Large-scale neural networks are thought to be an essential substrate for the implementation of cognitive function by the brain. If so, then a thorough understanding of cognition is not possible without knowledge of how the large-scale neural networks of cognition (neurocognitive networks) operate. Of necessity, such understanding requires insight into structural, functional, and dynamical aspects of network operation, the intimate interweaving of which may be responsible for the intricacies of cognition. Knowledge of anatomical structure is basic to understanding how neurocognitive networks operate. Phylogenetically and ontogenetically determined patterns of synaptic connectivity form a structural network of brain areas, allowing communication between widely distributed collections of areas. The function of neurocognitive networks depends on selective activation of anatomically linked cortical and subcortical areas in a wide variety of configurations. Large-scale functional networks provide the cooperative processing which gives expression to cognitive function. The dynamics of neurocognitive network function relates to the evolving patterns of interacting brain areas that express cognitive function in real time. This article considers the proposition that a basic similarity of the structural, functional, and dynamical features of all neurocognitive networks in the brain causes them to function according to common operational principles. The formation of neural context through the coordinated mutual constraint of multiple interacting cortical areas, is considered as a guiding principle underlying all cognitive functions. Increasing knowledge of the operational principles of neurocognitive networks is likely to promote the advancement of cognitive theories, and to seed strategies for the enhancement of cognitive abilities.

ABSTRACT. 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.

and integration of brain responses to object