Categorial compositionality II: Universal constructions and a general theory of (quasi-)systematicity in human cognition

PLoS Computational Biology

Volumn 7, Issue 8, 2011, Pages

  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

ALGEBRA; COGNITIVE SYSTEMS;

ADJUNCTIONS; COGNITIVE ARCHITECTURES; COGNITIVE BEHAVIOR; COMPLETE THEORY; COMPOSITIONALITY; FUNCTORS; GENERAL THEORY; HUMAN COGNITION; SYSTEMATICITY; UNIVERSAL CONSTRUCTIONS;

ARCHITECTURE;

ARTICLE; BRAIN FUNCTION; COGNITION; CONTROLLED STUDY; LANGUAGE ABILITY; LEARNING; MATHEMATICAL ANALYSIS; MENTAL CAPACITY; MENTAL TASK; NEUROPSYCHOLOGY; THEORY CONSTRUCTION; THEORY VALIDATION; THINKING; BIOLOGY; HUMAN; METHODOLOGY; NEUROSCIENCE; PHYSIOLOGY; PSYCHOLOGICAL MODEL; PSYCHOLOGICAL THEORY;

COGNITION; COMPUTATIONAL BIOLOGY; HUMANS; MODELS, PSYCHOLOGICAL; NEUROSCIENCES; PSYCHOLOGICAL THEORY;

EID: 80052332172     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1002102     Document Type: Article

References (25)

1. Fodor JA, Pylyshyn ZW, (1988) Connectionism and cognitive architecture: A critical analysis. Cognition 28: 3-71.
2. Aizawa K, (2003) The systematicity arguments. Studies in Mind and Brain New York Kluwer Academic.
3. Fodor JA, McLaughlin BP, (1990) Connectionism and the problem of systematicity: Why Smolensky's solution doesn't work. Cognition 35: 183-204.
4. Phillips S, Wilson WH, (2010) Categorial compositionality: A category theory explanation for the systematicity of human cognition. PLoS Comput Biol 6: e1000858 doi:10.1371/journal.pcbi.1000858.
5. Rumelhart DE, Hinton GE, Williams RJ, (1986) Learning representations by back-propagation of error. Nature 323: 533-536.
6. Tenenbaum JB, Griffiths TL, Kemp C, (2006) Theory-based Bayesian models of inductive learning and reasoning. Trend Cogn Sci 10: 309-318.
7. Mac Lane S, (2000) Categories for the working mathematician. Graduate Texts in Mathematics. second edition New York Springer.
8. Magnan F, Reyes GE, (1995) Category theory as a conceptual tool in the study of cognition. In: Macnamara J, Reyes GE, editors. The logical foundations of cognition Chapter 5 New York Oxford University Press: 57-90.
9. Goguen JA, (1972) Realization is universal. Theor Comput Syst 6: 359-374.
10. Johnson K, (2004) On the systematicity of language and thought. J Philos 101: 111-139.
11. Hadley RF, (1994) Systematicity in connectionist language learning. Mind Lang 9: 247-272.
12. Arbib MA, Manes EG, (1975) Arrows, structures, and functors: The categorical imperative. London Academic Press.
13. Barr M, Wells C, (1990) Category theory for computing science. Prentice Hall International Series in Computer Science. First edition. New York Prentice Hall.
14. Pierce BC, (1991) Basic category theory for computer scientists. Foundations of Computing Cambridge (US) MIT Press.
15. Phillips S, Wilson WH, Halford GS, (2009) What do Transitive Inference and Class Inclusion have in common? Categorical (co)products and cognitive development. PLoS Comput Biol 5: e1000599 doi:10.1371/journal.pcbi.1000599.
16. Goldblatt R, (2006) Topoi: The categorial analysis of logic. New York Dover Publications, revised edition.
17. Fodor JA, (2008) LOT 2: The language of thought revisited. New York Oxford University Press.
18. Bauderon M, Jacquet H, (2001) Node rewriting in graphs and hypergraphs: A categorical framework. Theor Comput Sci 266: 463-487.
19. Lambek J, (2004) A computational algebraic approach to English grammar. Syntax 7: 128-147.
20. Coecke B, (2006) Introducing categories to the practicing physicist. 3 Monza (Italy) Polimetrica Publisher. Advanced Studies in Mathematics and Logic.: 45-74.
21. Clark S, Coecke B, Sadrzadeh M, (2008) A compositional distributional model of meaning. In: Bruza P, Lawless W, van Rijsbergen K, Sofge D, Coecke B, editors. Proceedings of the Second Symposium on Quantum Interaction 133-140 Oxford,England College Publications.
22. Ehresmann AC, Vanbremeersch JP, (2007) Memory evolutive systems: Hierarchy, emergence, cognition. Studies in Multidisciplinarity 4 Oxford, UK Elsevier.
23. Gomez J, Sanz R, (in press) Hippocampal categories: a mathematical foundation for navigation and memory. In: Hernandez C, Sanz R, Gomez J, Smith LS, Hussain A, editors. From brains to systems: Brain inspired cognitive systems London Springer, Advances in Experimental Medicine and Biology, chapter 13.
24. Healy MJ, Olinger RD, Young RJ, Taylor SE, Caudell TP, et al. (2009) Applying category theory to improve the performance of a neural architecture. Neurocomputing 72: 3158-3173.
25. Walters RFC, (1991) Categories and computer science. Cambridge Computer Science Texts Cambridge, UK Cambridge University Press.