Relational processing in higher cognition: Implications for analogy, capacity and cognitive development. Halford, G., S., Wilson, W., H., & Phillips, S. Paper abstract bibtex It is proposed that models based on processing relations capture the structure sensitivity of higher cognitive processes while they can also be compared with more basic processes such as associations. Relations have the following properties that are not shared by associations: there is an explicit symbol for each relational instance, allowing it to be manipulated, higher-order relations can be formed that have lower-order relations as arguments, given any N-1 components of an n-ary relation the remaining component can be retrieved (omni-directional access), and representation of relational instances is a prerequisite to analogical mapping. A model is proposed in which each component of a relational instance is represented by a vector, and the binding is represented by computing the outer product of the vectors. This architecture has been used to model analogy and human memory. It can also be used to model structural effects on both similarity and category formation. Computational cost increases exponentially with representational rank, defined as number of components that are bound into a representation. Thus the model provides a natural explanation for processing capacity limitations in humans and higher animals. Each rank corresponds to a class of psychological processes, neural nets, and empirical criteria. The ranks and typical concepts which belong to them, are: Rank 0, elemental association; Rank 1, content-specific representations and configural associations; Rank 2, unary relations, class membership, variable-constant bindings; Rank 3, binary relations, proportional analogies; Rank 4, ternary relations, transitivity and hierarchical classification; Rank 5, quaternary relations, proportion and the balance scale. Rank 6, quinary relations. Rank 0 can be performed by 2-layered nets, rank 1 by 3-layered nets, and ranks 2-6 by tensor products of the corresponding number of vectors. All animals with nervous systems perform rank 0, vertebrates perform rank 1, other primates perform rank 2-3, but ranks 4-6 are uniquely human. Rank also increases with age. Implications of this model are developed for human reasoning and cognitive development. Paper presented to workshop on analogy,

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title = {Relational processing in higher cognition: Implications for analogy, capacity and cognitive development},
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abstract = {It is proposed that models based on processing relations capture the structure sensitivity of higher cognitive processes while they can also be compared with more basic processes such as associations. Relations have the following properties that are not shared by associations: there is an explicit symbol for each relational instance, allowing it to be manipulated, higher-order relations can be formed that have lower-order relations as arguments, given any N-1 components of an n-ary relation the remaining component can be retrieved (omni-directional access), and representation of relational instances is a prerequisite to analogical mapping. A model is proposed in which each component of a relational instance is represented by a vector, and the binding is represented by computing the outer product of the vectors. This architecture has been used to model analogy and human memory. It can also be used to model structural effects on both similarity and category formation. Computational cost increases exponentially with representational rank, defined as number of components that are bound into a representation. Thus the model provides a natural explanation for processing capacity limitations in humans and higher animals. Each rank corresponds to a class of psychological processes, neural nets, and empirical criteria. The ranks and typical concepts which belong to them, are: Rank 0, elemental association; Rank 1, content-specific representations and configural associations; Rank 2, unary relations, class membership, variable-constant bindings; Rank 3, binary relations, proportional analogies; Rank 4, ternary relations, transitivity and hierarchical classification; Rank 5, quaternary relations, proportion and the balance scale. Rank 6, quinary relations. Rank 0 can be performed by 2-layered nets, rank 1 by 3-layered nets, and ranks 2-6 by tensor products of the corresponding number of vectors. All animals with nervous systems perform rank 0, vertebrates perform rank 1, other primates perform rank 2-3, but ranks 4-6 are uniquely human. Rank also increases with age. Implications of this model are developed for human reasoning and cognitive development. Paper presented to workshop on analogy,},
bibtype = {article},
author = {Halford, Graeme S and Wilson, William H and Phillips, Steven}
}

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