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Schemas, Logics, and Neural Assemblies

Ron Sun
Department of Computer Science
The University of Alabama
Tuscaloosa, AL 35487

[email protected]

INDEX TERMS: neural networks, schemas, reasoning, logic, variable binding Abstract
To implement schemas and logics in connectionist models, some form of basic-level organization is needed. This paper proposes such an organization, which is termed a discrete neural assembly. Each discrete neural assembly is in turn made up of discrete neurons (nodes), that is, a node that process inputs based on a discrete mapping instead of a continuous function. A group of discrete neurons (nodes) closely interconnected form an assembly and carry out a basic functionality. Some substructures and superstructures of such assemblies are developed, to enable complex symbolic schemas to be represented and processed in connectionist networks. The paper shows that logical inference can be performed precisely, when necessary, in these networks and with certain generalization, more flexible inference (fuzzy inference) can also be performed. The development of various connectionist constructs demonstrates the possibility of implementing symbolic schemas, in their full complexity, in connectionist networks.

Acknowledgment: I wish to thank the two anonymous reviewers for their detailed critiques. This work is supported in part by the RGC grant #1640 from the Research Grant Committee, the University of Alabama.