meaning. In Proceedings of the Second Symposium on Quantum Interaction, ed. P. Bruza, W. Lawless, K. van Rijsbergen, D. Sofge, B. Coecke, and S. Clark, 133-140. Oxford: College Publications.
8. Coecke, B. 2006. Introducing categories to the practicing physicist. In What Is Category Theory? vol. 3, 45-74. Monza, Italy: Polimetrica.
9. Ehresmann, A. C., and J.-P. Vanbremeersch. 2007. Memory Evolutive Systems: Hierarchy, Emergence, Cognition, vol. 4. Oxford: Elsevier.
10. Eilenberg, S., and S. Mac Lane. 1945. General theory of natural equivalences. Transactions of the American Mathematical Society 58: 231-294.
11. Elman, J. L. 1990. Finding structure in time. Cognitive Science 14: 179-211.
12. Fodor, J. A., and B. P. McLaughlin. 1990. Connectionism and the problem of systematicity: Why Smolensky’s solution doesn’t work. Cognition35 (2): 183-204.
13. Fodor, J. A., and Z. W. Pylyshyn. 1988. Connectionism and cognitive architecture: A critical analysis. Cognition28 (1-2): 3-71.
14. Hadley, R. F. 1994. Systematicity in connectionist language learning. Mind and Language9 (3): 247-272.
15. Halford, G. S., and W. H. Wilson. 1980. A category theory approach to cognitive development. Cognitive Psychology 12: 356-411.
16. Halford, G. S., W. H. Wilson, and S. Phillips. 1998. Processing capacity defined by relational complexity: Implications for comparative, developmental, and cognitive psychology. Behavioral and Brain Sciences21 (6): 803-831.
17. Hinton, G. E. 1990. Mapping part-whole hierarchies in connectionist networks. Artificial Intelligence46 (1-2): 47-76.
18. Kelly, G. M. 2005. Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories10.
19. Kemp, C., and J. B. Tenenbaum. 2008. The discovery of structural form. Proceedings of the National Academy of Sciences of the United States of America105 (31): 10687-10692.
20. Kendler, T. S. 1995. Levels of Cognitive Development. Mahwah, NJ: Erlbaum.
21. Mac Lane, S. 2000. Categories for the Working Mathematician, 2nd ed. New York: Springer.
22. Marcus, G. F. 1998. Rethinking eliminative connectionism. Cognitive Psychology37 (3): 243-282.
23. Marquis, J.-P. 2009. From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory. New York: Springer.
24. McLaughlin, B. P. 2009. Systematicity redux. Synthese 170: 251-274.
25. Phillips, S. 1998. Are feedforward and recurrent networks systematic? Analysis and implications for a connectionist cognitive architecture. Connection Science10 (2): 137-160.
26. Phillips, S., Y. Takeda, and A. Singh. 2012. Visual feature integration indicated by phase-locked frontal-parietal EEG signals. PLoS ONE7 (3): e32502.
27. Phillips, S., and W. H. Wilson. 2010. Categorial compositionality: A category theory explanation for the systematicity of human cognition. PLoS Computational Biology 6 (7): e1000858.
28. Phillips, S., and W. H. Wilson. 2011. Categorial compositionality II: Universal constructions and a general theory of (quasi-)systematicity in human cognition. PLoS Computational Biology 7 (8): e1002102.
29. Phillips, S., and W. H. Wilson. 2012. Categorial compositionality III: F-(co)algebras and the systematicity of recursive capacities in human cognition. PLoS ONE7 (4): e35028.
30. Phillips, S., W. H. Wilson, and G. S. Halford. 2009. What do Transitive Inference and Class Inclusion have in common? Categorical (co)products and cognitive development. PLoS Computational Biology5 (12): e1000599.
31. Rosen, R. 1958. The representation of biological systems from the standpoint of the theory of categories. Bulletin of Mathematical Biophysics 20: 317-341.
32. Rumelhart, D. E., G. E. Hinton, and R. J. Williams. 1986. Learning representations by back-propagation of error. Nature 323: 533-536.
33. Smolensky, P. 1990. Tensor product variable binding and the representation of symbolic structures in connectionist systems. Artificial Intelligence46 (1-2): 159-216.
34. Suppes, P., and J. L. Zinnes. 1963. Basic measurement theory. In Handbook of Mathematical Psychology, ed. R. D. Luce, R. R. Bush, and E. Galanter. London: Wiley.
35. van Gelder, T. 1990. Compositionality: A connectionist variation on a classical theme. Cognitive Science 14: 355-384.
36. Wilson, W. H., N. Marcus, and G. S. Halford. 2001. Access to relational knowledge: a comparison of two models. In Proceedings of the 23rd Annual Meeting of the Cognitive Science Society, ed. J. D. Moore and K. Stenning, 1142-1147. Austin, TX: Cognitive Science Society.