Generalized Lattices Express Parallel Distributed Concept Learning
Summary. Concepts have been expressed mathematically as propositions in a distributive lattice. A more comprehensive formulation is that of a generalized lattice, or category, in which the concepts are related in hierarchical fashion by lattice-like links called concept morphisms. A concept morphism describes how an abstract concept can be used within a more specialized concept in more than one way as with “color”, which can appear in “apples” as either “red”, “yellow” or “green”. Further, “color” appears in “apples” because it appears in “red”, “yellow” or “green”, which in turn appear in “apples”, expressed via the composition of concept morphisms. The representation of such concept relationships in multi-regional neural networks can be expressed in category theory through the use of categories, commutative diagrams, functors, and natural trasformations. Additionally, categorical model theory expresses the possible worlds described by concepts. The analysis of morphisms between the possible worlds highlights the importance of reciprocal connections in neural networks.
KeywordsCommutative Diagram Knowledge Representation Natural Transformation Category Theory Math Image Vision
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