David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Axiomathes 16 (1-2):165-214 (2006)
We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks.
|Keywords||category cognition colimit functor limit natural transformation neural network semantics|
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References found in this work BETA
Antonio R. Damasio (1989). Time-Locked Multiregional Retroactivation: A Systems-Level Proposal for the Neural Substrates of Recognition and Recall. Cognition 3 (1-2):25-62.
Michael A. Arbib (1970). Brains, Machines, and Mathematics. Journal of Symbolic Logic 35 (3):482-483.
Citations of this work BETA
R. Brown, J. F. Glazebrook & I. C. Baianu (2007). A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems. [REVIEW] Axiomathes 17 (3-4):409-493.
Ion C. Baianu (2007). Categorical Ontology of Levels and Emergent Complexity: An Introduction. [REVIEW] Axiomathes 17 (3-4):209-222.
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