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

A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary co...

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Autores principales:	Steven Phillips, William H Wilson
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2011
Materias:	Biology (General) QH301-705.5
Acceso en línea:	https://doaj.org/article/e14de81a409542bfbfa35526b264aa68
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spelling	oai:doaj.org-article:e14de81a409542bfbfa35526b264aa682021-11-18T05:50:22ZCategorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.1553-734X1553-735810.1371/journal.pcbi.1002102https://doaj.org/article/e14de81a409542bfbfa35526b264aa682011-08-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/21857816/?tool=EBIhttps://doaj.org/toc/1553-734Xhttps://doaj.org/toc/1553-7358A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary collection. The classical account supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to--compatible with--their structure. Classical compositionality, however, does not explain why these two components must be compatible; they are only compatible by the ad hoc assumption (convention) of employing the same mode of (concatenative) compositionality (e.g., prefix/postfix, where a relation symbol is always prepended/appended to the symbols for the related entities). Architectures employing mixed modes do not support systematicity. Recently, we proposed an alternative explanation without ad hoc assumptions, using category theory. Here, we extend our explanation to domains that are quasi-systematic (e.g., aspects of most languages), where the domain includes some but not all possible combinations of constituents. The central category-theoretic construct is an adjunction involving pullbacks, where the primary focus is on the relationship between processes modelled as functors, rather than the representations. A functor is a structure-preserving map (or construction, for our purposes). An adjunction guarantees that the only pairings of functors are the systematic ones. Thus, (quasi-)systematicity is a necessary consequence of a categorial cognitive architecture whose basic processes are functors that participate in adjunctions.Steven PhillipsWilliam H WilsonPublic Library of Science (PLoS)articleBiology (General)QH301-705.5ENPLoS Computational Biology, Vol 7, Iss 8, p e1002102 (2011)
institution	DOAJ
collection	DOAJ
language	EN
topic	Biology (General) QH301-705.5
spellingShingle	Biology (General) QH301-705.5 Steven Phillips William H Wilson Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.
description	A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary collection. The classical account supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to--compatible with--their structure. Classical compositionality, however, does not explain why these two components must be compatible; they are only compatible by the ad hoc assumption (convention) of employing the same mode of (concatenative) compositionality (e.g., prefix/postfix, where a relation symbol is always prepended/appended to the symbols for the related entities). Architectures employing mixed modes do not support systematicity. Recently, we proposed an alternative explanation without ad hoc assumptions, using category theory. Here, we extend our explanation to domains that are quasi-systematic (e.g., aspects of most languages), where the domain includes some but not all possible combinations of constituents. The central category-theoretic construct is an adjunction involving pullbacks, where the primary focus is on the relationship between processes modelled as functors, rather than the representations. A functor is a structure-preserving map (or construction, for our purposes). An adjunction guarantees that the only pairings of functors are the systematic ones. Thus, (quasi-)systematicity is a necessary consequence of a categorial cognitive architecture whose basic processes are functors that participate in adjunctions.
format	article
author	Steven Phillips William H Wilson
author_facet	Steven Phillips William H Wilson
author_sort	Steven Phillips
title	Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.
title_short	Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.
title_full	Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.
title_fullStr	Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.
title_full_unstemmed	Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.
title_sort	categorial compositionality ii: universal constructions and a general theory of (quasi-)systematicity in human cognition.
publisher	Public Library of Science (PLoS)
publishDate	2011
url	https://doaj.org/article/e14de81a409542bfbfa35526b264aa68
work_keys_str_mv	AT stevenphillips categorialcompositionalityiiuniversalconstructionsandageneraltheoryofquasisystematicityinhumancognition AT williamhwilson categorialcompositionalityiiuniversalconstructionsandageneraltheoryofquasisystematicityinhumancognition
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Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.

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